Design, Channel Modeling and Simula ion o
LED-Based Sho -Range Unde wa e Op ical
Communica ion Sys ems
Disse a ion
zu E langung des akademischen G ades eines
Dok o s de Ingenieu swissenscha en (D .-Ing.)
de Technischen Fakul ä
de Ch is ian-Alb ech s-Uni e si ä zu Kiel
o geleg on:
Jan S icklus
aus
Esbje g
Kiel, 2023
II
Tag de Ein eichung: 20.07. 2023
Tag de Dispu a ion: 18.12. 2023
Be ich e s a e : P o . D .-Ing. Pe e A. Höhe
P o . D .-Ing. Ke in Köse
P e ace
I s ill emembe he i s ime I me P o . D .-Ing. Pe e A. Höhe , a an au onomous unde wa e
ehicle es in he na al base o Ecke n ö de. To his ime I ha e been wo king o mo e han
wo decades o he GEOMAR Helmhol z Cen e o Ocean Resea ch Kiel as an enginee in lab-
o a o ies and in he AUV-Team on wo ldwide ope a ions a sea, and I was s ill looking o new
challenges...
My ields o in e es , he unde wa e LED illumina ion, ligh measu emen and p essu e-neu al
echnology ma ched o he esea ch opic o unde wa e op ical communica ion o he In o ma ion
and Coding Theo y G oup o he Facul y o Enginee ing o he Ch is ian-Alb ech s-Uni e si y o
Kiel. P o . Höhe ga e me he oppo uni y o wo k as an ex e nal doc o a e s uden in his g oup.
Th oughou his ime, he o e ed guidance, suppo and encou agemen . He enabled cons uc i e
discussions and p o ided aluable sugges ions, bu also admi ed independen wo k. In all hese
yea s I ha e lea ned an inc edible amoun and also disco e ed my own limi .
Fo all his, I would like o exp ess my deepes g a e ulness o my supe iso .
My e y special hank belongs o D . Jo-Anne Wa ho and P o . D . Colin De ey om he
GEOMAR Magma ic and Hyd o he mal Sys ems g oup, o hei kindness and ole ance owa ds
me and my esea ch ac i i ies side by side wi h he geoch onology-labo a o y wo k. My since e
hank goes o my suppo e om he e y i s hou D . Tom Kwasni schka.
I am e y g a e ul o he ma e ial p o isioning by he Robex-p ojec and he GEOMAR echnology-
ans e , wi hou his wo k could no ha e been conduc ed.
Fu he mo e, I would also like o hank he GEOMAR Oceanic Vision G oup, as well as D . Ma -
in Hie onymi and D . Rüdige Rö ge s om he Op ical Oceanog aphy g oup o he Helmhol z-
Zen um He eon, and o cou se he ICT g oup o he Facul y o Enginee ing o ui ul dis-
cussions and suppo . Addi ionally I hank P o . D . Ke in Köse , P o . D . Michael Hö and
P o . D . S ephan Pachnicke o hei willingness o se e he boa d o examine s.
Finally, I hank my wi e S enja and my daugh e s Li and Mie o hei endless pa ience o e all
he yea s.
Ecke n ö de, July 2023
Jan S icklus
IV
Abs ac
The numbe and complexi y o subsea applica ions is cons an ly inc easing, as a e he demands
on da a a ic. Fas unde wa e op ical wi eless communica ion (UOWC) ep esen s a solu ion
o sho e dis ances. This hesis ocuses on he adap ion o his echnology o he challenging
condi ions in he channel.
Oceanic wa e ea u es a na ow spec al window o leas a enua ion in he blue egime, which
changes o g een o coas al wa e s. In conjunc ion wi h he spec al p ope ies o he LEDs
emission and he de ec o s esponsi i y, his esul s in a h ee old ela ionship. In o de o enable
an ene gy-e icien sys em design in coas al wa e s and o bypass he g een-gap in LEDs, he use
o con e ed-g een LEDs is p oposed and in es iga ed. Since he majo i y o deploymen s will
no ake place in he deep da k ocean, na u al ambien ligh will be p esen in a ying o ms
and s eng hs. The e ec and he cons ain s o op ical il e ing o supp ess his dis u bance is
examined, a model is de eloped, and simula ions o op imiza ion a e ca ied ou . Well selec ed
hin ilm il e s ep esen an e ec i e solu ion. Since he signal- o-noise a io is e y impo an o
subsequen signal p ocessing in an UOWC sys em, in-dep h noise analyses a e pe o med, com-
p ising di e en de ec o ypes and a ious ope a ing condi ions. The applicabili y is compa ed
and p esen ed in de ail. LEDs can be used as pho ode ec o s, and his is examined o single-colo
powe LEDs in e ms o a po en ial dual-use in UOWC. The p ope ies a e ho oughly in es i-
ga ed in he spec al, empo al and spa ial domains. An unexpec ed high esponsi i y and a
dis inc bandpass cha ac e is ic is disco e ed, and a po en ial o low-cos applica ions is clea ly
iden i ied. Housings and po s a e ine i able o op ical unde wa e de ices, bu p essu e-neu al
embedding can be an al e na i e. A comp ehensi e su ey o hese echnologies is gi en and
he op ical pa h is analyzed. The o al cha ac e is ics o assemblies in a ious con igu a ions a e
de e mined by unde wa e goniome ic measu emen s and compa ed o calcula ions. Design con-
side a ions a e ex ac ed and he implemen a ion o mul iple segmen ed ansduce s is discussed.
The exac p edic ion o he link budge elies on indi idual sys em a enua ion coe icien s ksys,
bu hese exhibi many dependencies. In o de o gene a e i s spec al cu e se s o hese coe -
icien s o di e en wa e ypes, ex ensi e Mon e Ca lo simula ions o he unde wa e ligh ield
a e conduc ed. Impac ac o s a e iden i ied and sys ema ically examined. The magni ude o
he occu ing empo al dispe sion is de e mined o ealis ic wo s -case scena ios. Addi ionally, a
me hod o expe imen al de e mina ion o ksys is de eloped and ield es s a e conduc ed. This
wo k p o ides concep s and answe s o essen ial ques ions in he op ical and elec ical domains o
UOWC o de elope s and use s.
Keywo ds: Unde wa e op ical communica ion, hin ilm il e , con e ed g een LED, spec al
adap ion, noise analysis, dome po , p essu e-neu al po ing, Mon e Ca lo simula ion.

VI
Ku z assung
Die Anzahl und Komplexi ä on Un e wasse anwendungen nimm s ändig zu, ebenso wie die An-
o de ungen an den Da en e keh . Schnelle op ische d ah lose Un e wasse kommunika ion (UOWC)
s ell eine Lösung ü kü ze e Dis anzen da . Diese A bei be ass sich mi de Anpassung diese
Technologie an die he aus o de nden Bedingungen in diesem Kanal.
Ozeanisches Wasse weis ein schmales spek ales Fens e mi de ge ings en Dämp ung im
blauen Be eich au , das bei Küs engewässe n in den g ünen Be eich übe geh . In Ve bindung
mi den spek alen Eigenscha en de LED-Emissionen und de Emp indlichkei des De ek o s
e gib sich eine d ei ache Abhängigkei . Um ein ene giee izien es Sys emdesign auch in küs en-
nahen Gewässe n zu e möglichen, und die g üne E izienzsenke on LEDs zu umgehen, wi d die
Ve wendung on kon e ie -g ünen LEDs o geschlagen und un e such . Da die meis en Ein-
sä ze nich in de dunklen Tie see s a inden we den, bleib das na ü liche Umgebungslich in
un e schiedliche Fo m und In ensi ä exis en . Die Wi kung und die G enzen op ische Fil e zu
Un e d ückung diese S ö ung we den un e such , ein Modell en wickel und Simula ionen zu Op-
imie ung du chge üh . Gu angepass e In e e enz il e können eine e ek i e Lösung da s ellen.
Da das Signal-Rausch-Ve häl nis ü die nach olgende Signal e a bei ung in einem UOWC-Sys em
seh wich ig is , wu de eine eingehende Rauschanalyse du chge üh , die e schiedene De ek o -
ypen und un e schiedlichs e Be iebsbedingungen um ass . Die Anwendba kei wi d e glichen
und im De ail o ges ell . LEDs können auch als Pho ode ek o en eingese z we den, dieses wi d
ü ein a bige Hochleis ungs-LEDs im Hinblick au eine mögliche Doppelnu zung in de UOWC
un e such . Es inde eine eingehende Analyse de Eigenscha en im spek alen, zei lichen und
äumlichen Be eich s a . Eine une wa e hohe Ansp echemp indlichkei und eine ausgep äg e
Bandpass-Cha ak e is ik wi d nachgewiesen, ein Po enzial ü kos engüns ige Anwendungen is
deu lich e kennba . Gehäuse und Fens e sind ü op ische Un e wasse -Ins umen e unumgäng-
lich, ein d uckneu ale Ve guss kann dazu eine Al e na i e da s ellen. Es wi d ein um assende
Übe blick übe diese Technologien gegeben und de op ische P ad analysie . Die Gesam cha-
ak e is ik on Baug uppen in e schiedenen Kon igu a ionen wi d du ch goniome ische Un e -
wasse messungen e mi el und mi Be echnungen e glichen. Übe legungen zum Design we den
ex ahie und die Implemen ie ung on meh ach segmen ie en Sende- und Emp angseinhei en
wi d disku ie . Die genaue Vo he sage des Budge s eine Ve bindung häng on den indi iduellen
Sys emdämp ungskoe izien en ksys ab, welche jedoch iele Abhängigkei en au weisen. Um e s -
mals spek ale Ku ensä ze diese Koe izien en ü e schiedene Wasse ypen zu e zeugen, we den
um ang eiche Mon e Ca lo-Simula ionen des Un e wasse -Lich eldes du chge üh . Die Ein luss-
ak o en we den e mi el und sys ema isch un e such . Das Ausmaß de au e enden zei lichen
S euung wi d ü die ungüns igs en Fälle ealis ische Szena ien bes imm . Zusä zlich wi d eine
Me hode zu expe imen ellen Bes immung on ksys en wickel und en sp echende Feld e suche
we den du chge üh . Diese A bei lie e En wickle n und Anwende n Konzep e und An wo en
au wesen liche F agen im op ischen und elek ischen Be eich de UOWC.
S ichwö e : Op ische Un e wasse kommunika ion, In e e enz il e , kon e gie g üne LED, spek-
ale Anpassung, Rauschanalyse, Kuppelpo , d uckneu ale Ve guss, Mon e Ca lo Simula ion.
VIII
Con en s
1 In oduc ion 1
1.1 Backg ound........................................ 1
1.2 S a eo heA ...................................... 2
1.3 ScopeandAim...................................... 4
1.4 Au ho ’sCon ibu ions.................................. 5
1.5 ThesisOu line ...................................... 6
2 Fundamen als 7
2.1 Unde wa e Op ical Communica ion Sys ems Desc ip ion . . . . . . . . . . . . . . 7
2.1.1 Op icalF on Ends................................ 8
2.1.2 Unde wa e Op ical Link Con igu a ions . . . . . . . . . . . . . . . . . . . . 12
2.1.3 En i onmen al Condi ions and Channel Impac s . . . . . . . . . . . . . . . 14
2.1.4 UOWCLinkBudge ............................... 15
2.1.5 Pho onic De ices and Ampli ie s . . . . . . . . . . . . . . . . . . . . . . . . 16
2.1.6 Rele an Aspec s o Digi al Communica ions in UOWC . . . . . . . . . . . 22
2.2 Ligh in heMediumWa e ............................... 25
2.2.1 Abso p ion, Sca e ing and A enua ion . . . . . . . . . . . . . . . . . . . . 25
2.2.2 Classi ica ion o Wa e Types . . . . . . . . . . . . . . . . . . . . . . . . . . 34
2.2.3 Re ac i e Index, Tu bulence and Scin illa ion . . . . . . . . . . . . . . . . . 36
2.2.4 Sola Spec al I adiance and Ambien Ligh Unde wa e . . . . . . . . . . 38
2.2.5 Unde wa e Ligh Field Fluc ua ions . . . . . . . . . . . . . . . . . . . . . . 39
2.2.6 Bioluminescence, Fluo escence and Raman Sca e ing . . . . . . . . . . . . 40
2.3 Chap e Summa y .................................... 40
3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s 43
3.1 In luencing Fac o s o he LED Wa eleng h Selec ion . . . . . . . . . . . . . . . . . 43
3.1.1 P opaga ion Window in Na u al Wa e s . . . . . . . . . . . . . . . . . . . . 43
3.1.2 LED P ope ies and A ailabil y . . . . . . . . . . . . . . . . . . . . . . . . . 47
3.1.3 Spec al P og ession o Responsi i y . . . . . . . . . . . . . . . . . . . . . . 50
3.1.4 Th ee old Rela ionship o E iciency, A enua ion and Responsi i y . . . . . 51
3.2 Op ical Fil e ing o Ambien Ligh Supp ession . . . . . . . . . . . . . . . . . . . 54
3.2.1 Unde wa e Ambien Ligh . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2.2 LED Based Ligh Sou ce . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
3.2.3 Pho ode ec o ................................... 60
3.2.4 Op ical Bandpass Fil e s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
3.2.5 In luence on Op ical Signal- o-Noise Ra io and Op imiza ion . . . . . . . . 66
3.3 Noise Sou ces and Noise P ope ies . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.1 F om Op ical o Elec ical SNR . . . . . . . . . . . . . . . . . . . . . . . . . 74
3.3.2 TIAAmpli ica ion ................................ 74
3.3.3 NoiseSou ces................................... 76
3.3.4 Simula ion o TIA-Ampli ied Pho ode ec o s . . . . . . . . . . . . . . . . . 78
3.3.5 Noise Composi ion o TIA Ampli ied PIN-PD and APD . . . . . . . . . . . 79
3.4 The Applicabili y o PIN-PDs and APDs in Compa ison . . . . . . . . . . . . . . . 81
3.4.1 Gene al Ambien Ligh Pe o mance o PIN-PD and APD . . . . . . . . . . 81
4Chap e 1 In oduc ion
Table 1.2: O e iew o UOWC sys ems on he ma ke in ea ly 2021, wi h op ical and
mechanical p ope ies.
Manu ac u e Op ical Po , Housing ype, Housing size
Type Beam angle Dep h a ing
Aquamodem OP la , 17◦PH, 3000 m 29 cm x 7 cm diam.
Hyd omea 100 cas , 120◦PN, 6000 m 10 cm x 5 cm x 3 cm
Hyd omea 250LP cas , 120◦PN, 6000 m 10 cm x 5 cm x 3 cm
Hyd omea 500ER cas , 120◦PN, 6000 m 10 cm x 5 cm x 3 cm
Hyd omea LumaX cas , 120◦PN, 6000 m 10 cm x 6 cm diam.
Ma inelink dome, 90◦PH, 1000 m 36 cm x 20 cm diam.
WOCS 40220
Sona dyne dome, 120◦PH, 4000 m 25 cm x 13 cm diam.
Bluecomm 100
Sona dyne dome, 180◦PH, 4000 m Tx: 20 cm x 13 cm diam.
Bluecomm 200 Rx: 38 cm x 13 cm diam.
Sona dyne dome, 180◦PH, 4000 m Tx: 20 cm x 13 cm diam.
Bluecomm 200UV Rx: 38 cm x 13 cm diam.
Da a in Tables 1.1 and 1.2 a e ex ac ed om [31, 32, 33, 34]. Abb e ia ions:
a alanche pho o diode (APD), posi i e in insic nega i e pho o diode (PIN PD), mul-
iplie ube (PMT), p essu e housing (PH), p essu e neu al (PN), ecei e (Rx),
ansmi e (Tx).
sec o . Howe e , no in o ma ion is a ailable on his. The in ended use o he o e ed sys ems is
mainly o ehicle o ixed node da a ans e , e.g., ROV o an ancho ed senso ca ying deep sea
obse a o ies.
1.3 Scope and Aim
The scope o his hesis is ocused on UOWC, based on sys ems wi h LEDs as ansmi e s
and pho odiodes as ecei e s. The de elopmen o such sys ems akes place in many s eps and
i e a ions. Assemblies consis o se e al componen s, and designing, modeling and simula ion
a e in e ela ed. The unde wa e en i onmen wi h i s a ie y o in luencing ac o s ep esen s
a challenging su ounding. E en hough a lo o esea ch has been done in he ield o UOWC,
he e a e s ill a numbe o less conside ed a eas. The ollowing opics will be co e ed in his
disse a ion: LED wa eleng h adap ion, ambien ligh il e ing, op imized de ec o selec ion, LEDs
in dual-use, unde wa e housing echnology, assembly ligh pa h cha ac e is ics, and Mon e Ca lo
(MC) unde wa e ligh ield simula ion, including he gene a ion o sys em ela ed a enua ion
coe icien s.
This wo k aims o suppo enginee s and de elope s in unde s anding he UOWC sys ems ela-
ions and p o ides suppo in many aspec s om design o ope a ion. The objec i es a e easible,
e sa ile and a o dable uni s o di e en communica ion pu poses unde ha sh condi ions. Fu -
he mo e, hei compac sizes allow in eg a ion in o ehicles, a all anges o dep hs, and o e s
ene gy e iciency in ba e y powe ed ehicles o ancho ed sys ems. The goal is o dec ease ime
expendi u e and i e a ions du ing he enginee ing p ocess o adap ed UOWC assemblies and o
sho en he necessa y ope a ional es s, o ul ima ely ge a sys em ha ul ills he equi emen s.
Fu he mo e, a goal is o ake his ascina ing echnology a s ep u he owa ds he physical
implemen a ion o unde wa e swa m communica ion.

1.4 Au ho ’s Con ibu ions 5
1.4 Au ho ’s Con ibu ions
The majo con ibu ions o his wo k can be spli in o six main opics. These, and he espec i e
link o he au ho ’s pee e iewed scien i ic publica ions a e gi en below.
LED colo apdap ion Mos UOWC-publica ions a e limi ed o he use o blue LEDs, because o
hei e iciency and sui abili y o oceanic wa e s. The leas a enua ion window o coas al wa e s
like he Bal ic Sea is in he g een wa eleng h ange, jus whe e he so-called ’g een gap’ o LEDs
is loca ed. The adap ion o LED colo s o wa e ypes and pho ode ec o (PD) esponsi i ies is
examined in gene al, and in pa icula he use o con e ed g een LEDs as an e icien al e na i e.
Pa s o his opic wi hin Chap e 3 ha e been published in [35].
Ambien ligh supp ession In mos s udies on UOWC, a deep da k ocean wi hou ambi-
en ligh is assumed. Howe e , only a ce ain pa o he applica ions will ake place in his
en i onmen , and coas al wa e s a e likely o be much mo e common. Na u al ambien ligh can
pene a e o dep hs o mo e han 100 me e s. The a ious p ope ies o his ligh ield and ela ed
supp ession by di e en op ical il e s is in es iga ed in de ail. Pa s o his opic wi hin Chap e 3
ha e been published in [36].
Noise and de ec o applicabili y The signal- o-noise a io (SNR) in he elec ical domain
is an impo an pa ame e o signal p ocessing. In o de o op imize his wi h ega ds o UOWC,
an in-dep h noise analysis is ca ied ou o di e en de ec o ypes and sizes using sepa a ed
signal and in e e ence ligh le els. Unde wa e ambien ligh ci cums ances a e ans e ed and
ope a ing condi ions a e a ied, hus a ge ing he subjec comp ehensi ely and as close o eali y
as easible. Pa s o his opic wi hin Chap e 3 ha e been published in [35].
LEDs as PDs The e e se mode o LED ope a ion is known in p inciple bu is no e y common.
Wi h emphasis on a po en ial dual-use in UOWC, single-colo powe LEDs exhibi ing la ge die
a eas a e examined he e. The measu emen s in he spec al domain yielded unexpec ed esul s.
The LEDs applied as pho ode ec o s p o ided imp essi e esponsi i y alues and p onounced
bandpass cha ac e is ics, hus hey ep esen an low-cos al e na i e o PD il e combina ions.
Pa s o his opic wi hin Chap e 3 ha e been published in [37].
UOWC assemblies Housing and po echnologies a e essen ial o unde wa e op ical ap-
plica ions. Ou side he ield o imaging, whe e po s a e ecognized due o he dis o ions, hese
echnologies a e gi en li le no ice. He e, he c i e ia, concep s and aspec s ela ing o UOWC a e
compiled and p esen ed in a in eg a ed o m. The ligh pa h is in es iga ed, he cha ac e is ics
o he assemblies a e examined, and heo e ical esul s a e suppo ed by p ac ical measu emen s.
Pa s o his opic wi hin Chap e 4 ha e been published in [17, 38].
Sys em a enua ion coe icien This alue is o decisi e impo ance when de e mining he link
budge in UOWC. In many publica ions in he ield, only e y common coe icien s a e applied o
calcula ions o simula ions. While he wa e ypes a e s ill oughly dis inguished, he wa eleng h
and he sys em p ope ies a e o en no u he conside ed. He e, Mon e Ca lo simula ions a e
applied o gene a e se s o cu es o sys em- ela ed a enua ion coe icien s as unc ion o he
wa eleng h and o a ious beam angles. Fu he dependencies a e addi ionally in es iga ed. A
me hod o an expe imen al de e mina on is also de eloped. Pa s o his opic wi hin Chap e 5
ha e been published in [35].
6Chap e 1 In oduc ion
1.5 Thesis Ou line
The emainde o his disse a ion is o ganized as ollows.
Chap e 2 gi es an insigh in o he opic o op ics in he unde wa e a ea. Fundamen als a e
p o ided and a sys em o e iew is gi en. The medium wa e and i s p ope ies, he en i onmen al
condi ions and impac s a e explained. In addi ion, a gene al model as well as some communica ion
echnology basics a e gi en.
Chap e 3 examines he op imiza ion o selec ed unde wa e op ical communica ion elemen s.
The i s i em discussed is he LED colo adap ion o wa e p ope ies, he second i em is a il e
op imiza ion o ambien ligh supp ession, and he hi d i em is he imp o ed selec ion o pho-
ode ec o ypes ela ed o he signal- o-noise a io. The las i em in oduces he applica ion o
LEDs as pho ode ec o s.
Chap e 4 p esen s di e en unde wa e housing concep s o op ical applica ions. The ligh pa h
o la and dome po s, as well as o anspa en embedding is examined. Bo h he in luences
o undamen al pa ame e s and geome ic condi ions a e in es iga ed. The spa ial cha ac e is-
ics o he sou ce and de ec o and he po p ope ies a e me ged in o assembly cha ac e is ics,
measu emen s and calcula ions o hese a e compa ed. Finally, conside a ions o he design o
assemblies a e gi en and he implemen a ion o mul iple segmen ed ansduce s is discussed.
Chap e 5 desc ibes Mon e Ca lo simula ion, and he implemen a ion and he cons ain s a e
discussed. Fo ypical unde wa e op ical communica ion sys em con igu a ions, se s o ela ed
a enua ion coe icien s a e gene a ed. Po en ial in luencing pa ame e s a e examined. This is
ollowed by a desc ip ion and e alua ion o an expe imen al de e mina ion o he sys em ela ed
coe icien .
Chap e 6 con ains he conclusions and iden i ies po en ial subjec s o u u e wo k.
Chap e 2
Fundamen als
2.1 Unde wa e Op ical Communica ion Sys ems Desc ip ion
A subsea op ical communica ion sys em is cha ac e ized by he ansmission o modula ed op ical
signals o e a ce ain dis ance h ough he medium wa e o he pu pose o da a ans e . This is
gene ally ca ied ou in he wa eleng h a ea whe e he wa e shows a ela i ely low a enua ion,
o en s a ed as " anspa en window". This includes mos ly he ul a iole (UV) and he isible
(VIS) wa eleng h ange, see Fig. 2.1.
VIS
UVC UVA
UVB
100
280 380 780
Wa eleng h [nm]
200 500 600 700
300 400
315
F equency [THz]
600 400
500
800
1000
1500
UOWC
Figu e 2.1: Sec ion o he elec omagne ic spec um con aining he spec al ange ap-
plicable o UOWC.
Physical
channel
unde wa e
PD
LED
D i e
TIA
MOD DEM
Op ical domain
Elec ical domain
Digi al domain
s ( )
( )
i ( )
i ( )
F
PD
Da a ou
Da a in
P
P
T,op
R,op
T ansmi e Recei e
Figu e 2.2: Unde wa e wi eless communica ions ansmission scheme, in compliance
o he block diag am gi en in [39].
As depic ed in he block diag am in Fig. 2.2, an UOWC sys em consis s o he main elemen s
ansmi e (Tx) and ecei e (Rx), sepa a ed by he physical channel. The ansmi e includes
a modula o (MOD) in he digi al domain, a d i e in he elec ical domain ollowed by an LED
as a ligh sou ce en e ing he op ical domain. Digi al inpu da a a e con e ed by he modula o
8Chap e 2 Fundamen als
o a wa e o m signal s( )which is he inpu o he d i e . The d i e deli e s he o wa d cu en
iF( ) o he LED ha ou pu s a adian powe PT,op ( ), also s a ed as adian lux ΦT( ). This
op ical powe pene a es he wa e and is a enua ed acco ding o he dis ance a eled un il
i pa ially hi s he pho ode ec o (PD). On he ecei e side, he op ical domain ends a he
PD and is ollowed by a ansimpedance ampli ie (TIA) in he elec ical domain, and inally by
a demodula o (DEM) in he digi al domain. This means he ecei ed op ical powe PR,op ( ),
espec i ely ΦR( ), is con e ed o a pho ocu en iPD( ), which is ampli ied o an ou pu ol age
( )and he digi al da a is inally es o ed om his.
In a wide con ex , his scheme can be seen as he i s laye o he physical laye in common
communica ion models [40]. This wo k ocuses on he op ical domain and he adjacen elec ical
domain on he ecei e side.
2.1.1 Op ical F on Ends
In elec o-op ical sys ems o unde wa e applica ions, a sepa a ion o elec ical componen s om
he medium wa e is indispensable. This applies o all na u al wa e s, especially seawa e as i
is e y conduc i e and co osi e. Ma e ials used o his pu pose mus no only be insula ing
bu also op ically anspa en . In case o UOWC, ou di e en ma e ial o media a e gene ally
in ol ed: ai , wa e , glass, and plas ics. The co esponding ypical e ac i e indices a e lis ed in
Table 2.1.
Table 2.1: Typical e ac i e indices o selec ed media in he VIS wa eleng h ange.
Ma e ial, media Re ac i e index
Ai 1.0
Wa e 1.34
Glass 1.45 - 1.7
Plas ics 1.5 - 1.6
𝜃
𝜃
n
n
1
2
1
2
𝜃𝜃
11
𝜃
c
..
Figu e 2.3: Re ac ion o ligh a an in e ace o wo media wi h n1> n2on he le
side and o al e lec ion on he igh , including he co esponding angles
alid o n1> n2.
I ligh c osses he bounda y o wo di e en media o e ac i e indices n1and n2, he inciden
ay is e ac ed, see Fig. 2.3. The inciden angle θ1and he e ac ion angle θ2a e measu ed om
he no mal o he in e ace, and he ela ionship is known as Snell’s law [41]:
sin(θ2)
sin(θ1)=n1
n2
.(2.1)
2.1 Unde wa e Op ical Communica ion Sys ems Desc ip ion 9
I n1> n2and he inciden angle θ1exceeds he c i ical angle θc, o al e lec ion occu s:
θc= a csinn2
n1.(2.2)
The phase eloci y o ligh in a medium is gi en by he a io o he ligh speed in he acuum
c0= 2.998 ·108m/s and he e ac i e index no he medium:
=c0
n.(2.3)
Inciden ligh o Φi(λ)passing he bounda y o wo media is no only e ac ed, bu gene ally a
pa ial e lec ion o Φ (λ)occu s, which leads o a educed ansmission o Φ (λ), see also Fig. 2.4.
This is desc ibed by he ansmi ance T(λ)and e lec ance R(λ):
T(λ) + R(λ)=1.(2.4)
Fo unpola ised ligh , like om LEDs, and small inciden angles (less han 30◦) he ollowing
app oxima ion can be used [41]:
R(λ) = n2−n1
n2+n12
.(2.5)
I should be no ed ha he wa eleng h dependence o he e ac i e index o he abula ed ma e-
ials abo e in he isible wa eleng h ange (VIS) is small. This is in he o de o one pe cen , wi h
sligh ly highe alues o small wa eleng hs. I should also be men ioned, ha he in e nal abso p-
ion o hese ma e ials is ypically less han hal a pe cen in he VIS ange o hicknesses in he
millime e ange, hus negligible in mos cases. A ypical ai -glass in e ace wi h pe pendicula
inciden ligh shows a ansmi ance o 96 %.
Φ (λ)
Φ (λ)
i
n
Φ (λ)
n
12
Figu e 2.4: Pa ial e lec ion o ligh a an in e ace o wo media wi h n1> n2.
T ansmi e Side
The op ical pa h om he ligh sou ce o he medium wa e commonly con ains se e al s ages,
c . Fig. 2.5. The co e o he LED (die) is in mos cases co e ed wi h po ing compound, ei he
la o shaped as a lens, which o ms he p ima y op ic. The gene al in eg a ion in o he LED
housing is conside ed as one s age, wi h cha ac e is ics p o ided by da a shee s. The a he weak
concen a ed beam cha ac e is ic in his s age can be used di ec ly wi hou u he concen a ion.
F equen ly, he beam is u he o med by seconda y op ics. This includes con ex, o al in e nal
e lec ion (TIR), F esnel lenses o e lec o s in a wide ange o designs. Be o e he ligh eaches
he en i onmen al medium wa e , i usually passes an op ical po . In a e cases his can be ep-
esen ed di ec ly by he p ima y o seconda y op ics, bu mainly hese a e la o hemisphe ical
po s o a laye o cas ing ma e ial. To desc ibe he ansmi e , i is use ul o combine he cha -
ac e is ics o he indi idual componen s in he ligh pa h. This is compa able o an unde wa e
goniome e measu emen , which deli e s he angula in ensi y o he whole se up. The adian
in ensi y Iedesc ibes he powe o adian lux pe uni solid angle, and he SI uni is Wa /s .

10 Chap e 2 Fundamen als
P ima y
op ic
Seconda y
op ic
LED
die
Medium wa e
Po
IIe,T
e,
0
Figu e 2.5: Gene al ligh pa h in he op ical domain o he ansmi e side o an
UOWC sys em.
Fo his di ec ional adiome ic quan i y, he index ’e’ (ene ge ic) is used o p e en con usion
wi h he basic o mula symbol I o elec ic cu en . Acco ding o he "Ten Times Law" [41] wi h
an ope a ing dis ance much la ge han he die diame e , he LED can be in e p e ed as a poin
sou ce. Fu he mo e, a o a ional symme y can be assumed. A p onounced spec al cha ac e -
is ic o he adian in ensi y Ie(λ)is o be expec ed wi h he LED. Wi h lenses, e lec o s and
anspa en window ma e ials, on he o he hand, hese a e only o be expec ed o a limi ed ex en
wi hin he pa ial VIS wa eleng h egime used om UOWC sys ems. The esul ing ansmi ed
in ensi y a he po -wa e in e ace Ie,Tdepends o cou se on he ini ial Ie,0 alue and he gain
Gop o lenses o e lec o s, which gene ally leads o a educed beam angle. The ull beam angle is
ep esen ed by β. The di ec ional componen s o he in ensi y a e e e ed o he inclina ion om
he cen e line, gi en by γT, see Fig. 2.6. Along wi h he wa eleng h dependence, his esul s in he
e m (λ, γT). Ro a ional symme y is assumed, as i is ound in mos p ac ical cases. To make
a dis inc ion om he e m “ ield o iew”, which is o en used on bo h sides, he denomina ion
“beam angle” is used on he ansmi e side, and “ ield o iew” is only used on he ecei e side.
Each ansi ion h ough he in e ace o wo media esul s in a loss Lop . This yields he o mal
desc ip ion o :
Ie,T=Ie,0·Gop ·Lop · (λ, γT), o −β1/2< γT< β1/2,else Ie,T= 0 .(2.6)
Exp essed in a p ac ical o m, using a no malized angula dis ibu ion unc ion ST,no m(γT), alid
Poin
sou ce
𝛽
𝛽
1/2
1/2
Poin
sou ce
𝛾
Cen e Pa h o
ecei e
T
Figu e 2.6: Basic ansmi e geome y. Angle βis ep esen ing he beam angle, di-
ec ional componen s ela e o he inclina ion angle γT.
o one wa eleng h and wi hin he beam angle, gi es:
Ie,T(γT) = Ie,Tmax ·ST,no m(γT).(2.7)
The ST,no m(γT) unc ion can be de e mined ei he by calcula ion o by measu emen s wi h an
unde wa e goniome e . He e he adian in ensi y o he ansmi e se up is measu ed a a ying
angles and a ixed dis ance. Since such senso s a e a e and only ela i e alues a e necessa y,
in p ac ice i adiance senso s a e o en used in combina ion wi h ape u es, ubes and ba les.
To ob ain he unc ion, he achie ed alues a he di e en angles γTa e no malized wi h he
encoun e ed maximum alue, which in mos cases occu s a γT=0◦.
2.1 Unde wa e Op ical Communica ion Sys ems Desc ip ion 11
Recei e Side
The ligh pa h on he ecei e side is simila o he ansmi e side, bu in e e se o de , see
Fig. 2.7. The i s s age o he ligh is lea ing he medium wa e h ough an op ical po , which
can be ei he la o hemisphe ical, o a laye o cas ing ma e ial. The nex s ages may con ain an
op ical concen a o and il e be o e he ays espec i ely pho ons a e eaching he pho ode ec o .
Op ical concen a o s (OC) simila o e lec o s can ha e di e en shapes such as a unca ed cone
concen a o (TCC), pa aboloid p o ile concen a o (PPC) o compound pa abolic concen a o
(CPC). O cou se lenses can also be used as concen a o s. Op ical il e s o di e en ypes and
cha ac e is ics a e mainly used o ambien ligh supp ession.
Fil e
Medium wa e
Po
Concen a o
PD
II
e,R e,PD
Figu e 2.7: Gene al ligh pa h in he op ical domain o he ecei e side o an UOWC
sys em.
The desc ip ion o he ecei e side is ela ed o ha o he ansmi e . The incoming adian
in ensi y Ie,Ra he wa e -po in e ace has o pass se e al s ages o ansi ion be o e i inally
becomes Ie,PD a he pho ode ec o . He e i unde goes gains Gop om concen a o s and losses
Lop om media ansi ions and il e s in he passband. A s ong wa eleng h dependence is o
cou se o be expec ed o he il e s, and simila ly de ec o s can also exhibi his o a ce ain ex en .
Wi h lenses, concen a o s and anspa en window ma e ials, his dependence is gene ally mino .
The ays a e accompanied by e ac ion when passing he media bounda ies on ou e om he
wa e o he PD, which has a pa icula e ec wi h la ge inclina ion angles γR. The in ensi y
Ie,PD ha eaches he ac i e su ace o he pho ode ec o wi hin he ield o iew α, de e mines he
powe ecei ed and inally he cu en gene a ed. The wa eleng h and inclina ion dependencies a e
exp essed wi h he e m (λ, γR). The geome y is gi en in Fig. 2.8, and a o a ional symme y
is assumed. A gene alized desc ip ion including gains and losses is gi en by:
Ie,PD =Ie,R·Gop ·Lop · (λ, γR), o −α1/2< γR< α1/2,else Ie,PD = 0 .(2.8)
Cen e
𝛼
1/2
1/2
𝛼
De ec o
a ea
𝛾
De ec o
a ea
R
Figu e 2.8: Basic ecei e geome y. Angle α ep esen s he ield o iew, di ec ional
componen s ela e o he inclina ion angle γR.
A mo e applicable o m o he equa ion abo e employing an angula dis ibu ion unc ion
SR(γR), ha includes gains and losses, alid o one wa eleng h and wi hin he ield o iew
is:
Ie,PD(γR) = Ie,R·SR(γR).(2.9)
Ie,R(γR)is he incoming adian in ensi y a inclina ion γR. The SR(γR) unc ion needs o be
calcula ed. Rela ed o he cen e o a dome po in an unde wa e en i onmen , o example, his
12 Chap e 2 Fundamen als
would esul in alues sligh ly below 1 o all angles wi hin he hemisphe e. Sec ion 4.2 con ains
he modeling o he ligh pa h o di e en unde wa e housing concep s.
2.1.2 Unde wa e Op ical Link Con igu a ions
In he case o UOWC, h ee di e en link con igu a ions a e gene ally dis inguished:
•Line-o -sigh (LOS) link.
•Non-line-o -sigh (NLOS) link.
•Re o- e lec ing link.
Line-O -Sigh Link
The mos common link con igu a ion is line-o -sigh (LOS). This di ec link ep esen s an unob-
scu ed s aigh line be ween he ansmi e and ecei e wi hin he beam angle and he ield o
iew, espec i ely, as depic ed in Fig. 2.9. Misalignmen is an issue in he poin - o-poin con ig-
u a ions, and ela ed discussion can be ound in [42, 43, 44]. A close look a he link budge
is ou lined in Sec ion 2.1.4. Di ec UOWC links can be in e up ed o dis u bed by a a ie y o
Tx Rx
LOS
Subsea
Figu e 2.9: Di ec line o sigh link o UOWC.
possibili ies, o example, by objec s such as ehicles, ish, algae and bubbles. The e ec o block-
ing and shadowing on UOWC in he LOS se up has been s udied in [45]. In he li e a u e, he
LOS link ype is some imes e e ed o as di use link o la ge ansmi e beam angles such as
hose ound in LEDs. This p obably se es he simple pu pose o di e en ia ion om lase -based
sys ems, as s ingen LEDs do no p oduce di use ligh , bu ins ead yield incohe en di ec ed
ligh .
Figu e 2.10 illus a es LOS scena ios including su ace and sea loo e lec ions as well as pa ic-
ula e sca e ing. Su ace e lec ions in UOWC only occu when a sys em is ope a ed close o he
su ace and he angle θSexceeds he c i ical angle θc. In he seawa e -ai bounda y his is app ox-
ima ely 48◦, c . (2.2). Sea loo e lec ions a e negligible in mos cases due o s ong abso p ion and
mino e lec ance o he g ound. Pa icula e lec ion on he o he hand, can occu anywhe e in
he wa e column and depends on he wa e ype and hus he numbe o sca e ing componen s.
E en he clea es oceanic wa e s a e con aining sca e ing cons i uen s. Pa icula e sca e ing in
na u al wa e s akes place mos ly in a o wa d di ec ion a small angles. Fo mo e in o ma ion
e e o Sec ion 2.2.1. The o de o magni ude o sca e ed signal componen s eaching he ecei e
depends on he dis ance, he densi y o sca e s and he ield o iew. Re lec ed signal componen s
gene ally co e a longe dis ance han he di ec ones, so hey a i e a he ecei e wi h a delay
compa ed o he s aigh ones. This can lead o bi e o s and in e symbol in e e ence (ISI),
espec i ely. The en i e sca e ing p ocess has an e ec on he impulse esponse, and ela ed e-
sea ch can be ound in Sec ion 5.2.6 and [46, 47, 48]. Due o he high speed o ligh in wa e , gi en
2.1 Unde wa e Op ical Communica ion Sys ems Desc ip ion 13
Tx Rx
LOS
Su ace
Subsea
𝜃
Tx Rx
LOS
Seafloo
Pa icles
Tx Rx
LOS
𝜃
B
S
Figu e 2.10: Line o sigh scena io o UOWC wi h mul ipa h caused by su ace, pa i-
cles o sea loo e lec ions, wi h espec i e illus a ions om op o bo -
om.
by (2.3), he delay imes a e e y sho (in he nanosecond ange) a ypical maximum dis ances
o ens o me e s o LED based sys ems. Since he bandwid h o powe LEDs gene ally is a mos
in he ange o ens o MHz, he e will be ha dly any mul ipa h ela ed in e e ence. In much
as e lase based sys ems, howe e , he empo al dispe sion leading o ISI can play a majo ole,
see [49, 50, 51, 52]. Spa ial dispe sion is a se ious issue o lase -based sys ems, bu o sho e
anging LED based applica ions wi h compa a i ely la ge beam angles i is less signi ican .
Non-Line-O -Sigh Link
The NLOS link is based on e lec ion, and he e is no di ec pa h be ween ansmi e and ecei e
wi hin hei beam angle and he ield o iew. The o igin o he e lec ions a e ei he pa icles in
he wa e column o he medium change a he wa e su ace, as depic ed in Fig. 2.11.
Howe e , he applica ion o hese wo indi ec links is limi ed. The ad an age is he insensi i i y
o he alignmen . The disad an age o he pa icula e e lec ion is he low e icency and need o
he p esence o enough pa icles. The e o e, his applica ion is o sho e dis ances in u bid
coas al wa e s o in ha bou s. This opic is co e ed by [53, 54]. The app oach o o al su ace
e lec ance is in luenced by he wind-induced s ongly- a ying su ace condi ions and in pa icula
is limi ed due o he una oidable su ace p oximi y. Rela ed li e a u e is gi en in [55, 56].
Ano he possible con igu a ion would be o use e lec ions om he sea loo simila o he su ace
e lec ions o es ablish an indi ec link. This app oach is p obably mo e o a heo e ical na u e,
since he g ound is likely o be highly abso ben and only sligh ly e lec i e in mos cases. The
au ho is no awa e o any case in he li e a u e whe e his e ec is in en ionally used in UOWC.
20 Chap e 2 Fundamen als
OpAmp
R
-
+
C
Uou
UR
-
PD
IPD
Figu e 2.16: Elemen a y ci cui o a one-s age ansimpedance ampli ie as commonly
u ilized o PIN-PDs and APDs. The disc e e de ices R and C a e
he eedback esis o and he eedback capaci o , espec i ely. A e e se
ol age URis applied o he anode in o de o educe he capaci ance o
PIN-PDs, o in case o APDs, o enable he a alanche e ec .
sui able o use in he ecei e on end o UOWC sys ems.
Pho ode ec o s like PIN-PDs and APDs ha e a wide linea ope a ing ange, and he gene a ed
pho ocu en he e o e includes many o de s o magni ude. These iny cu en s, ypically anging
om mic oamps o nanoamps in UOWC en i onmen s, need ans o ma ion in o ol ages sui -
able o subsequen signal p ocessing, p ima ily A/D con e sion. This is commonly pe o med
by one-s age and some imes by wo-s age ansimpedance ampli ie s (TIAs). One-s age TIAs
mainly consis o an OpAmp, a eedback esis o R , and a eedback capaci o C , as depic ed in
Fig. 2.16. The eedback esis o de e mines he ampli ica ion and he accep able ligh le el be o e
sa u a ion o he ampli ie . The dimensioning o C mus be done e y ca e ully, because i has a
signi ican in luence on he s abili y, he impulse esponse, and he cu -o equency. The equi ed
capaci ance alues a e o en in he ange o a ew pico a ad, and he s ay capaci ances can be
co espondingly signi ican , so i is ad isable o make measu emen s in addi ion o simula ions
wi h app op ia e ools like [74].
A his poin , an example will se e o illus a e he ela ionships and he de elopmen o hese
alues. Fo his pu pose, a simpli ied simula ion o a poin ligh sou ce o powe Pop and o a
PD o a ea Ade and esponsi i y Ris ca ied ou a di e en dis ances o coas al oceanic wa e .
The pa ame e s a e speci ied in Table 2.2. Fu he simula ion condi ions include an ideal sou ce
wi h uni o m dis ibu ion, no inclina ion o sou ce and PD, and no ambien ligh . The exponen ial
a enua ion o he medium wa e is aken in o accoun , and he a enua ion coe icien applied
is he widely used c, which is gene ally alid o beams. The a enua ed sou ce powe is sp ead
o e he su ace o a sphe ical cap, ep esen ed by he lowe e m in he o mula, and o ms he
i adiance EPD a he de ec o [35]:
EPD =Pop ·e−c
2π 2(1 −cos(β/2)).(2.17)
The op ical powe a he de ec o su ace PPD yields:
PPD =Pop ·e−c
2π 2(1 −cos(β/2)) ·Ade .(2.18)
The gene a ed de ec o cu en IPD and he ou pu ol age Uou a e gi en by:
IPD =EPD ·Ade ·R (2.19)
Uou =IPD ·R .(2.20)

2.1 Unde wa e Op ical Communica ion Sys ems Desc ip ion 21
Table 2.2: Simula ion pa ame e s.
T ansmi op ical powe Pop 5 W
Beam angle β70 ◦
Wa eleng h λ514 nm
A enua ion coe icien c0.3 1/m
Responsi i y R0.37 A/W
De ec o a ea Ade 10 mm2
TIA eedback esis o R 100 kΩ
[m]
5 20
10
2
1
0.5
604 mW/m²
2.23 uA
223 mV
3.26 W/m²
12.1 uA
1.21 V
15.1 W/m²
56.1 uA
5.61 V
2.19 mW/m²
8.11 nA
811 uV
39.3 mW/m²
145 nA
14.5 mV
27.3 uW/m²
101 pA
10.1 uV
Poin
ligh sou ce
Pho ode ec o in a ying posi ions
PD
E =
I =
U =
PD
ou
PD
Figu e 2.17: Dependence o he i adiance EPD eaching he PD, he gene a ed pho-
ocu en IPD, and he ou pu ol age Uou on he dis ance . Sys em
pa ame e s o he co esponding simula ion a e chosen o be ypical e-
alis ic alues as gi en in Table 2.2.
As a esul , he simula ion shows he d as ic changes o he ele an alues o e many decades
wi hin a ealis ic ope a ing ange o 0.5 o 10 me e s, see Fig. 2.17. As i can be seen om (2.17),
he powe is a enua ed as a unc ion o he dis ance by he squa e law and exponen ially by
Bee ’s law. The use ul ange o he TIA is limi ed a he uppe end by he sa u a ion o he
ampli ie and a he lowe end by he noise. Apa om he signal componen , he sa u a ion can
also be in luenced o a conside able ex en by possible ambien ligh , despi e op ical il e ing. To
ease subsequen signal p ocessing, such as A/D con e sion and elec ical il e ing, app oaches like
loga i hmic ampli ica ion o swi chable espec i ely p og ammable gain can be pu sued. In u n,
howe e , some a en ion mus be paid o he C dimensioning and impulse esponse, as well as o
he modula ion scheme in case o signal supe posi ion, o example. In p inciple, o cou se, he e
is also he possibili y o sa u a ion o he pho ode ec o , gene ally less wi h he PIN-PDs han
wi h he APDs.
The second impo an aspec is he noise. In he case o UOWC, especially he a ea whe e he
signal- o-noise a io (SNR) is jus su icien o ansmission wi h an admi ed e o a e. Th ee
p edominan noise sou ces can gene ally be iden i ied: he mal noise, sho noise, and ampli ie
noise. The mal noise (Johnson-noise) is gene a ed by he he mal agi a ion o cha ge ca ie s,
i is p esen in all elec ical ci cui s, and inc eases wi h empe a u e. Sho noise is caused by
he andom luc ua ion o pho ons pe uni ime hi ing he de ec o a ea. The o igin makes no
di e ence o he PD, and he e is no dis inc ion be ween signal and ambien ligh . The hi d main
componen o be conside ed in he examina ion o noise is he ampli ie noise. This is desc ibed by
he pa ame e s o ol age noise densi y and cu en noise densi y, which a e speci ied as elec ical
cha ac e is ics in he ampli ie ’s da a shee . Low-noise ampli ie s a e o cou se p e e able o
22 Chap e 2 Fundamen als
TIA applica ions. The use o sui able simula ion ools is ecommended o handle he plu ali y o
a iables. A gene al ema k a his poin is ha he de ec o da k cu en noise is negligible in
mos cases.
Usually PIN-PD-based sys ems a e mo e obus o ambien ligh condi ions, bu hey a e slowe
and less sensi i e, whe eas APD-based sys ems cope wo se unde ambien ligh condi ions due o
sho noise, bu o e compa a i ely be e sensi i i y and highe speed, c . [75]. Mo e in-dep h
discussion o his opic is included in Sec ion 3.4.
2.1.6 Rele an Aspec s o Digi al Communica ions in UOWC
In ensi y Modula ion and Di ec De ec ion
An LED based UOWC sys em ollows he in ensi y modula ion and di ec de ec ion (IM/DD)
p inciple. In ensi y modula ion can be gene a ed by a ying he LED o wa d cu en . Di ec
de ec ion is achie ed by a pho ode ec o in he ecei e , which con e s he op ical powe eaching
he su ace o an elec ical cu en . Fea u es which should be men ioned a his poin a e ha
LEDs as non-cohe en ligh sou ces p ohibi he use o any phase in o ma ion. Fu he mo e his is
a baseband echnique wi hou equency con e sion. The wa e o m signal s( )mus be eal- alued
and non-nega i e. The LED o wa d cu en and emi ed powe a e no en i ely p opo ional, a
leas no o la ge signal a ia ions. In he op ical domain o UOWC we ind a p opo ionali y
be ween he ansmi ed powe PTop and he ecei ed powe PRop . In he elec ical domain,
he ecei ed powe is p opo ional o he squa e o he pho ode ec o cu en . The undamen al
ela ionship be ween he ecei ed powe s in he op ical domain PRop and in he elec ical domain
PRel is gi en by:
PRel ∼κR2P2
Rop .(2.21)
He ein, Ris he eponsi i y o he pho ode ec o , and his is a de ice and wa eleng h dependen
pa ame e . The shaping gain ac o κdepends on p ope ies o a signal x( ), which co esponds
o s( )used he e, and is gi en by:
κ,x2
¯x2.(2.22)
La ge ampli ude luc ua ions and hus high κ a ios lead in o be e powe e iciency o he mod-
ula ion scheme o he same ecei ed powe . Mo e de ailed in o ma ion can be ob ained in [39,
76, 77].
AWGN Channel Model
s ( )
( )
n ( )
h ( )
Figu e 2.18: Addi i e whi e Gaussian noise (AWGN) channel model.
The AWGN channel model is a undamen al in communica ion echnology [78, 79]. As depic ed
in Fig. 2.18, s( )is he in ensi y modula ed inpu signal, h( )is he channel ans e unc ion,
n( )is he addi i e whi e Gaussian noise, and ( ) he channel ou pu signal. The co esponding
o mula is (* deno es linea con olu ion):
( ) = s( )∗h( ) + n( ).(2.23)
2.1 Unde wa e Op ical Communica ion Sys ems Desc ip ion 23
To he signal a noise p ocess is added, which has a la spec al powe noise densi y o e he band-
wid h, he so-called whi e noise. This noise is Gaussian dis ibu ed, and i has a ze o mean. Based
on AWGN, he Shannon-Ha ley heo em s a es he channel capaci y, which is o la ge in e es o
communica ion sys ems. The heo e ical maximal channel capaci y is a unc ion o he channel’s
bandwid h and he signal- o-noise a io, and can be app oxima ed o in ensi y modula ion by
app op ia e o mulas. The elec ical SNR and no he op ical is included he e. Since he e is
no well es ablished heo e ical model o he UOWC channel [80], he AWGN channel model is
o en used o UOWC sys ems, e en i i s alidi y is limi ed. One limi a ion has i s cause in he
noise con ibu ion om he sho noise, which is signal dependen . In case o UOWC, his signal
is gene a ed by he LED sou ce. Ambien ligh also causes sho noise, which is independen om
he LED sou ce. The sho noise dis ibu ion shi s om Poisson wi h small numbe o e en s,
o simila o Gaussian o la ge numbe s. T ans e ed o he numbe o inciden pho ons a he
pho ode ec o , his means lea ing he (single) pho on coun ing egime a inc easing i adiances.
Ano he limi a ion is ha he Shannon-Ha ley heo em assumes Gaussian dis ibu ed channel
inpu symbols. This assump ion iola es he cons ain o non-nega i e channel inpu s. None he-
less, Shannon-Ha ley heo em can be used as a ough es ima e in UOWC, pa icula ly when he
noise sou ces a e sepa a ely analyzed and he he mal noise con ibu ion o he ampli ie noise
a e clea ly dominan o e he sho noise con ibu ion. A noise analysis o di e en exempla y
ope a ing condi ions is p o ided in Sec ion 3.3.3.
UOWC Modula ion Schemes
The selec ion o he modula ion scheme has a la ge impac on he espec i e sys em pe o mance,
his implies a ca e ul conside a ion o he mu ually in luencing c i e ia:
•Bandwid h pe o mance.
•Powe e iciency.
•Signal o noise (SNR) equi emen s.
•Bi e o a e (BER) speci ica ion.
•Implemen a ion e o .
Highes possible da a a es also equi e la ge bandwid h, bu hese a e gene ally limi ed by he
LED and he PD capaci ance. Since mobile unde wa e de ices and also ancho ed sys ems a e
almos exclusi ely ba e y-powe ed, he ene gy e iciency is he key o long ope a ing imes. This
applies no only o he LED and he absolu e ansmi ed powe , bu also o he modula ion
scheme. While he BER is a sys emic bounda y condi ion, he SNR s ongly depends on he
dis ance Tx-Rx. A high design complexi y and he esul ing implemen a ion e o a e also ele an
o cos , space and ene gy. Modula ion schemes o non-cohe en IM/DD UOWC sys ems a e
in mos cases single-ca ie ypes wi h wo ampli ude le els. These so-called bi-phase schemes
a e ha dwa e iendly due o he swi ching p ocess. Non- e u n- o-ze o On-O -keying (NRZ-
OOK) and pulse-posi ion-modula ion (PPM) a e o en used, he i s because o good bandwid h
p ope ies and he simples implemen a ion, and he second because o low SNR equi emen s.
The gene ally popula pulse-wid h-modula ion (PWM) is a ely used in his a ea because o i s
poo powe e iciency. A his poin , he asynch onous digi al pulse in e al modula ion (DPIM)
should be men ioned [81], as well as he di e en ial pulse posi ion modula ion (DPPM) [82]. Mo e
in-dep h li e a u e is gi en in [39, 83].
Fo an accu a e unc ion a ce ain bi e o a e (BER) needs o be ul illed. Wi hou channel
coding his a ge ed bi e o a e h eshold is mos ly se o a alue in he ange o 10−2 o 10−6.
Di e en modula ion schemes equi e indi idual SNRs in o de o achie e he a ge ed BER. The
mos commonly applied modula ion schemes in UOWC, NRZ-OOK and PPM, need an SNR in he
24 Chap e 2 Fundamen als
Table 2.3: Compa ison o common modula ion schemes o UOWC. Values o SNR
ex ac ed om g aphics gi en in [39].
NRZ-OOK 4-PPM 8-PPM 16-PPM
Bandwid h e iciency Rb=B Rb= 0.5B Rb= 0.375B Rb= 0.25B
SNR
o 10−2BER 7.2 dB 5.0 dB 4.0 dB 3.2 dB
o 10−3BER 9.8 dB 7.3 dB 6.0 dB 5.2 dB
o 10−4BER 11.4 dB 8.8 dB 7.4 dB 6.4 dB
o 10−5BER 12.6 dB 9.9 dB 8.4 dB 7.4 dB
o 10−6BER 13.5 dB 10.7 dB 9.3 dB 8.2 dB
Powe e iciency κ2 4 8 16
Da a a e Rb, bandwid h B
elec ical domain oughly in he ange o 5dB o 15dB o a ce ain BER, c . Table 2.3. The alues
o he SNR pe bi (Eb/N0) a e aken as he basis ins ead o he SNR pe symbol (Es/N0), since
hese a e he mo e p ac ical choice in he case o bandwid h limi ed sys ems and hus cons an
ime slo s o chip du a ions. Assuming he a e age powe is cons ained, he L−PPM scheme
shows be e immuni y agains noise wi h inc easing ca dinali y L, and his highe sensi i i y
leads in o la ge achie able dis ances in p ac ice [83]. To a oid he communica ion su e ing om
d op ou s when he equi ed SNR is unde cu , an adap i e sys em could change he modula ion
scheme o a less noise sensi i e one. Fo example om NRZ-OOK o 8-PPM, hough a he
expense o bi a e. Reducing he dis ances unde o he wise iden ical condi ions quickly leads o
a signi ican imp o emen in he SNR, and hus o eliable communica ion down o e y sho
dis ances, which hen can lead in o sa u a ion p oblems. I is wo h men ioning a his poin , ha
channel coding can co ec a limi ed numbe o e o s in a ecei ed message. This leads in o an
educ ion o he BER o a bi a y low alues. In compa ison o he uncoded case, his co esponds
o an imp o emen o he SNR o inc ease o he dis ance, espec i ely. UOWC sys ems applying
o wa d e o co ec ion (FEC) like Reed Solomon (RS) coding a e p esen ed in [80, 84]. Gene al
o e iews o modula ion schemes and ela ed opics a e ga he ed in [13, 15, 17].
Inpu Ou pu A chi ec u es
SISO
LED PD
LED
LED
LED
MISO
1
PD
2
N
...
SIMO
LED
PD
PD
PD
MIMO
LED
LED
LED PD
PD
PD
11
1
22
N
N
2
N
...
...
...
TTR
R
Figu e 2.19: D awing depic s he ou gene al inpu -ou pu schemes om single-inpu
single-ou pu (SISO) o mul iple-inpu mul iple-ou pu (MIMO). NTis
he numbe o elemen s on he ansmi e side and NRon he ecei e
side.
The basic sys em in op ical ansmission comp ises one ligh sou ce and one pho ode ec o as
2.2 Ligh in he Medium Wa e 25
he ecei ing elemen , which is also known as single-inpu single-ou pu sys em (SISO). This is
clea ly he mos widely used and equen ly compa ed ype in he UOWC sec o . I se e al ligh
sou ces a e used on he ansmi e side and se e al pho ode ec o s on he ecei e side, his is
e e ed o as mul iple-inpu mul iple-ou pu (MIMO) echnology, see Fig. 2.19. Special cases
o MIMO a e he single-inpu mul iple-ou pu (SIMO) and mul iple-inpu single-ou pu (MISO)
sys ems, which only use one ligh sou ce o one pho ode ec o , espec i ely, [39]. MIMO enables
an imp o emen o he sys em a ailabili y (spa ial di e si y) and da a a e (spa ial mul iplexing),
ei he by ansmi ing he same o di e en in o ma ion by all sou ces, espec i ely. Fu he
cha ac e is ics and ea u es on he use o MIMO echnology in he ield o UOWC a e ha he
Rx and Tx elemen s can be a anged close o spa ially sepa a ed, and one o di e en colo s
can be used. Fu he mo e single-use o mul i-use communica ion is easible, and localiza ion
is possible. Since mos UOWC applica ions will be mobile, hus needing hemisphe ical o e en
sphe ical Rx and Tx cha ac e is ics, which leads o conside ably o e lapping segmen s in he
p ac ical implemen a ion. This au oma ically c ea es a MIMO sys em in ce ain a eas. Fo
ene gy-c i ical applica ions like mobile UOWC, he SIMO a chi ec u e is p e e able o he MISO
in mos scena ios. A comp ehensi e in oduc ion o he en i e opic is gi en in [17]. A compa a i e
pe o mance analysis o he di e en a chi ec u es including LED based UOWC was ca ied ou
in [85], and a s udy dedica ed o SIMO is gi en in [86]. The easibili y o implemen ing MIMO
capable UOWC ansmi e s is p esen ed in [30].
2.2 Ligh in he Medium Wa e
Na u al wa e s as medium o he unde wa e op ical channel a e challenging o UOWC sys em
designe s due o hei widely a ying pa ame e s. The op ical p ope ies o wa e a e g ouped in o
wo classes, inhe en op ical p ope ies (IOP) and appa en op ical p ope ies (AOP) [87]. IOPs
depend on he medium i sel like i s composi ion and p esen pa icles, and he abso p ion and
sca e ing coe icien s a e wo p ominen examples. AOPs depend on he medium i sel and on
he s uc u e o illumina ion, he di ec ionali y o he ligh ield, such as he di use a enua ion
coe icien o ins ance, mo e de ails a e gi en in [88].
2.2.1 Abso p ion, Sca e ing and A enua ion
Abso p ion
Compa ed o ai , wa e is a s ong abso bing medium o ligh . Pho ons o he pene a ing ligh
a e i e e sibly emo ed om hei pa h and he ene gy is con e ed by he wa e molecules o
o he abso bing cons i uen s. These e ec s show a high spec al dependency. Wi h espec o
Mobley [87], he spec al abso p ion coe icien is de ined as depic ed in Fig. 2.20 and by ollowing
equa ion:
a(λ) = lim
∆ →0
Φa(λ)
Φi(λ)·1
∆ .(2.24)
The main op ically ac i e abso bing componen s in na u al wa e s a e:
•aw, abso p ion by he wa e i sel .
•aphy , abso p ion by phy oplank on.
•aCDOM, abso p ion by colo ed dissol ed o ganic ma e .
•aNAP, abso p ion by non-algae pa icles o de i us.

26 Chap e 2 Fundamen als
Φ (λ)
Φ (λ)
Φ (λ)
i a
Δ
Figu e 2.20: Geome y o de ine spec al abso p ion in a olume o wa e as gi en by
Mobley. Φa(λ)is he pa o he monoch oma ic inciden beam Φi(λ)
which is abso bed in a laye o wa e wi h hickness ∆ ,Φ (λ)is he
ansmi ed powe , and uni s a e W/nm.
The o al spec al abso p ion coe icien a(λ)can be exp essed as he sum o hese g ouped
abso bing cons i uen s [89]:
a(λ) = aw(λ) + aphy (λ) + aCDOM(λ) + aNAP(λ).(2.25)
The uni o abso p ion coe icien is 1/m. Due o he di e en spec al p og ession and a iabili y
o hese cons i uen s, his equi es a close look. The abso p ion by he wa e aw(λ)i sel is gi en
in Figs. 2.21 and 2.22 o pu e wa e and pu e seawa e wi h a salini y o 35 %, espec i ely. A
s ong ise in abso p ion can be egis e ed in he ange abo e 600 nm. The di e ence be ween
bo h ypes is ela i ely small, and he dependence on empe a u e and salini y is known o be low
[87].
200 300 400 500 600 700 800
0
0.5
1
1.5
2
2.5
3
3.5
Wa eleng h [nm]
Abso p ion coe icien [1/m]
Sea wa e , pu e
Figu e 2.21: Spec al abso p ion aw(λ)o pu e sea wa e . The so-called anspa en
window is clea ly iden i iable. Plo ed om abula ed da a gi en in [90].
Phy oplank on is he gene ic e m o li ing mic oalgae con aining chlo ophyll pigmen s. Cha -
ac e is ic o phy oplank on is he s ong abso p ion in he blue wa eleng h egime and a peak
in he deep ed. Due o a a iable mix u e o species in na u al wa e s he spec al beha io also
a ies. A spec al abso p ion model was de eloped by B icaud e al. [92], gi en as abula ed
nume ical cons an s Aphy (λ)and Bphy (λ), and is shown in (2.26). A chlo ophyll concen a ion
ela ed gene al abso p ion spec a can be calcula ed by:
aphy (λ) = Aphy (λ)·hchli−Bphy (λ).(2.26)
The chlo ophyll concen a ion chl anges oughly om 0.1 mg/m3 o clea oceanic wa e s o
10 mg/m3in p oduc i e coas al a eas, and can ise up o 100 mg/m3in lakes, see also Fig. 2.23.
2.2 Ligh in he Medium Wa e 27
400 450 500 550 600 650 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Wa eleng h [nm]
Abso p ion coe icien [1/m]
Sea wa e , pu e
Wa e , pu e
Figu e 2.22: Spec al abso p ion aw(λ)o pu e wa e and pu e sea wa e . Plo ed
om abula ed da a gi en in [90, 91].
400 450 500 550 600 650 700
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
Wa eleng h [nm]
Abso p ion coe icien [1/m]
Chlo ophyll
concen a ion chl
20 mg/m³
10 mg/m³
5 mg/m³
1 mg/m³
0.1 mg/m³
Figu e 2.23: Spec al abso p ion o phy oplank on aphy (λ)in sea wa e as unc ion
o he chlo ophyll concen a ion. Values calcula ed and plo ed based on
[92].
Colo ed dissol ed o ganic ma e (CDOM) a e decaying o ganisms, also named yellow sub-
s ances o gelbs o . The abso p ion gene ally exponen ially dec eases wi h wa eleng h, and alues
depend on he concen a ion and he speci ic ype o yellow subs ances. The spec al cha ac e -
is ic o his abso bing cons i uen can be modeled by (2.27), acco ding o B icaud e al. [93].
Exponen ial coe icien s SCDOM and e e ence alues aCDOM(λ e )can be ound in [87, 89]:
aCDOM(λ) = aCDOM(λ e )·e(−SCDOM(λ−λ e )).(2.27)
Non-algae pa icles (NAP) o de i us, also desc ibed as deb is o plank on and sedimen s o m
ano he abso bing cons i uen . The spec al p og ession is simila o he cou se o CDOM, bu
wi h ypically smalle slopes. The equa ion o he model (2.28), as well as exponen ial coe icen s
SNAP and e e ence alues aNAP(λ e a e gi en in [89, 94]:
aNAP(λ) = aNAP(λ e )·e(−SNAP(λ−λ e )).(2.28)
The CDOM and NAP abso p ion e e ence alues a e o en gi en a wa eleng hs λ e o 400 nm
o 443 nm, espec i ely, and exponen ial coe icien s a e mos ly in he ange o 0.01 o 0.02.
28 Chap e 2 Fundamen als
Figs. 2.24 and 2.25 show he o al spec al abso p ion and he cons i uen s modeled o he
A lan ic Ocean and he Bal ic Sea, ep esen ing oceanic and coas al wa e s, espec i ely.
400 450 500 550 600 650 700
0
0.2
0.4
0.6
0.8
1
1.2
Wa eleng h [nm]
Abso p ion coe icien [1/m]
Abso p ion, o al
a
aM
Abso p ion
cons i uen s
aw
aphy
aCDOM
aNAP
Figu e 2.24: Modeled o al spec al abso p ion a(λ)and i s cons i uen s as well as
he o al o he simpli ied model aM(λ) o he Bal ic Sea. Pa ame-
e s a e ex ac ed om [94] and ep esen ypical alues o his a ea.
(Sea wa e , chl=5 mg/m3,aCDOM(433)=0.3 1/m and SCDOM=0.019,
aNAP(433)=0.15 1/m and SNAP=0.013).
To ease modeling, Mo el [95] p esen ed a simpli ied model based on he wo k by P ieu and
Sa hyend ana h [96], gi en as (2.29). This model o he o al abso p ion aM(λ)only needs he
spec al wa e abso p ion coe icien aw(λ), he chlo ophyll concen a ion chl, and one abula ed
chlo ophyll speci ic spec al alue Achl(λ):
aM(λ)=[aw(λ)+0.06 ·Achl(λ)·chl0.65]·[1 + 0.2·e(−0.014(λ−440))].(2.29)
Since he ela ionship o o he cons i uen s like CDOM is ixed, he p e e able usage is limi ed
o phy oplank on domina ed oceanic wa e s. Fo illus a ion, he cu es c ea ed acco ding o
his model ha e been in eg a ed in Figu es 2.24 and 2.25. In case o he CDOM- ich Bal ic he
di e ence o he wo modeled o al abso p ions is ob ious.
The abso bing componen s a e subjec o na u al luc ua ions due o dep h and he season
o he yea , which applies in pa icula o he chlo ophyll-con aining phy oplank on [95, 97].
The chlo ophyll concen a ion and acco dingly he abso p ion can show p onounced peaks in he
e ical wa e column a he pho ic zone up o 150 m dep h. This o cou se co esponds o UOWC
wi h e ical links, and his opic is in es iga ed in [98]. A good gene al e e ence o abso p ion
alues and hei a iabili y o di e en a eas is gi en in [94].
2.2 Ligh in he Medium Wa e 29
400 450 500 550 600 650 700
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Wa eleng h [nm]
Abso p ion coe icien [1/m]
Abso p ion, o al
a
aM
Abso p ion
cons i uen s
aw
aphy
aCDOM
aNAP
Figu e 2.25: Modeled o al spec al abso p ion a(λ)and i s cons i uen s as well as
he o al o he simpli ied model aM(λ) o he A lan ic Ocean. Pa am-
e e s a e ex ac ed om [94] and ep esen ypical alues o his a ea.
(Sea wa e , chl=0.2 mg/m3,aCDOM(433)=0.02 1/m and SCDOM=0.019,
aNAP(433)=0.05 1/m and SNAP=0.013).
Sca e ing
The e ec o sca e ing o ligh in wa e can be desc ibed as he p ocess when he pa h o a
pho on is changed in a di ec ion by in e ac ion wi h molecules o pa icles. This causes spa ial
and empo al dispe sion, and he la e is discussed a he end o his subsec ion. Wi h espec
o Mobley [87], he spec al sca e ing coe icien is de ined as depic ed in Figu e 2.26 and by
ollowing equa ion:
b(λ) = lim
∆ →0
Φs(λ)
Φi(λ)·1
∆ .(2.30)
Φ (λ)
Φ (λ)
i
Δ
Φ (λ)
s
ΔVΨ
ΔΩ
𝜑
Figu e 2.26: D awing shows he geome y o de ine spec al sca e ing in a olume o
wa e as gi en by Mobley. Φs(λ)is he pa o he monoch oma ic inci-
den beam Φi(λ) ha is sca e ed in a olume ∆Vo wa e wi h hickness
∆ ,Φ (λ)is he ansmi ed powe , and uni s a e W/nm. The ligh is
sca e ed in o a solid angle ∆Ω in di ec ion o Ψ, and he azimu hally
symme y o hese e en s is depic ed by ϕ.
36 Chap e 2 Fundamen als
400 450 500 550 600 650
0.01
0.02
0.05
0.1
0.2
0.5
1
2
5
10
Wa eleng h λ [ nm]
Abso p ion coe icien a [1/m]
Je lo wa e ype
coas al 9C
coas al 7C
coas al 5C
coas al 3C
coas al 1C
oceanic III
oceanic II
oceanic IB
oceanic IA
oceanic I
Figu e 2.33: Spec al abso p ion a o Je lo wa e ypes I o 9C. Plo ed om
da abase o [102], (da a o 5C o 600 nm o 650 nm a e in e pola ed).
Table 2.4: P ope ies o h ee di e en wa e s a λ= 514 nm.
Class Abso p ion aSca e ing bA enua ion cAlbedo ω0
[1/m] [1/m] [1/m]
clea oceanic 0.114 0.037 0.151 0.245
coas al ocean 0.179 0.219 0.398 0.550
u bid habou 0.366 1.824 2.190 0.833
In he case o widely a ying oceanic op ical pa ame e s a classi ica ion can only p o ide a
ough es ima e o alues, and a signi ican imp o emen can be achie ed h ough measu emen s.
The a iabili y o wa e op ical pa ame e s o UOWC sys ems is desc ibed in [116] and a gene al
o e iew o ins umen a ion o ocean moni o ing is gi en in [117]. Measu emen s o op ical wa e
pa ame e s can be ca ied ou wi h in si u unde wa e ansmissiome e s [118]. Ins umen s o
hese ype can be deployed a a iable dep hs and a e able o eco d he a enua ion and abso p ion
alues, o single wa eleng hs o spec al, depending on he e sion. Since op ical wa e p ope ies
ha e a la ge impac on UOWC sys ems, is i ecommendable o make such measu emen s and s a e
he alues as hey a e essen ial o pe o mance assessmen s. An expe imen in he ield including
such measu emen s is desc ibed in Sec ion 5.3.
2.2.3 Re ac i e Index, Tu bulence and Scin illa ion
Inhomogenei y o a ma e ial o medium like seawa e causes changes in he e ac i e index n
and induces sca e ing. Beside suspended pa icles and seawa e molecules, his is ano he cause
o sca e ing. The e ac ion index o seawa e is dependen o he pa ame e s empe a u e T,
salini y , wa eleng h λand p essu e p(i.e., densi y change by wa e dep h). Mo e de ails can be

2.2 Ligh in he Medium Wa e 37
ound in [119, 120]. The a ia ion o hese pa ame e s is ep esen ed as e ac i e index diag ams
in Figu es 2.34, 2.35 and 2.36. The e ac i e index o seawa e shows a ela i e linea inc ease
wi h ising salini y and p essu e.
0 5 10 15 20 25 30
1.335
1.34
1.345
1.35
1.355
Tempe a u e [°C]
Re ac i e index
400 nm
450 nm
500 nm
550 nm
600 nm
650 nm
Figu e 2.34: Spec al e ac ion index o seawa e o empe a u e a ia ion. Valid o
a dep h o 0 me e s and a salini y o 35 %. Plo ed om abula ed da a
o [119].
0 10 20 30 40
1.33
1.335
1.34
1.345
1.35
1.355
Salini y [‰]
Re ac i e index
400 nm
450 nm
500 nm
550 nm
600 nm
650 nm
Figu e 2.35: Spec al e ac ion index o seawa e o salini y a ia ion. Valid o a
dep h o 0 me e s and a empe a u e o 10◦C. Plo ed om abula ed
da a o [119].
Gene ally, he e ac i e index shows a slow and spacious change, bu he sensi i i y o hese
pa ame e s is ul ima ely based on he na u ally occu ing a ia ion. Eddies a e empo a y loops
o swi ling wa e , and ci cula cu en s. La ge eddies cascade down o smalle and smalle ones
un il hey inally lose hei ene gy. Wi hin hese eddies he di using empe a u e and o salini y
zones o m cu ed bounda ies wi h ocusing and de ocusing e ec s, and he oceanic u bulence
hus gene a es op ical u bulence. The e ec on he e ac i e index is known as scin illa ion. The
luc ua ion o he op ical in ensi y is gi en by he scin illa ion index σ2, which is de ined as he
no malized oo mean squa e de ia ion o he in ensi y Ie:
σ2=(hI2
ei−hIei2)
hIei2.(2.44)
Weak u bulen egimes a e indica ed by σ2<< 1and s ong ones by σ2>> 1, c . [121, 122].
Scin illa ion can ha e a se ious in luence on he UOWC sys ems pe o mance, he BER can
inc ease and in u n he ange can educe acco dingly. Some li e a u e has been published on his
38 Chap e 2 Fundamen als
0 25 50 75 100
1.335
1.34
1.345
1.35
1.355
1.36
1.365
P essu e [MPa]
Re ac i e index
400 nm
450 nm
500 nm
550 nm
600 nm
650 nm
Figu e 2.36: Spec al e ac ion index o seawa e o p essu e a ia ion. Valid o
a salini y o 35 % and a empe a u e o 10◦C. A p essu e o 10 MPa
equals o 100 ba and an app oxima e dep h o 1000 me e s. Calcula ed
and plo ed om abula ed da a o [119].
opic in he ecen yea s, bu is mos ly ela ed o lase -based sys ems, since hese a e gene ally
mo e a ec ed due o ypically longe anges and poin ing issues compa ed o LED-based sys ems.
Fu he in o ma ion on lase -based sys ems can be ob ained om [123, 124, 125, 126, 127, 128].
Publica ions on he impac o u bulence o LED-based sys ems a e a e, in [86] in es iga ions
we e ca ied ou wi h mo e ex eme pa ame e s, whe eas in [129] mode a e pa ame e s we e used,
esul ing in ela i ely small alues σ2o <0.08. Fo p ac ically achie able dis ances o a ew ens
o me e s in maximum hese alues a e e en less, and his clea ly indica es a limi ed in luence o
weak u bulence o LED-based UOWC sys ems.
In es iga ions on he u bulence o he mo ing ocean and p opelle induced scin illa ion can be
ound in [130, 131]. Bubbles a e ano he possible eason o u bulence, and esea ch on his opic
is gi en in [85, 132, 133, 134].
2.2.4 Sola Spec al I adiance and Ambien Ligh Unde wa e
In many publica ions ega ding UOWC and ela ed simula ions da kness is conside ed. This
assump ion is gene ally co ec o he deep sea in he ba hypelagic zone (midnigh ) a dep hs o
1000 me e s and mo e. In he adjacen mesopelagic zone ( wiligh ) om 200 me e s o 1000 me e s
and pa icula ly in he epilagic zone (sunligh ) o pho ic zone om he su ace o 200 me e s dep h,
sunligh pene a es he wa e column and is impo an o ma ine li e, bu can be a hu dle o
UOWC sys ems.
The ambien ligh unde wa e is he esul o na u ally occu ing sola i adiance, and a e -
e ence spec um is gi en in Fig. 2.37. The sola adia ion’s magni ude and spec um has s ong
in luencing ac o s, such as he zeni h angle o he sun, cloud co e age, wind speed o mois u e
le el in he a mosphe e. The cha ac e is ic o he dis ibu ed ligh eaching he sea su ace changes
om di ec ed in clea skies o di use in o e cas condi ions, as well as he magni ude o i adia ion
is dec eased o a en h. Wi hin he wa e , di ec ed ligh a els longe dis ances o pene a es
o la ge dep hs, and i becomes inc easingly di use due o sca e ing. Wi hin he wa e column
ligh is dis inguished be ween up- and downwelling i adiance, and each con ains all di ec ions in
a hemisphe e, c . Fig. 2.38. The amoun o he downwelling i adiance can be o de s o magni ude
la ge han he upwelling, he iewing di ec ion o a senso can he e o e be o g ea impo ance.
The a ea o leas ligh a enua ion o seawa e is ougly in he ange om 400 o 600 nm,
and he maximum o sola adia ion app oxima ely 450 nm o 600 nm. To educe o a oid sola
dis u bance, he gaps in he spec um (F aunho e lines) heo e ically could be used, bu hei
bandwid h is e y na ow. An e icien u iliza ion o LEDs is he e o e no easible. Lase s should
2.2 Ligh in he Medium Wa e 39
300 400 500 600 700 800 900
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
Wa eleng h [nm]
I adiance [W/(m2 nm)]
Figu e 2.37: Di ec spec al sola i adiance a he Ea h’s su ace o no mal di ec ion
a a sola zeni h angle o 48.2◦and s anda d a mosphe ic condi ions.
Plo ed om abula ed da a o Re e ence Sola Spec al I adiance ASTM
G-173-03 [135].
Su ace
Subsea
Pa icles
Sun
Ambien ligh
Downwelling i adiance
Upwelling i adiance
Viewing
di ec ions
Figu e 2.38: Di ec ions and s uc u e o ambien ligh unde wa e .
ha e exac ly he same wa eleng h, and ex emly na ow bandpass il e s would be necessa y,
which is di icul o achie e in eali y. Ano he app oach has been in es iga ed by Fa [136].
The use o sho wa eleng hs in he band o 350 nm o 400 nm whe e he sola adia ion d ops
o . Keda [137] examined he applica ion o UV ligh o 200 nm o 280 nm o UOWC in he
so-called sola blind ange below 300 nm. Bo h a emp s ha e o ba le he inc eased seawa e
a enua ion and a ailabili y o e icien ligh sou ces, o be able o ope a e in he egion o educed
o e en wi hou sola adiance. Simula ions o UOWC ne wo ks unde ealis ic en i onmen al
condi ions ha explici ly include di e en sola illumina ion can be ound in [138, 139]. Mo e
in-dep h in o ma ion and u he esea ch on ambien ligh il e ing is p o ided in Sec ion 3.2.
2.2.5 Unde wa e Ligh Field Fluc ua ions
Ai -sea in e ac ions, in conjunc ion wi h sunligh can ha e a s ong in luence on he a iabili y o
he unde wa e ligh ield. Wind and induced wa es gene a e a dynamic su ace a he medium
change om ai o wa e o di ec sunligh . This causes ocussing and de ocussing e ec s in he
nea su ace wa e . A ising adiance peaks in shallow wa e s can ha e a ac o o 10 compa ed
40 Chap e 2 Fundamen als
o he mean alues, he ime scale can be in he ange o 1 ms o 10 s, and he spa ial ex en is
om 1 cm o 100 m [140]. Howe e , in dep hs o 30 m luc ua ions o 50 % can s ill be obse ed
[141]. These e ec s a e gene ally s onge in he yellow- ed spec al egime compa ed o he blue-
g een one [142]. UOWC sys ems ope a ed in shallow wa e can be dis u bed by such occu ences
h ough inc eased noise le els o sho ime in e als, o e en wo se he sys em can be d i en
in o sa u a ion.
2.2.6 Bioluminescence, Fluo escence and Raman Sca e ing
Ano he sou ce o possible dis u bance o UOWC can be ligh induced by e ec s like biolumi-
nescence, luo escence and Raman sca e ing. Al hough he amoun o ligh o hese e ec s is
gene ally small, when hey ake place in close p oximi y o he ecei e hey may be able o gene -
a e no ewo hy dis u bances, especially when he communica ion signal is weak and he de ec o
is e y sensi i e. These e ec s can be signi ican in he da k a la ge wa e dep hs o a nigh .
Implica ions a e mo e likely o be expec ed in mul icolo o un il e ed applica ions.
Bioluminescence is he e m o ligh emi ed by ma ine o ganisms, sized om ish down o
bac e ia. The occu ence can be in all dep hs as well as all geog aphic zones o he oceans. The
colo is species dependen and is in he blue o yellow egime, whe e he ligh a enua ion o he
oceans is also leas . The spec al bandwid h o he emission can ake on alues om 26 nm o
100 nm FWHM, and he du a ion a ies om ens o milliseconds o con inuous emission.
Raman sca e ing is he e en o inelas ic sca e ing o pho ons in ma e , in his case by wa e
molecules. The pho ons pa h is edi ec ed and ene gy is exchanged, he wa eleng h shi s om λ0
o a longe wa eleng h λ. Fo ins ance blue ligh wi h λ0=450 nm will be Raman edis ibu ed
in seawa e o g een in a ela i e na ow band o 20 nm a λ= 530 nm. Calcula ions can be done
by using he Raman wa eleng h edis ibu ion unc ion.
Fluo escence is also an inelas ic sca e ing p ocess o no ewo hy ele ance in he wa e medium.
Inciden pho ons a e abso bed by molecules o subs ances in he wa e , and a e a e y sho ime
(in he o de o nanoseconds o picoseconds) hey a e emi ed again wi h a longe wa eleng h.
Basically i can be seen as an abso p ion ollowed by an emission. As an example, he exci a ion
o seawa e con aining yellow ma e and chlo ophyll wi h λ0o λex = 450 nm, would esul in
an emission λo λem wi h a wide band om app oxima ely 450 nm o 600 nm o yellow ma e
and wi h a na owe band om 660 nm o 720 nm o chlo ophyll. An ex ensi e explana ion o
hese opics is gi en in [87, 143].
2.3 Chap e Summa y
In his chap e , he undamen al p inciples and impac s o unde wa e op ical wi eless communi-
ca ion channels ha e been desc ibed. This includes he op ical pa h be ween he sou ce and he
de ec o when en e ing o lea ing he wa e medium. Re ac ion, ansmi ance and e lec ance
a e signi ican he e. The link be ween ansmi e and ecei e can be es ablished in di e en
con igu a ions, and he di ec line-o -sigh ep esen s he majo ype and he base o subsequen
examina ions. The esul ing link budge has been de eloped, and wo dis ance-dependen e ms
ha e a decisi e in luence, which a e he exponen ial dec ease by he Bee -Lambe law and he
in e se squa e law.
Rele an basics o pho onic de ices like spec al cha ac e is ics and he ope a ing anges o LEDs
and pho ode ec o s wi h espec o UOWC we e gi en, as well as he equi ed ansimpedance
ampli ica ion and some aspec s o digi al communica ions. A simula ion example using basic
pa ame e s has demons a ed he o de s o magni ude o be expec ed wi h espec o i adiance,
pho ocu en and dis ance.
As key elemen s o la ge impac , he inhe en op ical p ope ies o he wa e , he abso p ion
and he sca e ing ha e been desc ibed mo e in de ail. This conce ns he cons i uen s, modeling,
2.3 Chap e Summa y 41
spec al p ope ies and he esul ing a enua ion. The classi ica ion o a wide ange o na u al
wa e s o se e al oceanic and coas al ypes wi h espec o Je lo ha e been p esen ed. Tem-
pe a u e, salini y and dep h in luences on he wa e ’s e ac i e index a e discussed, which can
lead o u bulence and scin illa ion. O he po en ially dis u bing e ec s like bioluminescence,
luo escence and Raman sca e ing a e p esen ed.
Since UOWC does no only ake place du ing da k nigh s o in la ge wa e dep hs, in e e ing
ambien ligh due o sola i adiance mus be conside ed. The challenges he e a ise om he b oad
spec um, compa a i ely la ge in ensi ies, a a iable s uc u e, and a dis inc di ec ionali y.

42 Chap e 2 Fundamen als
Chap e 3
Examina ion and Op imiza ion o Selec ed
UOWC Sys em Componen s
3.1 In luencing Fac o s o he LED Wa eleng h Selec ion
In he ield o he UOWC, he choice o he ope a ing wa eleng h o colo is commonly based on
wo eali ies: he leas a enua ion window o seawa e lies in he blue o g een colo a ea and
wi hin his ange blue LEDs a e he mos e icien . The sho wa eleng h egion on he le side
o he leas a enua ion window was examined by [136], whe e he applica ion o nea ul a iole
(NUV) LED sou ces has been p oposed o UOWC. The sola i adiance dec eases in his UV ange
compa ed o he isible spec al ange, hus leading o a highe ole ance o dayligh , wi h he
disad an age o inc eased abso p ion by he wa e . In [144] he op imum wa eleng h o UOWC
in highly u bid habou wa e has been expe imen ally in es iga ed. Red LED ligh u ned ou
o be he bes choice unde such ex eme condi ions. The ed ligh is also subjec o a e y s ong
a enua ion, which only allowed e y low anges.
In ou own publica ion [35] he po en ial o using con e ed g een LEDs in coas al wa e s was
examined. Based on his wo k, he ollowing sec ion akes a b oade look a his opic. The
ques ion o he op imal LED wa eleng h does no always o e a simple answe , he e o e his
makes i necessa y o ake a close look a he ele an aspec s. In he case o UOWC, he goal
can be desc ibed as ollows: he elec ical powe used on he ansmi e side should gene a e as
much cu en as possible in he de ec o on he ecei e side, a e he medium has been passed. In
he ollowing, he elec ical and physical cha ac e is ics o he LED sou ce, he medium wa e and
he pho ode ec o a e p esen ed in mo e de ail. Subsequen ly, he wa eleng h-dependen h ee old
ela ionship o e iciency, esponsi i y, and a enua ion is p o ided as a con ex .
3.1.1 P opaga ion Window in Na u al Wa e s
The spec al cha ac e is ic o ligh a enua ion o di e en seawa e ypes (Je lo wa e ypes)
is ypically gi en in ables o loga i hmic scaled g aphics, c . [102] and Sec ion 2.2.2. Besides
he di e en wa e ypes and he wa eleng h, he s uc u e o he inciden ligh mus be aken
in o accoun . O he h ee pa ame e s no mally a ailable, he a enua ion coe icien cis alid o
collima ed beams, he di use a enua ion coe icien Kdis ela ed o di use downwelling sunligh ,
and he abso p ion coe icien ais independen om he ligh s uc u e. O cou se he ques ion
a ises, which exponen ial coe icien should be applied o ex inc ion calcula ions o LED-based
unde wa e sys ems. Depending on he ype and he op ics used, LEDs exhibi beam angles
anging om a ew deg ees o mo e han a hund ed deg ees, as well as di e en pa e ns o
in ensi y dis ibu ions. As poin sou ces LEDs a e essen ially no di use, bu a he mo e o
less di ec ed, al hough no s ongly collima ed like a lase beam. The e o e, a i s i can be
s a ed ha he beam a enua ion c ep esen s he uppe bound o he exponen ial coe icien , and
he abso p ion ais he lowe limi . The use o he in e jacen alue Kdcan only ep esen a
comp omise o LED u iliza ion unde wa e , and an indi idual sys em ela ed alue Ksys would
be mo e accu a e. Simula ions a e he bes way o illus a e he impac o applying he di e en
ex inc ion coe icien s. The esul s acco ding o (2.17) o he i adiance a he ecei e o one
44 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
oceanic and one coas al wa e ype each, a wo wa eleng hs and he same ini ial op ical powe and
wi hou inclina ion, a e shown in Figs. 3.1 and 3.2. The pa ame e s used a e gi en in Tables C.1
and C.2, which can be ound in he appendix.
In o de o ob ain he anges o leas a enua ion o he di e en wa e and ex inc ion coe i-
cien s, i is necessa y o e alua e he co esponding able alues and he g aphs gene a ed om
hem, c . Figs. 2.32 and 2.33. A combined ep esen a ion o hese a enua ion minimum a eas is
con ained in Fig. 3.3, based on a wo-sided ma gin o 20 %. The change in bene icial wa eleng h
om blue in clea oceanic wa e s o cyan and u he o g een in in e media e coas al wa e s
is con i med. Fu he mo e i can be obse ed om he p og ession, ha in e y u bid coas al
wa e s yellow is ge ing he mos ad an ageous colo . An imagined con inua ion o he end o
e en mo e u bid wa e s, as ound in habou s o lakes, indica es wa eleng hs e en in he o ange
o ed egime o be sui able.
0 5 10 15 20
10-4
10-3
10-2
10-1
100
Dis ance [m]
I adiance [W/m2]
Je lo wa e ype
oceanic 1B
475 nm
ex inc ion
a (abso p ion)
Kd (di use)
c (beam)
550 nm
ex inc ion
a (abso p ion)
Kd (di use)
c (beam)
Figu e 3.1: Simula ed i adiances a he ecei e o oceanic wa e . Calcula ion o
wo sou ce wa eleng hs and di e en ex inc ion coe icien s and o he wise
equal sou ce cha ac e is ics. De ailed pa ame e s a e gi en in Tables C.1
and C.2.
3.1 In luencing Fac o s o he LED Wa eleng h Selec ion 45
0 5 10 15 20
10-8
10-7
10-6
10-5
10-4
10-3
10-2
10-1
100
Dis ance [m]
I adiance [W/m2]
Je lo wa e ype
coas al 3C
475 nm
ex inc ion
a (abso p ion)
Kd (di use)
c (beam)
550 nm
ex inc ion
a (abso p ion)
Kd (di use)
c (beam)
Figu e 3.2: Simula ed i adiances a he ecei e o coas al wa e . Calcula ion o
wo sou ce wa eleng hs and di e en ex inc ion coe icien s and o he wise
equal sou ce cha ac e is ics. De ailed pa ame e s a e gi en in Tables C.1
and C.2.
52 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
Table 3.2: Achie able dis ances a a pho ocu en o 10 nA o wo wa e ypes.
Wa eleng h, LED colo Je lo 1B, oceanic Je lo 3C, coas al
Dis ance Dis ance
[m] [m]
450 nm, deep blue 21.3 8.31
475 nm, blue 19.1 8.92
500 nm, cyan 16.3 9.07
520 nm, g een 14.9 9.24
515 nm, con . g een 18.4 11.1
Table 3.3: A ainable pho ocu en s and a ios a 8 m dis ance in coas al wa e and
16 m dis ance in oceanic wa e .
Wa eleng h, LED colo Je lo 1B, oceanic Je lo 3C, coas al
Pho ocu en Pho ocu en
[nA] [nA]
450 nm, deep blue 21.8 ( 0.0 dB) 11.9 ( 0.0 dB)
475 nm, blue 15.8 (-2.8 dB) 15.6 (+2.4 dB)
500 nm, cyan 10.5 (-6.4 dB) 15.9 (+2.5 dB)
520 nm, g een 8.18 (-8.5 dB) 16.9 (+3.0 dB)
515 nm, con . g een 15.3 (-3.1 dB) 35.7 (+9.5 dB)
Assuming ha a signal cu en o 10 nA p o ides a necessa y dis ance om he noise loo
and hus a su icien SNR can be achie ed, he anges a ainable by he a ious LEDs can be
de e mined om he diag ams. Likewise, he pho ocu en s achie able by he di e en LEDs can
be ex ac ed o a ce ain dis ance, e.g., o 8 m in coas al wa e and 16 m in oceanic wa e . Based
on his a compa ison in decibels can be made. Tables 3.2 and 3.3 show he esul s.
The uppe diag am o oceanic wa e con i ms he expec a ion ha deep blue is he mos
a o able colo o longe dis ances in his wa e , due o he high wall-plug e iciency o he deep
blue LED and he low a enua ion a his wa eleng h, despi e he compa a i ely low esponsi i y.
A change o colo s om blue o cyan and g een leads o inc easing de e io a ion. The con e ed
g een a ian gi es be e esul s han he g een bu is wo se han he blue a g ea e dis ances.
In he case o he con e ed g een LED, an o e es ima ion is e iden i i is no simula ed in
spec ally spli powe .
In coas al wa e , he expec a ions a e di e en , as he con e ed g een LED is assumed o be he
mos a o able e sion ela ed o in ensi y, since he a enua ion is lowes and he esponsi i y is
highes in his wa eleng h a ea and he wall-plug e iciency also show high alues. Despi e he low
wall-plug e iciency o he di ec -colo g een LED, i pe o ms second bes a longe dis ances in
he impo an a ea, o he igh o he in e sec ion poin , c . Fig. 3.9. Al hough he pe o mance
is signi ican ly lowe han ha o he con e ed g een e sion, he blue colo s a e s ill sligh ly
below he non-con e ed g een. In e ms o in ensi y, he con e ed g een LED is clea ly he mos
a o able choice o his wa e ype. The main d awback is he low elec ical bandwid h due o he
limi ed speed o he con e sion p ocess. The second d awback is he la ge op ical bandwid h, ha
is disad an ageous o na ow op ical il e ing, which in u n bene i s he noise componen in he
SNR. Fu he mo e, he na ow il e ing would bu den he e iciency ad an age. The u iliza ion o
mul iple colo s and he app op ia e il e ing is basically a simila issue o adap i e o mul iplex
sys ems.

3.1 In luencing Fac o s o he LED Wa eleng h Selec ion 53
0 5 10 15 20 25
10-9
10-8
10-7
10-6
Dis ance [m]
Pho ocu en [A]
▶︎
▶︎
▶︎
▶︎
Je lo wa e ype
oceanic 1B
450 nm, deep blue
475 nm, blue
500 nm, cyan
520 nm, g een
515 nm, con . g een
515 nm, con . g een
(spec al powe spli sim.)
0 2 4 6 8 10 12
10-9
10-8
10-7
10-6
Dis ance [m]
Pho ocu en [A]
▶︎
▶︎
▶︎
▶︎
Je lo wa e ype
coas al 3C
450 nm, deep blue
475 nm, blue
500 nm, cyan
520 nm, g een
515 nm, con . g een
515 nm, con . g een
(spec al powe spli sim.)
Figu e 3.9: Simula ion o h ee old ela ionship om esponsi i y, a enua ion and
adian e iciency o wo wa e ypes and i e LED colo s. The uppe
g aph depic s he achie able anges a he same pho ocu en in an oceanic
wa e , he lowe g aph depic s he ob ainable pho ocu en s a he same
dis ance in coas al wa e .
54 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
3.2 Op ical Fil e ing o Ambien Ligh Supp ession
Nowadays, subsea ope a ions u ilize ad anced senso echnology and he e o e demand sophis i-
ca ed unde wa e communica ion. In he pas , he acous ic channel was almos en i ely used in
un e he ed mobile unde wa e applica ions. The dominance is s ill unb oken, and he la ge ange
ce ainly con ibu es o his, bu a low da a a e mus be accep ed, see also Fig. 1.2. Fo well o e
a decade, a emp s ha e been ongoing o u ilize he op ical unde wa e channel complemen a y
o communica ion applica ions, p omising highe da a a es a he expense o lowe achie able
dis ances in compa ison o he acous ic echnique [13, 15].
In unde wa e scena ios, mobile ehicles play a s eadily inc easing ole. These include emo ely
ope a ed ehicles (ROVs), au onomous unde wa e ehicles (AUVs), glide s and c awle s. Po en-
ial communica ion applica ions in scien i ic and comme cial explo a ion missions can be loca ed
in all dep h anges: nea he su ace, in he mid wa e o close o he sea loo . The communica-
ion can ake place be ween ship hulls, di e s, buoys, ancho ed obse a o ies and he ull ange
o unde wa e ehicles, as depic ed in Fig. 1.1. In mos cases, ehicles will be in ol ed. Op ical
communica ion be ween ixed poin s may be concei able, bu could al e na i ely be ealized by
means o cables o ibe s. In e -swa m communica ion can be seen as he mos challenging ask.
The majo i y o he a ailable ehicles a e assigned o smalle dep h a ings. The easons o
his can be seen in he cos s and he undamen ally g ea e in e es in coas al a eas. Field es s
a e he e o e o be expec ed in he uppe zones o coas al and oceanic wa e s u ilizing mid-size
AUVs wi h a limi ed dep h a ing and payload. Apa om special ope a ions, du ing da k nigh s
o in he deep sea, unde wa e op ical communica ion sys ems a e exposed o a ce ain po ion o
ambien sunligh . As an una oidable sou ce o dis u bance in e ms o sa u a ion and noise, his
ambien ligh can es ic he se iceabili y. These unwan ed e ec s can be educed by equipping
ma ching op ical il e s o he de ec o s. Mobile applica ions gene ally equi e wide ields o
iews (FOVs) o ansmi ing and ecei ing o a oid poin ing and acking issues. To achie e
a a o ed hemisphe ical o e en sphe ical cha ac e is ic, a combina ion o mul iple o - he-shel
pa s wi h in e media e FOVs is sel -e iden [30, 155, 156, 73]. In insic hemisphe ical de ec o s o
unde wa e applica ions a e only known as pho o mul iplie ubes (PMTs) [157]. Ligh sou ces,
such as lase s and lase diodes (LD) a e mos ly used in he special case o s a iona y se ups,
because o hei na ow beam and high demands wi h espec o poin ing and acking. Due
o hei high pe o mance in e ms o speed and ange, hey play a ce ain ole in isible ligh
communica ion (VLC) and also in unde wa e communica ions [59, 49]. On he o he hand, he
speed and powe densi y o LEDs is signi ican ly lowe . They also equi e mo e op ical bandwid h,
bu p o ide a wide adia ion pa e n [65]. Ne e heless, LEDs a e conside ed o be an eligible
low cos ligh sou ce wi hou a ecen al e na i e. A e iew o he di e en pho ode ec o ypes
wi h ega d o hei spec al p ope ies and sui abili y o ambien ligh is obliga o y.
The opic o ambien ligh dis u bance in he a ea o op ical communica ion has been add essed
in [79] o he in a ed adia ion (IR) ange, and subsequen ly o VLC in [158, 159, 160]. The
assump ion o o al da kness is used in mos s udies in he ield o UOWC. To he au ho ’s bes
knowledge, he e a e only a ew s udies a ailable, which add ess he sola noise impac in UOWC
in he isible [75, 161, 162] and he ul a iole (UV) ligh ange [136, 137]. In [162, 163] wo hin
ilm il e s we e deployed o use in an UOWC sys em due o impai men o sola adia ion. The
design o hin ilm il e s o mul i colo VLC was in es iga ed in [164], albei mo e in e ms o
c oss colo in e e ence. A ecen ly published wo k on he e ec i i y o op ical il e s in UOWC
is gi en in [165]. Ano he way o op ical in e e ence supp ession by he use o an liquid c is al
display (LCD) as a il e is p esen ed in [166, 167, 168]. The in en ion o he ollowing sec ion is o
b ing sys em designe s close o he impac o ambien ligh , in o de o c ea e e icien , easible,
and e sa ile layou s.
3.2 Op ical Fil e ing o Ambien Ligh Supp ession 55
3.2.1 Unde wa e Ambien Ligh
As al eady p esen ed in Sec ion 2.2, he op ical p ope ies o na u al wa e s a e e y di e se.
The cla i y o na u al wa e s is commonly classi ied in he Je lo classi ica ion scheme, unde he
assump ion o a homogeneous e ical dis ibu ion o wa e cons i uen s wi hin he uppe mixed
laye o he sea, clea sky, and high sola al i udes. In he ollowing, he ligh ield p ope ies o
h ee widesp ead wa e ypes a e examined mo e closely o he oceanic ypes IB and III, as well
as o he coas al ype C3.
Je lo ’s classi ica ion is based on only one pa ame e : he i adiance ansmi ance in su ace
wa e . F om a compa a i ely simple dep h-p o ile measu emen o downwelling plane i adiance
Ed(z, λ), one can de e mine he di use a enua ion coe icien o downwelling i adiance:
Kd(z, λ) = −1
Ed(z, λ)·dEd(z, λ)
dz .(3.3)
The i adiance ansmi ance T(z, λ)a wa eleng h λ om he su ace o dep h z, is ela ed o
( he assumed dep h-cons an ) a enua ion coe icien Kd ia
T(z, λ) = e−Kd(λ)z.(3.4)
Kdis an appa en op ical p ope y o a wa e body ha a ies sys ema ically wi h wa eleng h
and is a he insensi i e o ex e nal en i onmen al condi ions such as sola zeni h angle a ia ions
[102]. Kdis basically he measu e o how sunligh and skyligh is a enua ed in he wa e body.
The co esponding cu es o he Je lo wa e ypes a e gi en in Fig. 2.32. Solonenko and Mobley
[102] es ima ed he undamen al inhe en op ical p ope ies, i.e., abso p ion and sca e ing coe -
icien s o he wa e cons i uen s, o all Je lo wa e ypes. These pa ame e s we e used o un
adia i e ans e simula ions wi h Hyd oligh ( e sion 5.2, Nume ical Op ics L d., De on, UK),
please e e o [87] and o Appendix C.2. The nume ical model compu es he in-wa e adiance
dis ibu ion as a unc ion o dep h and wa eleng h, and p o ides o he quan i ies like up- and
downwelling i adiances.
Fig. 3.11 shows he compu ed decline o spec al downwelling i adiance wi h wa e dep h o
he h ee wa e ypes. In hese simula ions, he sky is cloud- ee wi h he sun a a 30◦zeni h
angle (co esponding o a sun ele a ion du ing noon a summe in cen al Eu ope) and a gen le
wind b eeze o 5 m/s. Addi ional Hyd oligh simula ions we e ca ied ou wi h di e en sun zeni h
angles (30◦, 50◦, and 70◦) as well as o clea sky and o e cas a mosphe ic condi ions.
Table 3.4: Downwelling Edand upwelling Eui adiances o di e en wa e ypes and
dep hs in he spec al ange om 350 nm o 750 nm.
Je lo 1B oceanic Je lo III oceanic Je lo 3C coas al
Dep h EdEuEdEuEdEu
[m] [W/m2] [W/m2] [W/m2]
2 319 9.0 306 51 236 20
5 240 8.0 187 37 110 12
10 175 6.6 92 20 37 4.5
20 107 4.5 25 5.9 5.3 0.7
50 32 1.5 1.0 0.27 0.04 0.006
100 4.7 0.24 0.03 0.009 0.0002 n. a.
200 0.14 0.007 0.0001 n. a. n. a. n. a.
The unde wa e ligh ield and i s change wi h dep h is an impo an ac o o u he in es-
iga ions o op ical il e s. Nea he su ace, he upwelling i adiances ha e alues om a ew
56 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
1 2 5 10 20 50 100
0.01
0.1
1
10
100
Dep h [m]
Ld di use / Ld di ec
Je lo wa e ype
coas al 3C
e ical upwa ds
aligned o sun
oceanic III
e ical upwa ds
aligned o sun
oceanic 1B
e ical upwa ds
aligned o sun
Figu e 3.10: Ra io o he di use o he di ec downwelling adiances as a unc ion
o he wa e dep h o oceanic and coas al wa e , o a senso looking
e ical upwa ds o aligned di ec in o he sun. Da a we e gene a ed
wi h Hyd oligh o a speci ic wa eleng h o 450 nm, c . [36].
pe cen up o a hi d o ha o he downwelling i adiance, see also Table 3.4. Wi h inc easing
dep h, he shape o he downwelling adiance ield g adually ans o ms om being di ec ed (wi h
a adiance maximum om he sun zeni h di ec ion) o di use. Fig. 3.10 shows how he impac
o he di ec downwelling adiance blu s wi h dep h o he h ee wa e ypes and wo iewing
di ec ions. The downwelling adiance ield is mos ly di use a 2 m dep h o 3C, 5 m o III, and
20 m o IB. No ably, and as a ough guide o p ac ical es ima es, an o e cas sky educes he
downwelling i adiance o a qua e , and p o ides comple ely di use condi ions. The shi in sun
ele a ion om noon o e ening also leads o a educ ion o one qua e .
In addi ion o he ime-a e aged adiance dis ibu ion ha Hyd oligh compu es, one has o
deal wi h ex eme adiance luc ua ions due o sunligh ocusing and de ocusing o sea su ace
wa es, see also Sec ion 2.2.5. Thus, adiance luc ua ions, mainly om he di ec ion o he di ec
sun, can be a signi ican sou ce o dis u bances in shallow dep hs. This ac has o be conside ed in
UOWC ope a ions, bu is no included in simula ions. Apa om wa e-induced ligh luc ua ions
and he senso poin ing di ec in o he sun di ec ion, he senso o ien a ion acing upwa ds is
gene ally he wo s case o ambien ligh exposu e and hus he main poin o conside a ion, bu
subs an ial po ions a e also o be expec ed in he ho izon al case. In he uppe zones, ema kably
high downwelling alues o up o hund eds o wa s pe squa e me e can occu , and hus LED
gene a ed alues a e exceeded, and ambien ligh il e ing becomes impo an .
3.2 Op ical Fil e ing o Ambien Ligh Supp ession 57
350 400 450 500 550 600 650 700 750
10-6
10-5
10-4
10-3
10-2
10-1
100
101
Wa eleng h [nm]
Downwelling i adiance Ed [ W / (m2 nm)]
Je lo wa e ype
oceanic IB
dep h
2 m
5 m
10 m
20 m
50 m
100 m
200 m
350 400 450 500 550 600 650 700 750
10-6
10-5
10-4
10-3
10-2
10-1
100
101
Wa eleng h [nm]
Downwelling i adiance Ed [ W / (m2 nm)]
Je lo wa e ype
oceanic III
dep h
2 m
5 m
10 m
20 m
50 m
100 m
200 m
350 400 450 500 550 600 650 700 750
10-6
10-5
10-4
10-3
10-2
10-1
100
101
Wa eleng h [nm]
Downwelling i adiance Ed [ W / (m2 nm)]
Je lo wa e ype
coas al 3C
dep h
2 m
5 m
10 m
20 m
50 m
100 m
Figu e 3.11: Plo s show he downwelling spec al i adiance o a ious dep hs, alid
o h ee Je lo wa e ypes unde 30◦sun zeni h angle, clea skies and
5 m/s windspeed. Plo ed om he da abase gene a ed by Hyd oligh .
Mo e in o ma ion is collec ed in [36].

58 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
3.2.2 LED Based Ligh Sou ce
Based on he LED undamen als and on he wa eleng h selec ion o LEDs o UOWC, see Sec-
ions 2.1.5 and 3.1, he s udy o il e ing op ions equi es a close look a he spec al p ope ies.
As an a ea o leas a enua ion o ligh in na u al wa e s, a spec al band o wa eleng hs in he
blue o g een ange can be iden i ied. Due o hei gene ally high elec o-op ical e iciency and
speed, blue LEDs a e a sui able choice and a e equen ly used as UOWC ansmi e s [35]. Fo
u he in es iga ion deep blue LEDs in he 450 nm ange a e chosen, whe eby he esul s a e
basically ans e able o o he colo s a espec i e wa eleng hs. The spec al emission o hese
single-colo LEDs is oughly Gaussian shaped wi h a ull wid h a hal maximum (FWHM) o
ypically 15 nm o 30 nm. In luencing ac o s o he LED peak wa eleng h a e empe a u e, cu -
en and binning, which a e basically colo -depended. Bo h he ypically small nega i e cu en
g adien (in -nm/A) and he mino empe a u e g adien (in nm/K) only lead o small de i-
a ions o a mos single nanome e s, a leas unde ealis ic ope a ing condi ions. In con as
o hese ope a ing pa ame e s, he selec ion pa ame e , he so-called binning, can ha e a mo e
signi ican in luence. Gene ally, LEDs a e asso ed by he manu ac u e depending on lux and
wa eleng h alues. Fo example, o a oyal blue LED his means ou bins o g oups, anging
om 440 nm o 460 nm. Such a a ia ion o se e al o ens o nanome e s o he nominal alue can
cause p oblems in combina ion wi h na ow bandwid h op ical il e s, so a ca e ul sys em design
is ecommended.
410 420 430 440 450 460 470 480 490
0
0.2
0.4
0.6
0.8
1
Wa eleng h [nm]
Rela i e in ensi y
Lumileds
Luxeon LXZ1
oyal blue
measu ed
Simula ion
Gaussian
Logis ic
powe peak
Figu e 3.12: Cu es o measu ed and simula ed ela i e in ensi y o a deep blue LED.
Fo model unc ions, pa ame e s and measu emen in o ma ion e e o
he Sec ion C.3.
The u iliza ion o he LED adian emission also depends on he spec al co e age. Fig. 3.12
gi es he measu ed ela i e spec al emission o a deep blue LED, which is sligh ly asymmec ical.
I is compa ed o he commonly used Gaussian app oxima ion and he be e ma ching logis ic
powe peak model unc ion [169]. Due o he de ia ion in simple models, he use o measu ed
spec a is wo hy o conside a ion. To iden i y he di e ences in he shape o he spec al emission
om di e se LED colo s, no only he in ensi y can be no malized, bu also he wa eleng h, wi h
he in en ion o s e ching o equal he FWHM, c . Fig. 3.13. Fo example, he e i is shown ha
g een is mo e sui able o il e ing han yellow.
A majo issue in il e ing hese bell-shaped in ensi y dis ibu ions is e iciency o co e age. This
can be ep esen ed by combining an ideal bandpass wi h a iable ansmission ange and he
3.2 Op ical Fil e ing o Ambien Ligh Supp ession 59
same cen al wa eleng h wi h he LED. A se o such cu es is gi en in Fig. 3.14. A second se ies
(Ledengin LZ4) o ano he manu ac u e showed compa able colo - ela ed esul s. Fo example,
compa ing yellow and g een a a passband o FHWM a io o 1, esul s in 60 % and 70 % co e age,
espec i ely.
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
No malized wa eleng h
No malized in ensi y
Lumileds
Luxeon LXZ1 se ies
PR01 oyal blue
PB01 blue
PE01 cyan
PM01 g een
PL01 ambe
λCWL
FWHM
λCWL
-FWHM/2
λCWL
+FWHM/2
▶︎
▶︎
▶︎
▶︎
▶︎
Figu e 3.13: In ensi y o di e en colo ed LEDs wi hin one se ies as a unc ion o
he wa eleng h in a double no malized way. Based on measu ed and
no malized spec a o Fig. 2.13.
01234
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Ra io passband / FWHM
Rela i e spec al co e age
Lumileds
Luxeon LXZ1 se ies
PR01 oyal blue
PB01 blue
PE01 cyan
PM01 g een
PL01 ambe
Figu e 3.14: Rela i e spec al co e age as unc ion o he a io o an ideal il e s pass-
band o he LEDs FWHM o di e en colo s o a powe LED se ies
(Lumileds Z) a no mal incidence.
60 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
3.2.3 Pho ode ec o
Types and Cha ac e is ics
The ou main pho ode ec o ypes used in UOWC a e PMTs, SiPMs, APDs and PIN-PDs, and
an in oduc ion is gi en in Sec ion 2.1.5. In common, hey ha e an op ical bandwid h o se e al
hund ed nanome e s, whe e PMTs and SiPMs (depending on he a ian ) a e gene ally somewha
na owe , and PIN-PDs a e a bi wide -banded. Unde wa e , he ambien ligh ha occu s has
a dep h-dependen bandwid h o app oxima ely 350 nm o 700 nm, while he op ical bandwid h
used by he LED ansmi e is only up o a ew ens o nanome e s. In o de o p o ec he
pho ode ec o as much as possible om he in e e ing ambien ligh , an app op ia ely adap ed
bandpass il e should be used, which allows he signal componen o pass and blocks he ambien
ligh o a ce ain ex en . Fo medium ligh condi ions, ound in shallow o medium unde wa e
dep hs, la ge-a ea Si PIN-PDs and APDs can be an app op ia e choice. Fu he mo e, hey a e
cheap and obus , and ha e a low in eg a ion e o . The highe sensi i i y o e ed om he o he
ypes such as SiPMs and PMTs is no ad an ageous in hese shallow ope a ing en i onmen s, no
e en unde il e ed condi ions. Bu unde almos pe ec da kness in he deep oceans hey achie e
he highes pe o mance and la ges anges [75].
Al e na i e pho ode ec o s o he lowe pa o he isible spec um could be in gallium phos-
phide (GaP) echnology, bu hese specialized p oduc s gene ally o e lowe sensi i i ies and
highe capaci ances compa able o silicon PIN-PDs. P e-assembled PIN-PD il e combina ions
a e a e on he ma ke and a e only a ailable o specialized applica ions. In mos ins ances hey
a e il e ed o pho o-op ical ligh measu emen s by ep oducing he In e na ional Elec o echnical
Commission (IEC) cu e o human eye colo sensi i i y, o wi h a la esponse o e a wide ange
o adiome ic measu emen s.
In his sec ion, he o e laps o he wa eleng h anges o LED, PD and ambien ligh a e a
p econdi ion, howe e o he p ope ies o echnical da a o he de ec o a e no equi ed, since
only he il e placed in on is examined.
3.2.4 Op ical Bandpass Fil e s
Te minology
0.0
0.2
0.4
0.6
0.8
1.0
Wa eleng h
Rela i e ansmission
CWL
FWHM
passband
Peak ansmission
50%
Peak ansmission
Blocking ange
T ansmission ange
Blocking ange
▶︎
▶︎
▶︎
Figu e 3.15: G aphic is showing an idealized bandpass il e .
Op ical bandpass il e s a e gene ally iden i ied by hei cen e wa eleng h (CWL) and hei
bandwid h in he passing ange a 50% o he peak ansmission, deno ed as FWHM o passband
3.2 Op ical Fil e ing o Ambien Ligh Supp ession 61
wid h (PB), see Fig. 3.15. Depending on he ype, eal bandpasses can show ipples in he
dis ibu ion, smoo h ounded slopes, o side lobes.
Colo ed Glass Fil e s
Op ical il e s made o colo ed glass a e widely used due o hei simplici y, obus ness and low
p ice. The main e ec o hese il e ypes is mo e o less selec i e abso p ion in a ce ain wa e-
leng h ange [41]. As bandpass il e s a isible wa eleng hs, hese il e s show ela i ely la ge
ansmission losses and weak slopes. Fu he disad an ages can be luo escen e ec s and side
lobes, i.e. unwan ed ansmission a highe wa eleng hs, c . Fig. 3.21. Gene ally, hese il e s a e
a ailable o he shel in di e en hicknesses and in a mode a e a ie y. Types a e gene ally no
cus om-made, due o he indus ial cas ing p oduc ion in huge ba ches. A ma ke su ey o band-
pass il e s shows only an a ailabili y in he blue o g een ange. The sea ch o a il e ma ching
app oxima ely he deep blue LEDs cen e wa eleng h o 450 nm p o ides only a ew esul s. Many
p oduc s a e only compa ible wi h each o he , limi ing he numbe o disc e e ypes. Since he well
ma ching il e BG 28 o he manu ac u e Scho is un o una ely discon inued, he B440 ype
p oduced by Hoya was chosen o u he in es iga ion; please e e o Fig. 3.16 and [170]. An ap-
p ecia ed ea u e is he ela i ely low dependence o he angle o incidence (AOI), due o a slowly
inc easing e ec i e hickness a ising angles om he pe pendicula o he inciden di ec ed ligh .
The cha ac e is ic o a pa icula glass il e can be changed by he ma e ial hickness. Inc easing
i will educe he ansmission and na ow he wid h o he bandpass. P oduc ion ela ed issues
may cause sligh a ia ions in hickness and di e ences be ween glass ba ches. The quali y o he
il e ’s ansmission can gene ally be in luenced by he ligh s uc u e, such as di use o di ec ed
om a poin sou ce. The colo ed glass il e shows a ce ain obus ness agains his al e a ion.
Measu emen s con i med only a mino de ia ion o he cu e o di use condi ions compa ed o
small AOIs. Fo u he in o ma ion on measu emen s, please e e o Appendix C.4.
380 400 420 440 460 480 500 520 540
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Wa eleng h [nm]
Rela i e ansmission, ela i e in ensi y
Hoya B440
AOI=0°
AOI=15°
AOI=30°
AOI=45°
di use
Lumileds Luxeon
LXZ1 Se ies
PR01 oyal blue
Figu e 3.16: Measu ed spec al ansmission cu es o a colo ed glass bandpass il e
Hoya B440 wi h a di ec ed ligh sou ce a di e en AOIs and wi h a
di use ligh sou ce. The measu ed ela i e in ensi y dis ibu ion o a
deep blue LED o app ox. 450 nm CWL is also gi en as a illed cu e o
illus a e he o e lap.
68 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
Table 3.6: Calcula ed ambien ligh supp ession o he ou di e en il e s in h ee
exempla y wa e ypes a a ying dep hs, up o meaning ul emaining ligh
alues. Gene ally calcula ed wi h il e cha ac e is ics o di use ligh , wi h
he excep ion o e y shallow wa e o 2 m o 5 m dep hs in he clea wa e
ype IB. He e he cha ac e is ics o he domina ing di ec ed ligh we e used
o hin ilm il e (AOI = 15◦), please e e o Fig. 3.10. Values o he hin
ilm il e s in wa e ype IB a a dep h o 10 m we e no calcula ed, since
he il e cha ac e is ic ei he o di use o di ec ed ligh we e applicable.
Wa e ype Dep h Colo ed glass Thin ilm Thin ilm Thin ilm
Hoya Tho labs Tho labs Sem ock
B440 450-10 450-40 457-50
Je lo 1B 2 m -8.53 dB -14.21 dB -9.05 dB -6.87 dB
5 m -7.75 dB -13.38 dB -8.22 dB -7.05 dB
10 m -7.14 dB n.a n.a n.a.
20 m -6.54 dB -12.98 dB -8.55 dB -6.40 dB
50 m -5.74 dB -12.11 dB -7.61 dB -5.40 dB
100 m -5.31 dB -11.76 dB -7.15 dB -4.82 dB
200 m -5.23 dB -12.09 dB -7.29 dB -4.64 dB
Je lo III 2 m -8.47 dB -14.90 dB -10.62 dB -8.47 dB
5 m -7.85 dB -14.31 dB -9.96 dB -7.77 dB
10 m -7.47 dB -13.99 dB -9.56 dB -7.31 dB
20 m -7.28 dB -13.99 dB -9.45 dB -7.03 dB
50 m -6.22 dB -12.92 dB -8.40 dB -5.88 dB
100 m -6.58 dB -14.57 dB -9.51 dB -6.38 dB
Je lo 3C 2 m -9.51 dB -15.89 dB -11.64 dB -9.36 dB
5 m -10.10 dB -16.83 dB -12.49 dB -9.92 dB
10 m -11.40 dB -19.07 dB -14.73 dB -11.56 dB
20 m -13.70 dB -22.79 dB -19.43 dB -14.98 dB
50 m -13.99 dB -24.25 dB -22.64 dB -16.30 dB
The analysis o Tables 3.5 and 3.6 and o he Figs. 3.23 and 3.24 shows ha he colo ed glass
il e o e s he lowes OSNR gain, bu also he smalles AOI dependence. The e ec i eness may
no be so high - bu compa ed o a con igu a ion wi hou a il e , i is a ac i e, as well as obus
and cheap, and will hus will be used in many cases. As demons a ed, he na owes es ed
hin ilm Tho labs 450-10 il e shows he bes OSNR o small AOIs, bu d ops o o la ge
AOIs. The hin ilm il e Sem ock 457-50, which has a wide passband and some shi ma gin,
pe o ms a a mo e balanced le el hus ep esen s he bes choice o he es ed componen s. The
a enua ion o he LEDs signal is low, wi h a simul aneous ole ance o la ge AOIs. This esul
would allow ene gy e icien applica ions wi h 60◦FOV wi h compa a i ely high imp o emen
o he OSNR, compa ed o a colo ed glass il e . This is impo an , since in many p ac ical
si ua ions he ambien ligh will be signi ican ly less, such as o o e cas , pe iods ou side o high
sun, ho izon al o downwa ds looking senso s and la ge ope a ion dep hs.

3.2 Op ical Fil e ing o Ambien Ligh Supp ession 69
0 15 30 45
-6
-4
-2
0
2
4
6
8
10
12
14
16
AOI [°]
OSNR gain [dB]
Colo ed glass il e
Hoya B440
Je lo wa e ype 3C
Dep h
2 m
10 m
Je lo wa e ype III
Dep h
2 m
10 m
Je lo wa e ype 1B
Dep h
2 m
20 m
0 15 30 45
-6
-4
-2
0
2
4
6
8
10
12
14
16
AOI [°]
OSNR gain [dB]
Thin ilm il e
Tho labs 450-10
Je lo wa e ype 3C
Dep h
2 m
10 m
Je lo wa e ype III
Dep h
2 m
10 m
Je lo wa e ype 1B
Dep h
2 m
20 m
Figu e 3.23: Gain in OSNR due o u iliza ion o a colo ed glass and a na ow band hin
ilm il e in di e en wa e s and dep hs o a ying angles o incidence.
0 15 30 45
-6
-4
-2
0
2
4
6
8
10
12
14
16
AOI [°]
OSNR gain [dB]
Thin ilm il e
Tho labs 450-40
Je lo wa e ype 3C
Dep h
2 m
10 m
Je lo wa e ype III
Dep h
2 m
10 m
Je lo wa e ype 1B
Dep h
2 m
20 m
0 15 30 45
-6
-4
-2
0
2
4
6
8
10
12
14
16
AOI [°]
OSNR gain [dB]
Thin ilm il e
Sem ock 457-50
Je lo wa e ype 3C
Dep h
2 m
10 m
Je lo wa e ype III
Dep h
2 m
10 m
Je lo wa e ype 1B
Dep h
2 m
20 m
Figu e 3.24: Gain in OSNR due o u iliza ion o wo hin ilm il e o in e media e
passband wid h in di e en wa e s and dep hs o a ying angles o inci-
dence.
70 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
A emp o Gene aliza ion
Due o he limi ed a ailabili y o hin ilm il e s wi h di e en passband wid hs (PB) o he same
cen e -wa eleng h om s ocks, only a small selec ion o il e s was accessible o es ing pu poses.
In addi ion, he il e s exhibi di e en quali ies in e ms o maximum ansmission, edge s eepness
and oundings. This allows ce ain basic p inciples o be iden i ied, bu no op imiza ions can be
de i ed. The e a e basically wo ques ions ha a ise om he abo e issue. The i s is how
he beha io changes by adding di e en shi ma gins (SM). The second is he ques ion o an
op imum in e ms o OSNR as a unc ion o he a io o he il e passband wid h o he LED
FWHM. To answe hese ques ions, simula ions a e bes sui ed.
Fo his pu pose, he p ope ies and beha io o he hin ilm il e mus be ep esen ed in a
model. Fo he case o di ec ed ligh impac ing pe pendicula o he il e ’s and he PD’s su ace,
as well as he ac ha eal il e ansmissions can each alue o close o 1, his is leading o:
T(λ) = 1 o λPBlowe ≤λ≤λPBuppe ,else T(λ)=0 (3.10)
wi h
λPBlowe =λPBcen e −PB
2;λPBuppe =λPBcen e +PB
2.(3.11)
The applica ion o his hin ilm il e model o he spec al co e age o an LED, including he
shi ma gin is shown in Fig. 3.25 o be e cla i ica ion.
0.0
0.2
0.4
0.6
0.8
1.0
Rela i e in ensi y
Rela i e ansmission
LED
Thin ilm il e
AOI=0°
spec al
Co e age
λCWL
Wa eleng h
λPBcen e
SM
mo ing di ec ion
inc easing AOI
▶︎
▶︎
▶︎
▶︎
▶︎
Figu e 3.25: Spec al co e age o an LED om idealized hin ilm il e including he
shi ma gin.
The base o he model o he beha io o he hin ilm il e unde di use ligh condi ions
consis s o wo pa s. The i s pa a e he au ho ’s own spec al measu emen s o he a ailable
il e s by u ilizing a di uso shee , and he second pa a e ansmission simula ions o a ious
il e s o di e en passband wid hs unde la ge cone angles, see Sec ion 3.2.4 and Appendix C.4.
This yields he ollowing model, and Fig. 3.26 shows he in e ela ionships g aphically:
T(λ) = 0 o λ<λdi lowe (3.12)
T(λ)=0.2 + 0.2·PB
FWHMLED ·(λ−λdi lowe )
(λdi cen e −λdi lowe ) o λdi lowe ≤λ≤λdi cen e (3.13)
T(λ)=0.2 + 0.2·PB
FWHMLED ·(λ−λdi uppe )
(λdi cen e −λdi uppe ) o λdi cen e ≤λ≤λdi uppe (3.14)
T(λ) = 0 o λ>λdi uppe .(3.15)
The model desc ibed in (3.12) o (3.15) is alid o a ios o he il e passband PB o he LED
op ical bandwi h FWHMLED o 0.2 o 4, and same cen e wa eleng hs λCWL o he LED and
3.2 Op ical Fil e ing o Ambien Ligh Supp ession 71
0.0
0.2
0.4
0.6
0.8
1.0
Eamb [W/m2]
LED
column_1
Rela i e in ensi y
λCWL
FWHM
Wa eleng h
LED
▶︎
▶︎
0.0
0.2
0.4
0.6
0.8
1.0
Eamb [W/m2]
ideal
column_1
Rela i e T ansmission
ideal
PB
Wa eleng h
λPBlowe
λPBcen e
λPBuppe
Thin ilm il e
(di ec ed)
▶︎
▶︎
▶︎
▶︎
0.0
0.2
0.4
0.6
0.8
1.0
Rela i e T ansmission
Wa eleng h
λdi lowe
λdi uppe
λdi cen e
Thin ilm il e
Tdi peak
model
(di use)
▶︎
▶︎
▶︎
▶︎
Figu e 3.26: Modeling o he hin ilm il e s ansmission o di use inciden ligh .
Example shows he il e ’s passband being wo imes he FWHM o he
LED.
λPBcen e o he il e . These alues also ep esen he gi en ones. The signi ican wa eleng hs o
he di use ansmission cu e a e gi en by:
λdi uppe =λPBuppe ;λdi cen e =λPBlowe ;λdi lowe = 0.9·λPBlowe .(3.16)
The ac o o 0.9 in (3.16) esul s om (3.5) a an e ec i e e ac ion index o 2 and an AOI o
60◦. The model does no ake in o accoun he sligh asymme y o he spec al in ensi y cou se
o he LED, so he peak is cen e ed wi hin he op ical bandwid h.
A e in oducing he modeling, his sec ion hen goes back o he i s ques ion o he shi
ma gins e ec . The SM deno es he amoun o shi o he il e cen e wa eleng h λPBcen e
compa ed o he LED cen e λCWL owa ds highe wa eleng hs, o compensa e o he AOI ela ed
shi in di ec ion o lowe wa eleng hs. The esul o se e al simula ions comp ising di e en
passband wid hs as well as shi ma gins is gi en in Fig. 3.27. In o de o ep esen a middle case
as a as possible, he LED chosen o simula ion is Luxeon Z se ies blue, due o an in e media e
spec al cou se wi hin colo s o he se ies, c . Fig. 3.13. Likewise, a il e wi h an in e media e
e ec i e index o e ac ion o 2 is selec ed. The ela i e spec al co e age is ep esen ed by he
uppe e m o (3.8). The calcula ion is done by summa ion o disc e e elemen s wi h 1 nm wid h.
The cu es shown indica e he ollowing ela ionships. In p inciple, la ge AOI can be achie ed
by inse ing some shi ma gin, bu a he expense o ansmission alues wi h small AOIs. This
is mo e p onounced wi h na owband il e s. The simula ion is based on ideal il e shapes o all
AOIs, bu in eali y hese deg ade wi h inc easing AOI. This is mo e dis inc i e o na owband
and simple designs, and many high-quali y il e s can hold he shape well up o 30◦. The e ec
72 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
o his deg ada ion is a smalle spec al co e age. All in all, applying a shi ma gin is a use ul
me hod o educe he e ec s o iewing angle dependency, bu o e doing can be coun e p oduc i e.
0 10 20 30 40 50
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
AOI [°]
Rela i e spec al co e age
PB = 2.0 · FWHMLED
SM = +2% o λCWL
SM = +1% o λCWL
SM = none
PB = 1.5 · FWHMLED
SM = +2% o λCWL
SM = +1% o λCWL
SM = none
PB = 1.0 · FWHMLED
SM = +2% o λCWL
SM = +1% o λCWL
SM = none
PB = 0.5 · FWHMLED
SM = +2% o λCWL
SM = +1% o λCWL
SM = none
Passband wid h (PB)
Shi ma gin (SM)
Figu e 3.27: Rela i e spec al co e age as a unc ion o he angle o incidence o ideal
il e s wi h di e en passband wid hs and di e en added wa eleng h shi
ma gins, bo h using ealis ic scales.
The second open ques ion is ela ed o a possible op imum in e ms o OSNR by a ia ion o he
il e s passband wid h. The ollowing condi ions a e applied o he simula ion: upwa ds looking
senso , pe pendicula incidence, LED ype Lumileds Z oyal blue wi h a λCWL o 448 nm and a
FWHM o 17.4 nm, equal il e passband cen e and LED cen e wa eleng h, and ambien ligh
condi ions gi en as downwelling i adiance wi hin a bandwid h o 350 nm o 750 nm, see Fig. 3.11.
A simula ion ange o he P BFil e o FWHMLED a io om 0.2 o 4 esul s in il e passbands
om 3.5 nm o 70 nm.
The uppe diag am in Fig. 3.28 gi es he simula ed supp ession o he LED ligh by he il e ,
u ilizing he di ec ligh il e model o (3.10) and he le e m o (3.9). This co esponds in
p inciple o he non-loga i hmic e sion in Fig. 3.14. Fo he calcula ion o he ambien ligh
supp ession o he oceanic Je lo IB wa e a a dep h o 2 m, he di ec il e ligh model and he
igh e m o (3.9) needs o be applied. Di use ambien ligh si ua ions a e ound in he emaining
wa e ypes and dep hs, such as Je lo IB 20 m, III and 3C. The di use il e model as gi en in
(3.12) o (3.15) needs o be used he e, as well as he igh e m o (3.9) again.
The lowe diag am in Fig. 3.28 depic s he combina ion o he signal componen supp ession and
ambien ligh supp ession by he hin ilm il e . In addi ion o he simula ed cu es, calcula ed
poin s om h ee eal il e s (based on measu ed ansmission alues) a e gi en o compa ison, c .
Fig. 3.18. Fo he p edominan ly occu ing di use ambien ligh si ua ion unde wa e , an OSNR
gain maximum esul s a a a io o he il e ’s passband o he LED FWHM o app oxima ely 1.
In he case o di ec ional ambien ligh , small a ios p o ide be e OSNR gain alues.
3.2 Op ical Fil e ing o Ambien Ligh Supp ession 73
0.2 0.5 1 2
-25
-20
-15
-10
-5
0
Ra io PBFil e / FWHMLED
Supp ession [dB]
Lumileds Z oyal blue
LED
Je lo wa e ype 1B
Dep h
2 m (di ec )
20 m (di use)
Je lo wa e ype III
Dep h
2 m (di use)
10 m (di use)
Je lo wa e ype 3C
Dep h
2 m (di use)
10 m (di use)
Thin ilm il e
(Dep h 2m)
□ Tho labs 450-10
◇ Tho labs 450-40
○ Sem ock 457-50
4
0.2 0.5 1 2
5
10
15
20
Ra io PBFil e / FWHMLED
OSNR gain [dB]
Je lo wa e ype 1B
Dep h
2 m
20 m
Je lo wa e ype III
Dep h
2 m
10 m
Je lo wa e ype 3C
Dep h
2 m
10 m
Thin ilm il e
(Dep h 2m)
□ Tho labs 450-10
◇ Tho labs 450-40
○ Sem ock 457-50
4
Figu e 3.28: The uppe diag am depic s he supp ession o ambien ligh by a modeled
ideal il e o di e en wa e ypes and dep hs, as well as he esidual
powe o he LED a e il e ing. The combina ion o bo h is gi en in
he lowe diag am, which co esponds o he del a in OSNR o hese
ci cums ances. Added calcula ed poin s based on measu ed il e cu es
a e shown o h ee eal hin ilm il e s.

74 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
3.3 Noise Sou ces and Noise P ope ies
3.3.1 F om Op ical o Elec ical SNR
The op ical signal o noise a io (OSNR) is gi en in (3.7) as he a io o signal o ambien i adiance
o powe . This a io can be imp o ed by il e ing, bu his imp o emen o gain canno be di ec ly
applied o he elec ical domain. The signal- o-noise a io (SNR) in he elec ical domain is gi en
as he a io o a e age ecei ed powe o he a e age noise powe a he same posi ion wi hin he
chain [39]:
SNR=
PRel
NRel
.(3.17)
A compa ison o he nume a o s and denomina o s o (3.7) and (3.17) shows why a di ec ans e
om OSNR o he elec ical SNR b eaks, which is also indica ed by (2.21).
The pho ode ec o canno dis inguish be ween wan ed signal ligh and unwan ed ambien ligh ,
and all inciden ligh will be ans e ed in o an elec ical cu en by he esponsi i y R. Gene ally,
he e a e di e en p opo ionali ies o he ecei ed powe s PRop and PRel in hei domains. In
he op ical PRop is p opo ional o he de ec o ’s e ec i e a ea Ae , in he elec ical domain PRel
is p opo ional o Ae 2. The a io o hese wo powe s is u he dependen on he signal shape,
which is desc ibed by he shaping gain ac o κ, c . Sec ion 2.1.6.
The denomina o consis s o s a is ically independen he mal and sho noise:
NRel =Nsho +N he m.(3.18)
Bo h o hese componen s can be dominan in UOWC, o example he he mal noise in a deep
da k en i onmen , and he sho noise unde ambien ligh condi ions.
A bina y in ensi y modula ion con ains wo signal s a es, H and L, which in he simple common
case co espond o op ical powe on and o , espec i ely. Ex ac ing he minimum equi ed SNR
o he mos common NRZ-OOK modula ion scheme om Table 2.3, esul s in a alue o 13.5 dB
o an ambi ious BER alue o 10−6, and a shaping gain ac o o 2. This SNR is based on signal
and noise a e ages, in simula ions bo h s a es a e conside ed sepa a ely in mos cases, he mo e
ele an s a e is gene ally wi h he signal se a peak powe . In he case o a dominan signal
independen noise ( he mal) and a κ alue o 2 his leads o a 3 dB inc ease in SNR, gi ing a o al
o 16.5 dB o he ON s a e. In he o he case o dominan signal dependen noise (sho ) he a io
s ays a 13.5 dB. Modula ion schemes o highe powe e iciency like 4-PPM, o lowe BER alues
a e equi ing less SNR. Gene ally, he SNR alues a e seen as minimum equi emen s. Thus, an
a e age SNR alue o 15 dB ep esen s he equi emen unde he condi ions men ioned, and is
he e o e used as a base o he ollowing in es iga ions.
3.3.2 TIA Ampli ica ion
A basic desc ip ion o he PD and TIA, as well as some basic o mulas o calcula ions, a e gi en
in Sec ion 2.1.5. Addi ional ela ionships equi ed o mo e in-dep h in es iga ions a e p o ided
in he ollowing sec ion. The elec ical on end o he ecei e in UOWC no mally consis s o
he PD i sel and a one-s age low-noise wideband p eampli ie in a ansimpedance con igu a ion,
as gi en in Fig. 3.29. The dynamic ange is limi ed by noise wi h small signals on he low side,
and by sa u a ion on he high side, due o ambien ligh o e en e y la ge signals.
Two opologies in he TIA s age a e common: he pho o ol aic and he pho oconduc i e mode,
espec i ely. In he pho o ol aic mode, he PD anode is g ounded, and he e e se ol age UR
is he eby ze o. Co espondingly, he PD is i ually sho -ci cui ed by he OpAmp. A possible
posi i e impac on he da knoise con ibu ion can p omo e high sensi i i y applica ions. In he
pho oconduc i e mode, URis >0, which leads o a junc ion capaci ance educ ion because he
e ec i e gap inc eases be ween he di e en ly doped semiconduc o laye s. Typically achie able
3.3 Noise Sou ces and Noise P ope ies 75
OpAmp
R
-
+
C
Uou
UR
-
PD
Ri
CD
E
E
sig
amb
I = I + I
PD sig amb
Figu e 3.29: One-s age TIA u ilized o PIN-PD o APD. The disc e e de ices R and
C a e he eedback esis o and he eedback capaci o , espec i ely. The
PD junc ion capaci ance is symbolized by CD, he shun esis ance by Ri.
capaci y educ ions a e in he ange o a ac o 2 o 10. Since he capaci ance is he gene ally
limi ing ac o o he speed o he bandwid h, his educ ion plays a big ole in mos applica ions.
APDs mus always be ope a ed wi h a high e e se ol age, o he wise he a alanche e ec will no
occu . Howe e , due o he in e nal gain, only smalle a eas a e usually equi ed, which means
ha he esul ing capaci ies a e smalle . Mo e de ailed in o ma ion abou he ansimpedance
ampli ie (TIA) and o he ci cui con igu a ions can be ound in [79, 177]. Calcula ions and
simula ions o TIA can be conduc ed wi h [74, 178].
The i adia ion eaching he PD ep esen s a supe posi ion o he signal and ambien compo-
nen s, which di e spec ally bu also empo ally. The signal pa consis s in mos cases o as
bina y o s ep in ensi y changes, and he ambien pa is usually a cons an amoun wi h ela i ely
slow changes. The ou pu ol age Uou is acco dingly de e mined by he sum o he espec i e
cu en s Isig and Iamb gene a ed by he PD and he eedback esis o R :
Uou =Usig +Uamb = (Isig +Iamb)·R .(3.19)
The espec i e ol age componen s Usig and Uamb can also be exp essed by he co esponding
i adiances Esig and Eamb and he PD pa ame e esponsi i y R, gain Gand de ec o a ea Ade :
Usig =R·G·Ade ·Esig ·R (3.20)
Uamb =R·G·Ade ·Eamb ·R .(3.21)
The SNR in decibels is gi en by he ollowing equa ion, whe e Un_sum ep esen s he sum o he
noise om di e en sou ces:
SNR = 20 ·logUsig
Un_sum [dB].(3.22)
The achie able cu -o equency o he TIA s age is gi en by:
−3dB =sGBW
2π·R ·(CD+C ).(3.23)
The gain bandwid h p oduc GBW is a cha ac e is ic alue o he ampli ie used. CDis he PD
junc ion capaci ance, and R and C a e he componen s dimensioned acco ding o he desi ed
ampli ica ion and quali y o o e shoo in he pulse esponse beha io . A equi ed GBW can be
app oxima ed by:
GBW ≈ 2
−3dB ·2π·R ·CD.(3.24)
76 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
3.3.3 Noise Sou ces
Wi h espec o he achie able communica ion speed and bi e o a es o an UOWC sys em, he
signal- o-noise a io (SNR) is he mos ele an pa ame e . The signal powe in LED-d i en and
ba e y-supplied sys ems is limi ed and also a enua ed geome ically and exponen ially by he
wa e wi h inc easing dis ance.
This implies special a en ion o he noise, o which se e al sou ces can be iden i ied. A clea
dominan ole canno be assigned o one ype o noise, as i depends on many en i onmen al
condi ions and componen pa ame e s. The examina ion o he noise should always ake place a
he same posi ion wi hin he chain o ci cui , he e he espec i e ol ages a he ou pu ac oss
he esis o R a e used. O cou se he espec i e cu en s can also be e alua ed as well as he
powe s, which a e hen e e ed o as noise equi alen powe (NEP) [161, 179]. The o mulas in
he ollowing a e alid o PIN-PDs, and la e hey will be ex ended o include APDs.
The Johnson o he mal noise, which is caused by he he mal agi a ion o cha ge ca ie s
(elec ons o holes) in a conduc o , is p esen in all passi e esis i e elemen s. The he mal noise
o he eedback esis o R exp essed as a ol age Un_ h is gi en in (3.25), whe e Tis he absolu e
empe a u e in Kel in, kB=1.38 10−23 Ws/K is he Bol zmann cons an , and NBW is he ela ed
noise bandwid h. The noise con ibu ions o he op-amp i sel a e ep esen ed by he ol age
noise densi y enin nV/√Hz, whe eby en ep esen s he he mal noise o he in e nal esis o s.
The espec i e ol age Un_enis gi en in (3.26). The he mal noise con ibu ion o Rican be
neglec ed due o ypically e y high alues whe e Ri>> R .
Un_ h =s4·kB·T·NBW
R ·R =p4·kB·T·R ·NBW (3.25)
Un_en=en·qNBWen(3.26)
Sho noise is caused by he andom luc ua ion o he numbe o pho ons hi ing he PD su ace
and gene a ing cha ge ca ie pai s, and his o m is known as quan um sho noise. The elec onic
sho noise is based on cha ge ca ie s c ossing a po en ial ba ie in p-n junc ions. Wi h a pho o-
diode, in gene al he wo ypes canno be dis ingushed and ollow a Poisson dis ibu ion, and he
desc ip i e equa ion is he same o bo h [3, 39]. Sho noise will be gene a ed in he pho ode ec o
by i s da k cu en Id, and he cu en s induced by he ambien and he signal inciden ligh , Iamb
and Isig, espec i ely. The co esponding noise ol ages a e gi en by (3.27) o (3.29), whe e he
elemen a y cha ge is e0=1.60 10−19 As. The sho noise o he ampli ie inpu bias cu en s is gi en
by he cu en noise densi y inin pA/√Hz. The espec i e ol age Un_inis gi en in (3.30).
Un_sho _da k =p2·e0·Id·NBW ·R (3.27)
Un_sho _amb =p2·e0·Iamb ·NBW ·R (3.28)
Un_sho _sig =q2·e0·Isig ·NBW ·R (3.29)
Un_in=in·√NBW ·R (3.30)
The mal and sho noise a e so-called whi e noise. They a e spec ally la , and show a cons an
magni ude o powe o e he equency. O he noise sou ces can gene ally be iden i ied, bu a e
no aken in o accoun he e due o hei mino na u e. Fo example noise due o impe ec ions in
he semiconduc o ma e ial, which shows 1/ cha ac e and is called pink noise [177].
The noise bandwid h NBW limi s he e ec i e ange o a whi e noise p ocess. The equi alen
noise bandwid h is seen as a so-called "b ick-wall" il e , which eplaces he in eg a ion o e all
3.3 Noise Sou ces and Noise P ope ies 77
equencies o he ans e unc ion. The NBW depends on he cu -o - equency and he quali y
ac o Q, which desc ibes he slope in he equency ans e unc ion and he shape in he pulse
esponse. Fo he common case o a maximal la esponse he Qis 0.7, which leads o a NBW
o he cu -o - equency −3dB mul iplied by 1.1. The NBW, alid o mos con ibu ions, can be
calcula ed as ollows:
NBW =π
2·Q·sGBW
2π·R ·(CD+C ).(3.31)
An excep ion is he NBWeno he ol age noise densi y con ibu ion, which is la ge due o gain
peaking in he equency dependen noise gain p o ile. I can be app oxima ed by:
NBWen≈NBW ·GBW ·2π·(R kRi)·(CD+C ).(3.32)
To calcula e he sum Un_sum o he di e en unco ela ed noise ol ages, hey need o be added
as oo -sum-o -squa es:
Un_sum =qUn_ h2+Un_sho _da k2+Un_sho _amb2+Un_sho _sig2+Un_in
2+Un_en
2.(3.33)
A alanche pho odiodes a e cha ac e ized by an in e nal gain Gand addi ional noise compa ed o
he PIN-PDs. Excess noise is added du ing he in e nal mul iplica ion p ocess, ep esen ed by
he excess noise ac o F, which is gain and wa eleng h dependen . In mos cases da a shee s
only speci y o one wa eleng h, and u he alues need o be eques ed om he manu ac u e .
Mo e in o ma ion on he APDs noise calcula ion can be ob ained in [68, 180]. Fo o he han he
e e enced gain in he da a shee , an app oxima ion o Fcan be made by using he excess noise
index xin:
F≈Gx.(3.34)
The sho noises esul ing om di e en cu en s a e hus a ec ed by an inc ease. In case o he
ambien and signal cu en s o APDs he co esponding ex ended equa ions o he noise ol ages
a e:
Un_sho _amb =p2·e0·G·F·Iamb ·NBW ·R (3.35)
Un_sho _sig =q2·e0·G·F·Isig ·NBW ·R .(3.36)
Fo APDs, he da k cu en Idneeds o be sepa a ed in o wo componen s, he no -mul iplied
su ace leaking cu en and he mul iplied bulk leaking cu en :
Id=Ids +Idb ·G. (3.37)
Thus, he acco ding noise ol age Un_sho _da k is gi en by:
Un_sho _da k =q2·e0·(Ids +Idb ·G2·F)·NBW ·R .(3.38)
Since he componen s o he da k cu en a e no mally no indica ed indi idually and he APD is
ypically ope a ed a highe gains o 10 o 100, he Ids becomes insigni ican in mos cases, which
leads o:
Un_sho _da k ≈q2·e0·(Id·G·F)·NBW ·R .(3.39)
84 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
10-5 10-4 10-3 10-2 10-1 100101102
0
10
20
30
40
50
60
70
80
Esig [W/m2]
SNR [dB]
Eamb [W/m2]
0
0.1
1
10
100
APD
S12053-10
▶︎
▶︎
▶︎
▶︎
10-5 10-4 10-3 10-2 10-1 100101102
0
10
20
30
40
50
60
70
80
Esig [W/m2]
SNR [dB]
Eamb [W/m2]
0
0.1
1
10
100
APD
S8664-50
▶︎
▶︎
▶︎
▶︎
Figu e 3.34: Gene al signal- o-noise pe o mance unde a ying signal and ambien
ligh condi ions o wo TIA ampli ied de ec o s in APD- echnology. The
uppe diag am is alid o a small-a ea (0.785 mm2) APD, he lowe o
a la ge-a ea (19.6 mm2) APD. The a ows indica e he equi ed signal
i adiance o 15 dB SNR a he wo ambien ligh ex emes.

3.4 The Applicabili y o PIN-PDs and APDs in Compa ison 85
3.4.2 SNR Pe o mance a UOWC Ligh Condi ions
T ansi ion om in Ai Condi ions o Unde wa e Ci cums ances
A ans e o he TIA ampli ied PDs in o an UOWC sys em in he unde wa e en i onmen
equi es he exp ession o he abs ac i adiance quan i ies by mo e desc ip i e and accessible
pa ame e s. In case o he Eamb his means a changeo e o dep h and ype o he wa e , as well
as he senso o ien a ion. Fo he Esig his leads o he conside a ion o he LED sou ce se up,
he use o he dis ance o he ecei e and also he wa e pa ame e s. A co esponding scena io is
gi en in Fig. 3.35, whe e he il e deployed will also be pa o he ollowing examina ions. The
goal is o gene a e signal- o-noise cha s o di e en PDs, showing he achie able dis ance as a
unc ion o he wa e dep h in a s anda d geome ic con igu a ion.
Su ace
Subsea
Viewing di ec ion
LED
Fil e
Pho ode ec o
AOI=0°
I adiance,
downwelling
diuse
Dis ance
Dep h d
𝛽
Figu e 3.35: Scena io showing he se up and he en i onmen al ci cums ances o sim-
ula ion.
The pa ame e s o he TIA and he PDs a e gi en in he Tables 3.7, 3.8 and 3.10, and a e eused
in he calcula ions as well as he da a o he unde wa e ambien ligh ield o he in e media e
Je lo III wa e ype gi en in Sec ion 3.2.1. Fu he pa ame e s need o be added, which speci y
he LED-sou ce and he op ical bandpass il e , see Tables 3.11 and 3.12, espec i ely. The a io
o he il e s op ical bandwid h o he LEDs FWHM is se o 1, ela ing o he de e mined OSNR
gain maximum in Fig. 3.28. Wi h he senso looking upwa ds (gene ally he wo s case) he
dis ance o he sou ce is limi ed by he dep h, e e ed o as he physical limi in he ollowing
sec ion.
Table 3.11: LED sou ce pa ame e s used in he simula ion, selec ed on a ealis ic scale
and co esponding o a clus e o Luxeon Lumileds LXZ1 oyal blue.
Cen e wa eleng h λCWL 448 nm
Spec al wid h FWHM 18 nm
Op ical powe Pop 10 W
Beam angle β70◦
The ollowing bounda y condi ions apply o he de e mina ion o Eamb: Je lo III oceanic wa e
ype, di use ambien condi ions, senso acing upwa ds (gene ally he wo s case), and a gi en
spec al downwelling i adiance Ed(λ)gene a ed by Hyd oligh simula ion so wa e o di e en
wa e dep hs zin ce ain en i onmen al condi ions, c . Fig. 3.11. The calcula ion o Eamb is done
86 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
Table 3.12: Fil e and geome ical pa ame e s used in he simula ion, modeled as gi en
in (3.10) o (3.16) and Fig. 3.26.
Cen e wa eleng h λPBcen e 448 nm
Passband wid h PB 18 nm
Angle o incidence AOI 0◦
PD acing di ec ion up
by mul iplying Ed(λ)wi h he spec al ansmission T(λ) o he di use case:
Eamb =
λdi uppe
Z
λdi lowe
Ed(λ)·Tdi (λ) dλ. (3.40)
The ollowing bounda y condi ions apply o he de e mina ion o Esig: wa e a enua ion pa am-
e e Kd, no inclina ion be ween LED and PD, equal dis ibu ion wi hin beam angle, and dis ance
. The calcula ion o Esig is gi en by he p oduc o (2.17) and he mul iplica ion o he no malized
spec al in ensi y o he LED Id(λ), wi h he spec al ansmission T(λ) o he di ec ed case:
Esig =Pop ·e−Kd
2π 2(1 −cos(β/2)) ·
λPBuppe
Z
λPBlowe
ILEDno m (λ)·Tdi (λ) dλ. (3.41)
The simula ion is pe o med o a single wa eleng h, despi e he ac ha na ow wa eleng h
bands a e used, because only small inaccu acies a e expec ed due o he piecewise linea i y. This
is pa icula ly ue o he LED signal componen , whe eas o he ambien componen an o e -
es ima ion is likely o occu due o he small cen e shi o he il e .
The calcula ions o each da a poin o he aspi ed diag ams a e ca ied ou in he ollowing
o de , aking in o accoun he bounda y condi ions: calcula e he Eamb o he selec ed wa e ype
and dep h by (3.40), hen de e mine he equi ed Esig o he espec i e SNR by he equa ions
o he TIA, inally pe o m an i e a i e calcula ion o he necessa y dis ance o he de e mined
Esig by (3.41).
Pe o mance Dependence o De ec o Type and A ea
The esul s o he p e ious calcula ions a e p esen ed in he Figs. 3.36 and 3.37, which p o ide
SNR cha s o bo h de ec o echnologies in di e en sizes. High SNR equi emen s signi ican ly
educe he achie able anges o all de ec o s. The educed ambien ligh in deepe wa e gene ally
leads o an inc ease in ange o a ce ain SNR. This e ec is pa icula ly p onounced o APDs,
bu is less o PIN-PDs. The wa e ype, o cou se, has an e ec on he ange. A clea e oceanic
wa e Je lo IB inc eases i , a mu kie coas al one like Je lo 3C leads o a educ ion. The gene al
e ec o a ying he wa e ype is shown in Fig. 3.41.
A di ec compa ison o he ou a ian s o a a ge SNR o 15 dB is gi en in Fig. 3.38. I one
compa es he small-a ea and he la ge-a ea de ec o s agains each o he , i becomes clea ha he
PIN-PD echnology is signi ican ly mo e pe o man in shallow and medium wa e dep hs and he
co esponding ambien ligh condi ions, and he APD echnology only ca ches up in la ge wa e
dep hs o inally show i s ad an age in deep da k en i onmen s. The compa ison o he small
APD wi h he la ge PIN-PD is pa icula ly in e es ing, since hey a e in he same p ice ange.
This PIN-PD shows a clea ad an age o e a wide ange by abou a ac o o 2 wi h ega ds o
he achie able dis ance, and e en keeps up in quasi-da kness.
3.4 The Applicabili y o PIN-PDs and APDs in Compa ison 87
2 5 10 20 50 100
0
5
10
15
20
25
30
Dep h [m]
Dis ance [m]
SNR
10 dB
15 dB
20 dB
30 dB
40 dB
50 dB
Je lo wa e ype III
PIN-PD
BPW34B
physical limi
2 5 10 20 50 100
0
5
10
15
20
25
30
Dep h [m]
Dis ance [m]
SNR
10 dB
15 dB
20 dB
30 dB
40 dB
50 dB
Je lo wa e ype III
PIN-PD
S3590-08
physical limi
Figu e 3.36: Signal- o-noise a io pe o mance o a small-a ea (7.45 mm2) de ec o in
PIN-PD echnology in he uppe diag am and o a la ge-a ea (100 mm2)
de ec o in he lowe diag am. The cha s display he achie able dis-
ance as a unc ion o he ope a ing dep hs,which is ep esen a i e o he
ambien ligh condi ions.
88 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
2 5 10 20 50 100
0
5
10
15
20
25
30
Dep h [m]
Dis ance [m]
SNR
10 dB
15 dB
20 dB
30 dB
40 dB
50 dB
Je lo wa e ype III
APD
S12053-10
physical limi
2 5 10 20 50 100
0
5
10
15
20
25
30
35
Dep h [m]
Dis ance [m]
SNR
10 dB
15 dB
20 dB
30 dB
40 dB
50 dB
Je lo wa e ype III
APD
S8664-50
physical limi
Figu e 3.37: Signal- o-noise a io pe o mance o a small-a ea (0.785 mm2) de ec o
in APD echnology in he uppe diag am and o a la ge-a ea (19.6 mm2)
de ec o in he lowe diag am. The cha s display he achie able dis ance
as a unc ion o he ope a ing dep hs, which a e ep esen a i e o he
ambien ligh condi ions.
3.4 The Applicabili y o PIN-PDs and APDs in Compa ison 89
2 5 10 20 50 100
0
5
10
15
20
25
30
35
Dep h [m]
Dis ance [m]
SNR=15 dB
PIN-PD
S3590-08
100 mm2
BPW34B
7.45 mm2
APD
S8664-50
19.6 mm2
G=50
S12053-10
0.785 mm2
G=50
Je lo wa e ype III
physical limi
Figu e 3.38: Compa a i e pe o mance o a small-a ea and a la ge-a ea de ec o each
using PIN-PD and APD echnologies.
In luence o De ec o O ien a ion
The amoun o ambien ligh a de ec o collec s unde wa e depends on he iewing di ec ion and
he ield o iew opening angle. The unde wa e ligh ield is desc ibed by he downwelling and
upwelling plane i adiances Edand Eu, as o example, supplied by Hyd oligh simula ions, see
also Table 3.4. They ep esen he wo ex eme di ec ions, a leas o he mo e common case o
di use condi ions. The excep ion would be in shallowe dep hs and clea wa e whe e he di ec
cha ac e p e ails, and a senso poin ed di ec ly a he sun’s incidence can gi e e en highe alues
compa ed o acing s aigh up. The di ec ional componen s o he unde wa e ambien ligh ield
can be depic ed by adiances L, which gi es he lux pe uni solid angle and a ea. Hyd oligh
simula ions esol e he ligh ield in 10◦ e ical and 15◦ho izon al esolu ions. The o a ion o
a de ec o in a ligh ield is illus a ed in Fig. 3.39. In deepe o s onge sca e ing wa e he
ho izon al di ec ion loses impo ance, he e o e he mean o all he ho izon al alues is used in
u he calcula ions o desc ibe he e ical angula p og ession. Fo his pu pose, he adiances
ha lie wi hin he PDs ield o iew (gi en by he angle α) a e cosine-weighed in espec i e o
he pe pendicula o he de ec o and a e summed. The sums o di e en o a ions o iewing
angles a e no malized o he maximum alue, which yields in upwa ds-looking case. The ela i e
p og ession o he i adiance on he de ec o s su ace as unc ion o he iewing angle is shown in
Fig. 3.40 o di e en wa e ypes, dep hs and ield o iews.
O cou se in shallowe wa e s he ho izon al o ien a ion o he senso a ea has an e ec , since
he adiances o ien ed o he sun become dominan , whe eby he di use cha ac e emains in
many cases. The di ec cha ac e only p e ails in clea wa e a small dep h, see also Fig. 3.10.
The ho izon al u n o an upwa ds-looking uni o m a eal senso would no change he i adiance
exposu e and esul in a ci cle on a pola plo o he senso s ou pu cu en . I he senso is
now il ed e ically and o a ed ho izon ally, an o -cen e ed ellipse o lobe wi h a mo e o less
p onounced peak is c ea ed. To calcula e his, he e ically il ed senso needs o be u ned
ho izon ally in he ull space ligh ield, which is ep esen ed by he adiance dis ibu ion. The

90 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
Su ace
Subsea
PD
𝛼
Figu e 3.39: Ro a ion o a pho ode ec o in he e ical ambien adiance ligh ield.
The h ee main acing di ec ions up, ho izon al and down a e indica ed.
espec i e inciden adiances a e added up in a cosine-weigh ed manne .
The in luence o he de ec o ’s o ien a ion o bo h echnologies in di e en wa e s is depic ed
in Fig. 3.41. The o ien a ion o he plana de ec o (s aigh up and down) ep esen s he wo
ex emes. The calcula ion and he p esen a ion a e done in he same way as o Fig. 3.38, and
he achie able ange a a ce ain dep h is de e mined o a SNR alue o 15 dB. Fo he APD
as well as o he PIN-PD, la ge dis ances esul om he downwa d o ien a ion. This e ec
is mo e p onounced wi h he APD and is also las ing longe a la ge wa e dep hs. The la ge
insensi i i y o ambien ligh o he PIN-PD is again e iden .
0 30 60 90 120 150 180
0.0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1.0
Viewing angle [°]
Rel. I adiance
Wa e ype, dep h
Je lo III, 50 m
FOV=180°
Je lo 3C, 20 m
FOV= 180°
Je lo 3C, 20 m
FOV= 90°
Je lo 3C, 20 m
FOV= 50°
upwa ds ho izon al downwa ds
Figu e 3.40: Rela i e i adiance impac on a pho ode ec o as a unc ion o he iewing
angle, om upwa ds- o a ed o downwa ds-looking.
3.4 The Applicabili y o PIN-PDs and APDs in Compa ison 91
2 5 10 20 50 100 200
0
5
10
15
20
25
30
Dep h [m]
Dis ance [m]
SNR=15 dB
acing upwa ds
wa e ype
Je lo 1B
Je lo III
Je lo 3C
acing downwa ds
wa e ype
Je lo 1B
Je lo III
Je lo 3C
PIN-PD
BPW34B
physical limi
de ec o acing upwa ds
2 5 10 20 50 100 200
0
5
10
15
20
25
30
35
40
45
Dep h [m]
Dis ance [m]
SNR=15 dB
acing upwa ds
wa e ype
Je lo 1B
Je lo III
Je lo 3C
acing downwa ds
wa e ype
Je lo 1B
Je lo III
Je lo 3C
APD
S12053-10
physical limi
de ec o acing upwa ds
Figu e 3.41: In luence o de ec o o ien a ion on ope a ing ange pe o mance, de-
pic ed o he ex eme iewing di ec ions (s aigh up and down). Cal-
cula ed o a signal- o-noise a io o 15 dB a a ious dep hs o Je lo
wa e ypes 1B, III and 3C. The uppe diag am depic s an example in
PIN-PD echnology, he lowe diag am o APD echnology.
92 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
Impac o Sou ce Powe Va ia ion
To ex end he ange o an UOWC sys em, inc easing he ansmi ed op ical powe is he mos
ob ious me hod. To illus a e he e ec s, simula ions a e ca ied ou unde euse o he p e ious
se ups: TIA in Table 3.7, PIN-PD and APD de ec o s in Table 3.8, hin ilm op ical il e in
Table 3.12 and LED sou ce in Table 3.11. The simula ions a e conduc ed wi h a a ia ion o ±
6 dB o he op ical sou ce powe while main aining an SNR alue o 15 dB o demons a e he
e ec s on he a ainable ange. The ou come o bo h de ec o ypes in a ious dep hs o oceanic
and coas al wa e s is gi en in Fig. 3.42.
The cu es show a kind o pa allel shi o he espec i e de ec o and wa e ype, whe e he
dis ances wi hin a ela ed se o cu es dec ease bo h absolu ely and ela i ely om clea o u bid
wa e , co esponding om oceanic Je lo 1B ia III o coas al 3C wa e ype. A look a he link
budge , see (2.17), gi es wo e ms ha con ain he dis ance , he in e se squa e law and Bee ’s
law, whe e he applied a enua ion coe icien co Kdco-de e mines he exponen ial a enua ion.
In he bes possible heo e ical case, in condi ions wi hou a enua ion, quad upling he powe
would double he dis ance. Highe a enua ion alues cause Bee ’s law o become dominan , and
he yield h ough powe inc ease d ops, and his applies o alues om app ox. 0.4 1/m o longe
dis ances.
Howe e , he e a e o he aspec s o his inc ease o powe . To s ay wi h he example o 10 W
op ical powe , which equals app oxima ely 25 W o elec ical powe o blue LEDs, a heo e ical
jump o 6 dB would mean 100 W elec ical powe . This quickly shows he limi s o p ac ical
easibili y. Ba e y-powe ed unde wa e ehicles and ancho ed senso s a e gene ally e y sensi i e
sys ems in e ms o ene gy consump ion, which is in he in e es o long ope a ing du a ion. An
LED can be ope a ed wi h highe powe wi hin limi s, bu his educes he e iciency, i.e., he
a io o op ical o elec ical powe . The ins alla ion o mul iple LED elemen s, on he o he hand,
may cause space, hea and op ical adap ion p oblems.
A simila e ec o an inc ease o he op ical LED powe can be achie ed by a ia ion o he
beam angle, which also e ec s he i adiance. Fig. 3.43 depic s he ela i e i adiance as a unc ion
o he beam angle a condi ions o a cons an op ical sou ce powe , and an equal beam dis ibu ion
wi hin he beam angle and a ixed ecei e dis ance. O cou se he educ ion o he beam angle has
a s ong impac on di ec ionali y ha can cause poin ing and acking issues. Also he numbe o
necessa y elemen s o c ea e a hemisphe ical cha ac e is ic is g owing.
Besides he ques ion o dis ance p og ession, he issue o an SNR change while keeping he
dis ance a powe a ia ions could a ise. An inc ease o 6 dB in he op ical sou ce powe esul s in
a 12 dB SNR change o he PIN-PD. In case o APD i depends on he ope a ing en i onmen al
condi ions, a e y low ligh le el wi hou sho noise a 6 dB powe change also esul s in a 12 dB
SNR change. In a eas whe e sho noise becomes inc easingly dominan , i educes inally o a
6 dB SNR imp o emen .
The impo ance and impac o op ical sou ce powe and ene gy e iciency sugges wo poin s:
he powe e iciency could be inc eased by ange- and SNR-adap i e s ee ing o he LED ou pu
as well as he implemen a ion o an ene gy e icien modula ion scheme, which o example could
include sho and la ge pulses om a high-o de PPM scheme.
3.4 The Applicabili y o PIN-PDs and APDs in Compa ison 93
2 5 10 20 50 100 200
0
5
10
15
20
25
30
35
40
45
Dep h [m]
Dis ance [m]
SNR=15 dB
acing upwa ds
Je lo wa e ype 1B
Pop +6 dB
Pop
Pop -6 dB
Je lo wa e ype III
Pop +6 dB
Pop
Pop -6 dB
Je lo wa e ype 3C
Pop +6 dB
Pop
Pop -6 dB
PIN-PD
BPW34B
physical limi
2 5 10 20 50 100 200
0
5
10
15
20
25
30
35
40
45
50
55
Dep h [m]
Dis ance [m]
SNR=15 dB
acing upwa ds
Je lo wa e ype 1B
Pop +6 dB
Pop
Pop -6 dB
Je lo wa e ype III
Pop +6 dB
Pop
Pop -6 dB
Je lo wa e ype 3C
Pop +6 dB
Pop
Pop -6 dB
APD
S12053-10
physical limi
Figu e 3.42: Impac o op ical sou ce powe a ia ion on he achie able ange o di -
e en wa e ypes. Simula ed o a cons an SNR o 15 dB and an upwa d
acing de ec o . The uppe diag am shows an example o PIN-PD ech-
nology, he lowe diag am o APD echnology.
100 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
400 450 500 550 600 650 700
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Wa eleng h [nm]
Responsi i y [A/W]
OSRAM LED as PD
QE=100% LB W5SM blue
LT W5SM g een
Os am PD LY W5SM yellow
SFH2400 LR W5SM ed
Figu e 3.47: Spec al esponsi i y measu emen s o Os am Golden D agon se ies LEDs
in ou colo s u ilized as pho ode ec o s. The measu emen s a e compa ed
wi h a Si-PIN pho ode ec o and i s heo e ical bound.
sessed, and alues o 5 % o 16 % o he blue-g een ange. In eg al calcula ions o e a wa eleng h
band we e pe o med by summa ion o disc e e elemen s o 1 nm wid h.
J=
700 nm
R
400 nm
Ie,n(λ)·Rn(λ)dλ
700 nm
R
400 nm
Ie,n(λ)dλ
(3.42)
Viewing he pu e bandpass il e ea u es such as wid h o he passing band and slope, LEDs
deployed as a PD can be an al e na i e o Si-PIN-PDs combined wi h a colo ed glass bandpass
il e , see Fig. 3.52 and [36]. Howe e , bonded a ian s a e a ely ound on he ma ke . Fu -
he mo e, colo ed glass bandpass il e s a e only a ailable in he blue-g een band, and no in he
yellow- ed band. Fig. 3.52 compa es he spec al sensi i i y o an LED deployed as a PD wi h a
Si-PIN pho ode ec o combined wi h a colo ed glass bandpass il e Hebo G08. Howe e , a hin
ilm il e gene ally deli e s s eepe slopes and can be designed o e wide anges wi h espec o
he cen e wa eleng h, and a e much na owe in he passband, bu has he disad an age o a
high p ice. In es iga ions o he in luence o he empe a u e on he pho ode ec o s esponsi i y
we e no ca ied ou , since hey a e known o be small and would no jus i y a conside able e o
o a supposedly insigni ican esul .

3.5 Single-Colo Powe LEDs used as Pho ode ec o s 101
400 450 500 550 600 650 700
0.0
0.2
0.4
0.6
0.8
1.0
Wa eleng h [nm]
Responsi i y, ela i e
in ensi y, ela i e
Os am LED Os am LED as PD
LB W5SM blue LB W5SM blue
LT W5SM g een LT W5SM g een
LY W5SM yellow LY W5SM yellow
LR W5SM ed LR W5SM ed
Figu e 3.48: No malized spec al measu emen s o Os am Golden D agon se ies LEDs,
deployed as emi e s (dashed lines) and as a de ec o s (solid lines). P e-
sen ed wi hou measu ed da a poin s o be e cla i y.
400 450 500 550 600 650 700
0.0
0.1
0.2
0.3
0.4
0.5
0.6
Wa eleng h [nm]
Responsi i y [A/W]
Lumileds LED as PD
QE=100% LXZ1-PB01 blue
LXZ1-PE01 cyan
Os am PD LXZ1-PM01 g een
SFH2400 LXZ1-PL01 ambe
LXZ1-PH01 ed o ange
LXZ1-PD01 ed
LXZ1-PA01 deep ed
Figu e 3.49: Spec al esponsi i y measu emen s o Lumileds Z se ies LEDs in se en
colo s u ilized as pho ode ec o s. The measu emen s a e compa ed wi h
an Si-PIN pho ode ec o and i s heo e ical bounda y.
102 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
400 450 500 550 600 650 700
0.2
0.4
0.6
0.8
1.0
Wa eleng h [nm]
Responsi i y, ela i e
in ensi y, ela i e
Lumileds LED Lumileds LED as PD
LXZ1-PB01 blue LXZ1-PB01 blue
LXZ1-PE01 cyan LXZ1-PE01 cyan
LXZ1-PM01 g een LXZ1-PM01 g een
LXZ1-PL01 ambe LXZ1-PL01 ambe
LXZ1-PH01 ed o . LXZ1-PH01 ed o ange
LXZ1-PD01 ed LXZ1-PD01 ed
LXZ1-PA01 deep ed LXZ1-PA01 deep ed
Figu e 3.50: No malized spec al measu emen s o Lumileds Z se ies LEDs, deployed
as emi e s (dashed lines) and as de ec o s (solid lines). P esen a ion
wi hou measu ed da a poin s o be e cla i y.
400 450 500 550 600 650 700
0.0
0.2
0.4
0.6
0.8
1.0
Wa eleng h [nm]
Responsi i y, ela i e
in ensi y, ela i e
Os am LED Os am LED as PD
LB W5SM blue LB W5SM blue
LR W5SM ed LR W5SM ed
Figu e 3.51: No malized spec al measu emen s o Os am Golden D agon se ies LEDs,
deployed as emi e s (dashed lines) and as de ec o s (solid lines). The
o e lap o he a eas illus a es he di e ence in spec al e iciency o he
blue and he ed a ian s.
3.5 Single-Colo Powe LEDs used as Pho ode ec o s 103
450 500 550 600 650
0.00
0.05
0.10
0.15
0.20
0.25
Wa eleng h [nm]
Responsi i y [A/W]
Lumileds, LED as PD
LXZ1-PL01
Os am PD SFH2400 and
Hebo G08 col. glass il e
Figu e 3.52: Compa ison o he measu ed spec al esponsi i y o an LED deployed as
a PD wi h an Si-PIN pho ode ec o adap ed wi h a colo ed glass bandpass
il e .
3.5.2 Analysis in he Tempo al Domain
Expe imen al Se up o Tempo al Measu emen s
Measu ing he ise ime m o an impulse esponse allows he de e mina ion o he bandwid h,
used he e o a pho ode ec o . Fo his ask, a as ligh sou ce is ideally used, which o e s a
sho ise ime s  m and hus esul s in he neglec o s. Typical bandwid hs o powe
LEDs including he d i e a e known o be in he ange o a ew MHz o ens o MHz, which
esul s in ise imes in he ange o ens o nanoseconds. Howe e , since i was he in en ion
o use a powe LED as an emi e in his expe imen , which ep esen s a ela i e slow ligh
sou ce, he iden i ica ion o s was necessa y. Figu e 3.53 depic s he con igu a ion used o hese
empo al measu emen s, comp ising a signal gene a o Rigol DG5072, a high-speed MOSFET
d i e Mic ochip TC4452 including an LED o he Os am Golden D agon se ies as a DUT, a
Tho labs PDA-10A 150 MHz ansimpedance ampli ie (TIA) PD-module, and a Rohde & Schwa z
HMO3004 digi al oscilloscope.The signal analysis o he oscilloscope di ec ly p o ides he 10 % o
90 % ise ime o he measu ed signal.
To measu e he ise ime o he LED as a PD, ep esen ing he DUT, he se up in Fig. 3.54
was used, including he sou ce in oduced in Fig. 3.53. The op ical bandwid h o he sou cing
LED should well o e lap he sensi i i y band o he DUT. The gene a ed pho ocu en was ed
in o a ansimpedance ampli ie Texas Ins umen s THS4631 e alua ion boa d, which o e ed a
gain bandwid h p oduc (GBP) o 210 MHz, and i was con igu ed wi h a eedback esis ance R
DUT
LED
Signal
gene a o
LED
d i e
Pho ode ec o
TIA module Oscilloscope
Figu e 3.53: Se up o measu ing he ise and all ime o LEDs used as ligh sou ce.
The sou ce pa o his se up has also been used o in es iga ion o he
empo al cha ac e is ics o he LEDs used as a PD.
104 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
LED
TIA
DUT
LED as PD
R
C
LED
d i e
Signal
gene a o
Oscilloscope
Figu e 3.54: Block diag am o he con igu a ion o de e mina ion o he ise and all
imes o LEDs deployed as PDs. The sou ce is con igu ed as in Fig. 3.53
and he i adia ed DUT is connec ed o a ansimpedance ampli ie , and
he ou pu is eco ded by a digi al oscilloscope.
o 47 kΩ, as well as a eedback capaci ance C , o accomplish a quali y ac o Qo app oxima ely
0.7. The capaci ance Co he DUT was measu ed di ec ly by u ilizing a Wa e ek LCR55 me e .
Using a TIA calcula o was ound o be help ul a his poin , which is a ailable online a [178].
The e alua ion o he esponse signal s o ed by he oscilloscope deli e ed he ise and all imes
and p o ided an es ima e o he achie ed quali y ac o .
As he main sou ce o unce ain y o he measu emen s in he empo al domain, he con igu a-
ion o he eedback capaci o and he esul ing quali y ac o was iden i ied. Timing and capaci y
alues we e de e mined wi h ela i ely high accu acy. Table C.6 gi es an o e iew.
Examina ion and Expe imen al Resul s o Tempo al Domain
The app oxima e bandwid h B esul ing om 10 % o 90 % ise ime measu emen s can be
calcula ed by:
B≈0.35
.(3.43)
This equa ion is alid o signals wi h app oxima ely he same ise and all ime [196]. This
condi ion was p esen in he expe imen s o he LEDs unde in es iga ion. Fo an expe imen al
de e mina ion o he ise ime d o he pho ode ec o , he ise ime s o he pulsed ligh sou ce
needs o be aken in o accoun unless s  d. The measu able ise ime m esul s om he
geome ic addi ion o s and d:
m =q s2+ d2.(3.44)
In he case o he conduc ed expe imen , which comp ised an LED as a sou ce and a as TIA-PD
module as a de ec o , he sho es measu ed alue o m was 40 ns. In conjunc ion wi h he
calcula ed alue o d o 2.3 ns used o he 150 MHz TIA-PD module, d was negligible and m
app oached s.
In Table 3.15 he measu ed alues m o he LEDs used as emi e s a e shown, gi en he se up
in Figu e 3.53. The calcula ed alues o he bandwid hs a e in he expec ed ange.
In he second pa o he expe imen , he in eg a ed pho ode ec o TIA module was exchanged
by a disc e e TIA, which was ed by an LED u ilized as PD. In Table 3.16 he measu ed alues
o m o he wo LED se ies employed as PD a e gi en, he co esponding se up is depic ed
in Fig. 3.54. The LED sou ces we e ma ched o he spec al sensi i i ies, see Table 3.15 and
Figs. 3.47 o 3.50. The ise imes o he LEDs employed as PDs and he ega ding bandwid hs
we e calcula ed.
3.5 Single-Colo Powe LEDs used as Pho ode ec o s 105
Table 3.15: Measu ed alues o 10% o 90% ise ime m o in es iga ed LEDs used
as an emi e .
Manu ac u e Type Colo Wa eleng h, m, meas. B, calc.
dom., [nm] [ns] [MHz]
Os am LD W5SM deep blue 455 40 8.75
Os am LT W5SM g een 528 63 5.56
Os am LY W5SM yellow 590 130 2.69
Os am LR W5SM ed 628 70 5.00
Table 3.16: LEDs used as a pho ode ec o , measu ed ise ime m, calcula ed ise ime
d and calcula ed bandwid h B, o a TIA con igu ed o app oxima ely
Q= 0.7.
Manu ac u e Type Colo s m d, calc. B, calc.
[ns] [ns] [ns] [MHz]
Os am LB W5SM blue 40 490 488.3 0.72
Os am LT W5SM g een 40 470 468.3 0.75
Os am LY W5SM yellow 63 139 123.9 2.83
Os am LR W5SM ed 70 182 168.0 2.08
Lumileds LXZ1 PB01 blue 40 505 503.4 0.70
Lumileds LXZ1 PE01 cyan 40 410 408.0 0.86
Lumileds LXZ1 PM01 g een 40 388 377.9 0.93
Lumileds LXZ1 PL03 ambe 130 294 263.7 1.33
Lumileds LXZ1 PH01 ed o ange 70 177 162.6 2.15
Lumileds LXZ1 PD01 ed 130 224 182.4 1.92
Lumileds LXZ1 PA01 deep ed 130 274 241.2 1.45
In Table 3.17 he measu ed junc ion capaci ances o he LEDs and he bandwid hs as esul o
he TIA simula ion a e abula ed o compa ison. The simula ed bandwid hs based on capaci ance
measu emen s and he achie ed bandwid hs o LEDs employed as a PD (d i ing a TIA in a
eal LED sou ced es se up) show mos ly good ag eemen . The de ia ion wi h espec o he
de e mined bandwid hs we e caused by he di icul y in uning he TIA exac ly o Q= 0.7due o
he limi ed a ailabili y o small g aded capaci o s in he low pico a ad ange. Bo h se ies o LEDs
employed as PDs showed la ge capaci ances in he blue-g een egime compa ed o he yellow- ed
egime as depic ed in Fig. 3.55, which esul s in longe ise imes and lowe bandwid hs.

106 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
450 500 550 600 650 700
0
200
400
600
800
1000
1200
1400
1600
1800
Wa eleng h [nm]
Capaci ance [pF]
Os am
LB W5SM blue
LT W5SM g een
LY W5SM yellow
LR W5SM ed
Lumileds
LXZ1 PB01 blue
LXZ1 PE01 cyan
LXZ1 PM01 g een
LXZ1 PL03 ambe
LXZ1 PH01 ed o ange
LXZ1 PD01 ed
LXZ1 PA01 deep ed
Figu e 3.55: Diag am depic s he measu ed capaci ance o e he nominal wa eleng h
o wo LED se ies.
Table 3.17: LEDs as a pho ode ec o and he co esponding measu ed capaci ance,
used eedback capaci ance, and simula ed TIA bandwid h o Q= 0.7,
GBP = 210 MHz and R = 47 kΩ. Fo compa ison: he e e ence Si-
PIN-PD Os am SFH 2400 has a capaci ance o 11 pF a ze o e e se
ol age, esul ing in a simula ed bandwid h o 7.8 MHz unde he same
condi ions.
Manu ac u e Type Colo C, meas. C B, sim.
[pF] [pF] [MHz]
Os am LB W5SM blue 950 5.5 0.86
Os am LT W5SM g een 680 4.7 1.02
Os am LY W5SM yellow 105 1.8 2.58
Os am LR W5SM ed 235 2.8 1.73
Lumileds LXZ1 PB01 blue 1600 7.2 0.67
Lumileds LXZ1 PE01 cyan 1120 6.0 0.80
Lumileds LXZ1 PM01 g een 1270 6.4 0.77
Lumileds LXZ1 PL03 ambe 420 3.7 1.30
Lumileds LXZ1 PH01 ed o ange 192 2.5 1.91
Lumileds LXZ1 PD01 ed 226 2.7 1.76
Lumileds LXZ1 PA01 deep ed 370 3.5 1.38
3.5 Single-Colo Powe LEDs used as Pho ode ec o s 107
3.5.3 Analysis in he Spa ial Domain
Expe imen al Se up o Spa ial Measu emen s
One o he main pa ame e s in he applica ion o op ical sys ems is he angle o incidence (AOI).
The e o e, o achie e p ecise alignmen and good epea abili y, an op ical bench was u ilized.
The ligh sou ce o spa ial measu emen s was an LED o he se ies Ledengin LZ4 [63]. The LED
colo s, blue and ambe , we e selec ed so ha he wa eleng h ma ches he DUT. In o de o be
able o a y he angle o incidence, he DUT was moun ed on a o a able de ice, see Fig. 3.56.
This se up ep esen s he simples o m o a so-called goniome e . P ecise di ec measu emen s
o he gene a ed pho ocu en we e made wi h a Kei hley 6517 elec ome e in he co esponding
nanoampe e ange. The de e mina ion o he ield o iew could be ca ied ou based on hese
measu emen s wi h a ying AOI. As no majo de ia ions om he adia ion cha ac e is ic o
he DUT as an LED sou ce we e expec ed and in o de o minimise he e o , only he smalles
possible compa isons wi hin and be ween he se ies we e made. Fo compa ison wi hin a se ies, ed
and g een Os am LEDs we e used, o he compa ison be ween se ies g een Os am and Lumileds
LEDs we e used. Values we e eco ded o AOIs be ween 0◦and 80◦ aken in 10◦inc emen s, and
he o a ion ook place in bo h di ec ions.
Ano he es was o e i y ha he DUT did no eac unexpec edly o changes in he di ec ion
o pola iza ion. Fig. 3.57 is depic ing he se up u ilized o his pu pose. Non-pola ized ligh om
an LED sou ce o app op ia e wa eleng h (ma ching he DUTs passing band) was used, which was
subsequen ly il e ed by a o a able Edmund Op ics glass pola ize 53344. A con inuous change
o he pola iza ion di ec ion om ho izon al o e ical could hus be achie ed h ough o a ing
he il e up o 90◦. Due o he ime and e o in ol ed, i was decided no o examine he ull
se ies, so only ed LEDs o bo h se ies we e chosen as example DUTs. As a ligh sou ce, an ambe -
colo ed Ledengin LZ4 LED was used, ope a ed unde s able condi ions in cons an cu en mode.
Pho ocu en s we e measu ed di ec ly wi h a Kei hley 6514 elec ome e , alues we e aken in 10◦
o a ion inc emen s, and he o a ion was ca ied ou in bo h di ec ions.
In p inciple, he elec ome e , which is specialized in measu ing iny cu en s, enables high
accu acies. To ensu e ha he ligh sou ce was no d i ing du ing he measu emen s, alues a
he ze o deg ee posi ion we e checked o be cons an be ween he indi idual measu ing posi ions.
These con ols p e en ed he d i om making signi ican con ibu ions. The manually o a able
posi ioning was subjec o a ce ain angula e o . Table C.6 p o ides an o e iew o he ela ed
unce ain ies.
LED
Cons an cu en
Powe supply
Elec ome e
DUT, LED as PD
on o a able uni
nA
Figu e 3.56: This illus a ion shows he p inciple sys em o de e mina ion o he di-
ec ional cha ac e is ic o a pho ode ec o . The DUT is o a ed so ha
he i adia ion hi s he ac i e a ea a a de ined angle.
108 Chap e 3 Examina ion and Op imiza ion o Selec ed UOWC Sys em Componen s
DUT
LED as PD
Ro a able
pola iza ion
fil e
LED
Cons an cu en
Powe supply
Elec ome e
nA
Figu e 3.57: This g aphic depic s he se up o checking a possible sensi i i y o pola -
iza ion. The ligh o a unpola ized LED sou ce passes h ough a pola iza-
ion il e . The pola iza ion di ec ion depends on he o a ion posi ion.
Examina ion and Expe imen al Resul s o Spa ial Domain
The measu emen s o he ela i e sensi i i y as a unc ion o he AOI o he LEDs employed as
a PD, showed no signi ican de ia ion wi hin he unce ain ies om he cu es gi en in he da a
shee s o he pa icula LEDs used as emi e , see Fig. 3.58.
When in es iga ing a possible in luence o he pola iza ion di ec ion o he inciden ligh on he
sensi i i y, no indica ions could be ound wi hin he scope o he measu ing accu acy. Please e e
o Fig. 3.59 and no e he e y small scaling.
3.5.4 Rele ance o he Resul s o Applicabili y
Two single-colo powe LED se ies we e employed as a PD and he spec al, empo al and spa ial
cha ac e is ics we e expe imen ally in es iga ed. The DUT ea u ed unexpec ed good esponsi-
i i y. P e ious publica ions examined mos ly low-powe and mid-powe LEDs, which gene ally
showed less esponsi i y. E en in compa ison o a common Si-PIN pho ode ec o and i s heo e -
ical sensi i i y bounda y, he es objec s showed conside able alues. The same LED employed
as an emi e and a de ec o , so-called dual-use, is gene ally applicable h ough he spec al o e -
lap. Howe e , since his o e lap is only small o medium, he same applies o he accompanied
e iciency. The yellow- ed egime showed signi ican ly la ge alues compa ed o he blue-g een
egime. The "g een gap" in e iciency o LEDs used as an emi e , which is cen e ed a ound 550 nm,
occu ed co espondingly shi ed o lowe wa eleng hs o app oxima ely 500 nm, o LEDs used
as PDs. Analogously i could be called "cyan gap" o sensi i i y. The examined LEDs u ilized
as a PD, exhibi ed ano he main ea u e - an inhe en op ical bandpass cha ac e is ic. This can
be a cos -e icien al e na i e o he adap ion o seconda y il e s o PDs. This is especially ue
since colo ed glass na ow bandpass il e s a e gene ally no a ailable in he yellow- ed egion,
hin ilm il e s a e gene ally expensi e, and o - he-shel PD il e combina ions a e a e. Fo he
speed, which is impo an in communica ion sys ems, he capaci ance has a signi ican in luence.
Compa ed o he Si-PIN-PD e e ence, he junc ion capaci ance o he examined LEDs employed
as PDs was ound o be one o wo o de s o magni ude highe . Acco dingly, his leads in o a
educed achie able bandwid h. The measu emen s om he yellow- ed egime o e a lowe ca-
paci ance compa ed o hei coun e pa s in he blue-g een a ea, hus allowing highe speed. The
angle o incidence p ope ies o he LEDs unde in es iga ion was disco e ed o be compa able
when ope a ed as an emi e and a de ec o , as expec ed. Fu he mo e, no dependence on he
pola iza ion di ec ion could be de e mined. The e is a la ge po en ial in LEDs used as PDs o
low-cos solu ions in isible ligh communica ion, dayligh il e ed o colo -selec i e applica ions.
3.5 Single-Colo Powe LEDs used as Pho ode ec o s 109
0 10 20 30 40 50 60 70 80 90
0.0
0.2
0.4
0.6
0.8
1.0
AOI [°]
Responsi i y, ela i e
in ensi y, ela i e
Os am
LT W5S g een
da ashee , as LED
measu ed, as PD
0 10 20 30 40 50 60 70 80 90
0.0
0.2
0.4
0.6
0.8
1.0
AOI [°]
Responsi i y, ela i e
in ensi y, ela i e
Os am
LT W5S g een
da ashee , as LED
measu ed, as PD
0 10 20 30 40 50 60 70 80 90
0.0
0.2
0.4
0.6
0.8
1.0
AOI [°]
Responsi i y, ela i e
in ensi y, ela i e
Lumileds
LXZ1 PD01 g een
da ashee , as LED
measu ed, as PD
Figu e 3.58: Plo s o e lay he ela i e esponsi i y and ela i e in ensi y as a unc ion
o he AOI o di e en LEDs deployed as a de ec o and as a ligh sou ce.
The DUT o igina e om wo se ies, and wi hin one se ies he colo was
a ied.
116 Chap e 4 UOWC Assemblies
Table 4.1: Typical e ac i e indices a λ= 589 nm o selec ed po ma e ials.
Ma e ial Re ac i e index n
Silicone 1.41 - 1.54
po ing compound
Qua z glass 1.46
Polyu e hane (PU) 1.47 - 1.51
po ing compound
Ac ylic glass (PMMA) 1.49
Bo osilica e-c own glass 1.52
Polyca bona e (PC) 1.58
The loss due o in e nal abso p ion in anspa en po ma e ials is hickness dependen , and
alues o a ew en h o a pe cen a e ypical in he wa eleng h ange used o UOWC o abou 450
- 600 nm. Smalle alues also a ise wi h glass, and la ge ones wi h plas ics and especially po ing
compounds, bu in p inciple hei impo ance is mino . This also applies o he wa eleng h-
dependen e ac ion changes in his wa eleng h band, which a e less han 1%.
The p o ec ion o he po agains bio ouling can be ealized h ough UV-C adia ion, see
Sec ion 2.1.3. The mos e ec i e wa eleng h o an i ouling applica ions is in he band o 250nm
o 280nm, he e o e u ilized window ma e ials need o ha e a high ansmi ance in his ange.
This is only he case o used-silica qua z glass, no o s anda d glass and anspa en syn he ics.
Snell’s law, F esnel’s Equa ions and Radiance
A ligh ay has o pass wo media changes when a eling om he wa e h ough a po in o an ai
illed p essu e housing, o ice e sa. The ay expe iences e ac ion a each o hese bounda ies,
and Snell’s law desc ibes he ela ionship be ween he angle o incidence and e ac ion, see (2.1)
and Fig. 2.3. The numbe o ansi ions can a y wi h he housing concep ; p essu e-neu al
po ed e sion may only ha e one, bu i mo e op ical elemen s o media a e in ol ed he numbe
inc eases.
In he ollowing sec ion, he example calcula ions a e conduc ed o he ansmi e side o
he la and dome po s. The e e ence axis o he calcula ions is pe pendicula o he la
po o adial in he case o he dome po , o bo h he ansmi e and ecei e sides, wi hou
inclina ion. A he ansmi e side, he sou ce is placed inside he housing, whe e ai ep esen s
he i s medium. The ay exi ing angle is θs, he i s bounda y inciden angle is θ1, and he
e ac ed angle becomes θ2. A e he ay has passed his second medium in o he hi d, he
e ac ed angle θ3a ises and he esul ing angle θ is gene a ed. Depending on he po shape,
some o hese angles may be equal, o he e may be addi ional sub angles like θ0
2. The nume a ion
o he e ac ion indices is done acco dingly om n1 o n3. The ela ionships a e illus a ed by
he diag ams in Figs. 4.2, 4.7 and 4.9.
Since Snell’s law only explains he di ec ional change o he inciden ay a he in e ace, he
ques ion o he amoun o e lec ed and ansmi ed ligh emains open. The answe is gi en
by F esnel’s equa ions, which desc ibe he ansi ion o elec omagne ic wa es a he in e ace in
e ms o e lec ance and ansmi ance o pola ized ligh . The s- and p-pola ized componen s a e
conside ed sepa a ely, and can la e be me ged o unpola ized ligh , as om an LED. A ansi ion
o inciden ligh a θ1 om a medium o n1in o ano he o n2 esul s in he ansmi ance T12(θ1)
and he e lec ance R12(θ1). Fo a subsequen hi d medium o n3 his acco dingly leads o T23(θ2)
and R23(θ2).
The amoun o ligh can be exp essed by he adiance concep , which u ilizes so-called ligh
pencils as beams. The adiance Lis a adiome ic di ec ional quan i y, and is powe pe uni a ea

4.2 Op ical Po s and Unde wa e Ligh Pa h 117
pe uni solid angle. A pa o he inciden adiance is e ac ed and ansmi ed by he media
bounda y. The emaining pa is e lec ed, while he law o conse a ion o ene gy is sa is ied.
The ela ionship o inciden and ansmi ed adiance is inally gi en by he ’n2law o adiance’,
see (C.16) and [87] o an in-dep h discussion. Co esponding se s o adap ed equa ions o he
la and dome po geome y a e gi en in he Appendices C.7 and C.8.
Pa ame e s and Assump ions o Calcula ions
Fo he subsequen examina ions ha ocus on he ansmi e side, Table 4.2 gi es he applied
pa ame e s including a ia ion ange. These a e adap ed o eal condi ions. Assump ions made
o he calcula ions include:
•No in e nal abso p ion in po ma e ial.
•Iso opic Poin sou ce.
•Radiances no malized o sou ce o L1= 1 [W/m2s ].
Table 4.2: Gene al pa ame e s o po ligh pa h examina ions, and index o de o
he ansmi e side.
Re ac ion index, ai n11.0 (no a ia ion)
Re ac ion index, po n21.5 (1.40 - 1.60)
Re ac ion index, wa e n31.34 (1.33 - 1.35)
Thickness, po p, dp 7 (1 - 20) [mm]
Radius, dome po , inne dpi 50 [mm]
4.2.2 Fla Po s
T ansmi e Side
Wa e
Ai
Po
𝜃
𝜃
𝜃
3
2
s
Sou ce
P essu e housing
inside
L1
L2
L3
n1n2n3
T12 T23
T13
R12 R23
R13
d p
sp
𝜃
2
𝜃
1
𝜃
=
Figu e 4.2: Unde wa e ligh pa h geome y o he ansmi e side, and he sou ce
in a p essu e housing including la po .
The basic case o he ansmi e side when using a la po is depic ed in Fig. 4.2, and he
pa ame e s o his example calcula ion a e gi en in Table 4.2. The pa h o he adiance is
symbolized by he blue a ows, s a ing a he inciden L1wi h a sou ce angle θs, a he i s
118 Chap e 4 UOWC Assemblies
bounda y su ace ansi ioning in o L2, and a he second o L3. Snell’s law p o ides θ2and θ3,
F esnel’s equa ions gi e he ansmi ances T12 and T23 as well as he e lec ances R12 and R23,
and inally he ’n2law o adiance’ yields L3. Since he po is assumed o be hin, i s hickness
p and he sou ce o po dis ance dsp a e insigni ican o now, as he hickness only causes a
magni ica ion e ec .
The esul s o hese calcula ions as a unc ion o θ1a e p esen ed in Fig. 4.3. O e all, he e
is a s ong e ac ion, he angle θ3is in maximum 48.3◦, and he o al e lec ion a he n2 o n3
bounda y is he e o e no eached. Fo small and medium θs alues, he e is app oxima ely 95.7
% o al ansmi ance T13 and 4.3 % o al e lec ance R13. I should be emphasized, ha o small
and medium θsa a io L3/L1o app oxima ely 1.7 occu s. The eason o he inc eased adiance
is he educed solid angle due o e ac ion, which can be imagined as collima ed ays.
0 10 20 30 40 50 60 70 80 90
0
5
10
15
20
25
30
35
40
45
50
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2
Inciden angle 𝜽1 [°]
Re ac ed angle 𝜽3 [°]
T13
R13
L3 / L1
T ansmi ance
e lec ance
𝜽3
adiance a io
Figu e 4.3: Fla po heo e ical e ac ion, ansmi ance, e lec ance, and adiance
a io o ansmi e side.
T ansmi e Side Pa ame e Va ia ions
Since he e ac ion index n2o he po depends on he ma e ial, and he wa e n3also may
be a ec ed by changes, hese indices a e indi idually a ied in o de o de e mine he espec i e
e ec s, and he ou come is shown in Fig. 4.4. The po e ac ion index n2 a ia ion in luences he
adiance a io L3/L1 o a small ex en , bu no he e ac ed angle θ3. The wa e e ac ion index
n3 a ia ion changes he adiance a io L3/L1and he e ac ed angle θ3, bu only bo h sligh ly.
So in his espec , he po ma e ial selec ion and he ope a ion si e choice a e ba ely es ic ed.
4.2 Op ical Po s and Unde wa e Ligh Pa h 119
40 50 60 70 80 90
30
35
40
45
50
1.2
1.4
1.6
1.8
2
Inciden angle 𝜽1 [°]
Re ac ed angle 𝜽3 [°]
n2=1.4
n2=1.5
n2=1.6
n2=1.4
n2=1.5
n2=1.6
Radiance a io L3 / L1
40 50 60 70 80 90
30
35
40
45
50
1.2
1.4
1.6
1.8
2
Inciden angle 𝜽1 [°]
Re ac ed angle 𝜽3 [°]
n3=1.33
n3=1.34
n3=1.35
n3=1.33
n3=1.34
n3=1.35
Radiance a io L3 / L1
Figu e 4.4: E ec o e ac ion index a ia ion o a la po . The po ma e ial n2is
a ied in he uppe diag am, and is o wa e n3in he lowe diag am.
Recei e Side
Wa e Ai
Po
𝜃𝜃
𝜃
3
2
1
De ec o
P essu e housing
inside
𝜃
𝜃
s=
𝜃
2
nnn
123
L
L
L
1
2
3
T12 T23
T13
R12 R23
R13
Figu e 4.5: Unde wa e ligh pa h geome y o de ec o in p essu e housing including
la po .
A change o he la po equipped housing o he ecei e side con igu a ion a ec s he di ec ion,
he o de o he media, and he indices, bu he p inciples s ay he same. Fig. 4.5 depic s his
si ua ion. Calcula ions a e ca ied ou as o he ansmi e side, and he esul s a e p esen ed
in Fig. 4.6. A s ong e ac ion is ob ained again, a an c i ical inciden angle θco 48.3◦and
120 Chap e 4 UOWC Assemblies
a esul ing angle θ2o 41.8◦,and he o al e lec ion condi ion o he po o he ai bounda y is
eached. Fu he inc eased inciden angles esul in o al e lec ion o he equal angle wi h a minus
sign. Fo small θs, he e a e he same o al ansmission T13 and o al e lec ance R13 alues as in
he ansmi e con igu a ion. Majo changes occu a one poin , o small and medium θs alues
a a io L3/L1o app oxima ely 0.53 is calcula ed. The eason o he dec eased adiance is he
expanded solid angle due o e ac ion, which can be isualized as widened ays. A a ia ion o
he wa e n1and he po n2in he same anges as be o e, again only esul s in small e ec s. I
is wo h men ioning ha he e is a shi o he c i ical angle by a ew deg ees when changing n2
by ±0.1.
0 10 20 30 40 50 60 70 80 90
-100
-80
-60
-40
-20
0
20
40
60
80
100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Inciden angle 𝜽1 [°]
Re ac ed angle 𝜽3 [°]
T13
R13
L3 / L1
T ansmi ance
e lec ance
𝜽3
adiance a io
Figu e 4.6: Calcula ed e ac ion, ansmi ance, e lec ance, and adiance a io on
he ecei e side o a la po .
4.2.3 Dome Po s
T ansmi e Side and Cen e ed Sou ce
I an unde wa e housing is econ igu ed om a la po o a dome po , he geome y changes
conside ably. Fo he ansmi e side, he special case o a poin sou ce loca ed in he dome
cen e is shown Fig. 4.7. As his ep esen s an ideal case, his posi ion is also called he ’swee
spo ’.
The ligh pa h is symbolized by blue a ows. Since he adiances L1,L2, and L3a e ound on a
s aigh line, and he ela ed angles θ1,θ2, and θ3a e ze o, no e ac ion occu s. These ela ions
a e consis en , independen om he sou ce angle θs, and which is equal o he esul ing angle
θ . Ne e heless, e lec ions a ise a he media ansi ions. The ou come o example calcula ions,
applying he pa ame e s om Table 4.2 bu excluding he i ele an hickness, is p esen ed in
Fig. 4.8. Fo all inciden angles θs, he e a e app oxima ely 95.7 % o al ansmi ance T13 and
4.3 % o al e lec ance R13. A adiance a io L3/L1o 0.957 occu s.
4.2 Op ical Po s and Unde wa e Ligh Pa h 121
Wa e
Ai Po
𝜃
𝜃
𝜃
3
2
1
Sou ce
P essu e
housing
inside
.
.
.
.
dpi
=0
=0
=0
𝜃
𝜃
s
L
L
L
2
3
1
dp
n
nn
123
T
12
T23
T
13
R12
R23
R13
Figu e 4.7: Unde wa e ligh pa h geome y o a p essu e housing including a dome
po and a cen e ed poin sou ce.
0 10 20 30 40 50 60 70 80 90
0
10
20
30
40
50
60
70
80
90
100
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Inciden angle 𝜽s [°]
Re ac ed angle 𝜽 [°]
T13
R13
L3 / L1
T ansmi ance
e lec ance
𝜽
adiance a io
Figu e 4.8: Calcula ed e ac ion, ansmi ance, e lec ance, and adiance a io o a
dome po housing. An iso opic poin sou ce is posi ioned in he dome
cen e .

122 Chap e 4 UOWC Assemblies
T ansmi e Side and Sou ce ou o he Cen e
A displacemen o he poin sou ce o de ec o om he cen e o he dome leads o a iola ion
o he ideal case. Two basic ypes o displacemen mus be dis inguished: he adial o m ha
p ese es he o a ional symme y and he la e al o m ha can c ea e dis o ions. Due o eal
dimensions o componen s, as o example o cen e ed la ge plana elemen s, i may be necessa y
o conside ou e a eas as la e al displacemen .
The examina ion o his beha io wi h a adially displaced sou ce is mo e impo an o applica-
ions in he ield, because mul iple elemen s canno be posi ioned wi hin, bu only adially a ound
he cen e , and he dome sizes chosen a e a he small. The geome ic ela ionships esul ing om
his case a e shown in Fig. 4.9. In addi ion o he pa ame e s de ined p e iously, he inne dome
po adius dpi and he dis ance cen e - o-sou ce dcs needs o be speci ied, as well as he dome
hickness dp. I can be seen ha he sou ce angle θsis no longe equal o θ1, and likewise θ3is
no longe he same as θ . Fu he mo e, an auxilia y angle θ0
2is c ea ed.
The esul s o hese calcula ions as a unc ion o θsp esen ed in Fig. 4.10, a e alid o he
base pa ame e s in Table 4.2 wi h a sou ce placed a a dcs o 25 mm, which co esponds o he
hal inne dome po adius. O e all, he e is no o e ly s ong e ac ion, and i is almos linea
o all inciden angles θs. The e is app oxima ely 95.7 % o o al ansmi ance T13 and 4.3 % o
o al e lec ance R13. The mos signi ican change compa ed o he ideal case conce ns he a io
o ansmi ed o inciden adiance. Fo small inciden angles θsa a io L3/L1o app oxima ely
1.27 occu s, and his alue dec eases in an a cua e cu e o ze o o a θs alue o 90◦.
Wa e
Ai
𝜃
𝜃
𝜃
3
2
1
Sou ce
P essu e
housing
inside
dpi
𝜃
𝜃
s
𝜃
'
2
dp
Po
L
L
L1
2
3
d
cs
Cen e
n
n
n
123
T
12
T23
T
13
R12
R23
R13
Figu e 4.9: Unde wa e ligh pa h geome y o p essu e housing including a dome po
and a sou ce posi ioned adially ou side o he cen e .
4.2 Op ical Po s and Unde wa e Ligh Pa h 123
0 10 20 30 40 50 60 70 80 90
0
10
20
30
40
50
60
70
80
90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Inciden angle 𝜽s [°]
Re ac ed angle 𝜽 [°]
T13
R13
L3 / L1
T ansmi ance
e lec ance
𝜽
adiance a io
Figu e 4.10: Theo e ical e ac ion, ansmi ance, e lec ance, and adiance a io o
a dome po housing. The poin sou ce is placed ou side he dome cen e
on he hal inne adius posi ion.
Sou ce Posi ion Va ia ion
As p e iously men ioned o he la po , he impo an pa ame e s o he dome po a e
now changed indi idually. The sou ce posi ion is adially a ied, while he base pa ame e s
(n1, n2, n3, dpi, dp) a e kep cons an . Calcula ions a e made o cen e - o-sou ce dis ances dcs o
0, 25, 37.5 and 47.5 mm, acco ding o ela i e alues o he inne dome po adius dpi o 0, 0.5,
0.75, and 0.95. The ou come is gi en in Fig. 4.11.
The a ia ion o he posi ion o e almos he en i e ange shows a la ge e ec on he e ac ion
and he L3/L1 a io. This can be desc ibed by a ans o ma ion om he ideal dome po in he
di ec ion o a la po , since he dome becomes ela i ely la e as he sou ce app oaches he
inside o he dome. Fo many con igu a ions, his in e media e ange will occu in eali y, due o
he space equi emen s o mul iple componen s in coo dina ion wi h he size o he dome po .
Fo example, he model shown in Fig. 4.32 exhibi s a dcs/ dpi a io o 0.65.
Re ac ion Index Va ia ion
The e ac ion index n2o he dome po and he wa e n3a e indi idually a ied in o de o
de e mine possible in luences. The esul s a e p esen ed in he o m o sec ions o he meaning-
ul a eas, see Figs. 4.12 and 4.13. Bo h he a ia ion o n2and n3show ha dly any e ec on
he e ac ion o θs o θ and he adiance a io L3/L1is in luenced o a small ex en , bu he
implica ions a e p ac ically negligible.
124 Chap e 4 UOWC Assemblies
0 10 20 30 40 50 60 70 80 90
0
10
20
30
40
50
60
70
80
90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Inciden angle 𝜽s [°]
Re ac ed angle 𝜽 [°]
L3 / L1
Sou ce posi ion
dcs=0
dcs=0.5 dpi
dcs=0.75 dpi
dcs=0.95 dpi
𝜽
Sou ce posi ion
dcs=0
dcs=0.5 dpi
dcs=0.75 dpi
dcs=0.95 dpi
Radiance a io L3 / L1
Figu e 4.11: Calcula ed e ac ion and adiance a io o a dome po . The sou ce
posi ion is adially a ied.
70 75 80 85 90
60
65
70
75
80
Inciden angle 𝜽s [°]
Re ac ed angle 𝜽 [°]
Po ma e ial
n2=1.4
n2=1.5
n2=1.6
0 5 10 15 20
1.2
1.25
1.3
Inciden angle 𝜽s [°]
Radiance a io L3 / L1
Po ma e ial
n2=1.4
n2=1.5
n2=1.6
Figu e 4.12: Calcula ed e ac ion and adiance a io o a dome po . The e ac ion
index o po ma e ial is a ied.
70 75 80 85 90
60
65
70
75
80
Inciden angle 𝜽s [°]
Re ac ed angle 𝜽 [°]
Wa e
n3=1.33
n3=1.34
n3=1.35
0 5 10 15 20
1.2
1.25
1.3
Inciden angle 𝜽s [°]
Radiance a io L3 / L1
Wa e
n3=1.33
n3=1.34
n3=1.35
Figu e 4.13: Calcula ed e ac ion and adiance a io o a dome po . The e ac ion
index o wa e is a ied.
4.2 Op ical Po s and Unde wa e Ligh Pa h 125
Dome Thickness Va ia ion
The las pa ame e o be al e ed in his se ies o examina ions is he dome po hickness dp. Wi h
a ange om 1 - 20 mm, his should co e he alues ound in eali y. Fo e e ence, a 100 mm
glass dome po speci ied o a 8000 m dep h has a wall hickness o only 7 mm. The esul s o
he calcula ions a e shown in Fig. 4.14. Again, only ela i ely mino e ec s a e con i med.
70 75 80 85 90
60
65
70
75
80
Inciden angle 𝜽s [°]
Re ac ed angle 𝜽 [°]
Po hickness
1 mm
7 mm
20 mm
0 5 10 15 20
1.2
1.25
1.3
Inciden angle 𝜽s [°]
Radiance a io L3 / L1
Po hickness
1 mm
7 mm
20 mm
Figu e 4.14: Calcula ed e ac ion and adiance a io o a dome po . The po hick-
ness is a ied.
B ie Re iew o Recei e Side
A di ec ion swap o he housing wi h a dome po o he ecei e side con igu a ion changes he di-
ec ion, he o de o he media, and he indices, bu he p inciples s ay he same. Figs. 4.15 and 4.16
show he ligh pa h o a cen e ed and a adially mo ed punc ual ecei e . The ideal si ua ion o
a cen e ed de ec o and inciden ays in a pe pendicula di ec ion o he dome su ace does no
cause e ac ion, hus θs=θ . The pa ame e s applied o calcula ions a e he same as be o e, see
Table 4.2. O cou se he wo media changes esul in ansmi ance and e lec ance alues, which
a e appa en ly equal o he ansmi e side, hus T13 o 95.7 % and R13 o 4.3 %. The same
applies o he calcula ed cons an adiance a io L3/L1o 0.957. The diag am o he ansmi e
side in Fig. 4.8 is he e o e also alid o he ecei e side.
Pa ame e a ia ions a he ecei e side a e only done o he de ec o posi ion, no o he
e ac ion indices no po hickness, due o mino e ec s only. Fo a simpli ied calcula ion he
po is assumed o be hin, hus θ2=θ0
2. The de ec o posi ion is adially a ied, while he
base pa ame e s (n1, n2, n3, dpi) a e kep cons an . Calcula ions a e made o cen e - o- ecei e
dis ances dc o 0, 25, 37.5 and 47.5 mm, acco ding o ela i e alues om he inne dome po
adius dpi o 0, 0.5, 0.75, and 0.95. The esul s o he e ac ed angle θ and he adiance a io
L3/L1as a unc ion o he inciden angle θsa e p esen ed in Fig. 4.17. The e ac ion o he
inciden angle θsde elops ela i ely linea and ge s s onge wi h inc easing dis ance om he
de ec o o he cen e . I ac s mo e and mo e simila o a la po , which would co espond o
dc = dpi. The adiance a io L3/L1is clea ly below 1 o inciden angles less han 40◦, and his
means he inciden ays a e widened. An imp ession o his is gi en in Fig. 4.18.
132 Chap e 4 UOWC Assemblies
LED
in
cen e De ec o
LED LED
o
cen e
LED
po ed dmeas
𝜃
Figu e 4.23: T ansmi e assemblies in di e en con igu a ions o unde wa e go-
niome e measu emen s.
side. An indoo basin was used, wi h a olume o abou 2 cubic me e s o il e ed esh wa e , he
co esponding e ac ion index hus esul s in n= 1.333. To a oid e lec ions om he sides o he
basin, he sand co e ed bo om and he wa e su ace, a geome y including a cen al posi ion and
a ela i e sho measu ing dis ance o dmeas = 267 mm was selec ed. This dis ance was kep he
same o all con igu a ions, and i was de ined o be be ween he LED die and he su ace o he
senso . A desc ip ion o he senso is gi en in Sec ion 5.3.2. Fo he in ended measu emen s his
i adiance senso , which ea u es a la ge FOV, needed o be econ igu ed o a adiance senso . This
can be done by adap ing a ube wi h an en ance hole including ligh ba les. The p incipal design
is desc ibed in [87]. The employed ube had a leng h o 100 mm and an en ance hole o 11.5 mm,
wi h a esul ing solid angle o app oxima ely 0.01 s . O cou se he o me i adiance calib a ion
is no longe alid, and i now ep esen s an uncalib a ed di ec ional adiance senso . Howe e , he
aluable p ope y o linea i y o e many decades emains, so p ecise a io measu emen s will s ill
be possible. Due o he s ong di ec ionali y, he senso is highly obus agains in e e ing ligh .
The oom ligh ing, o example, was only able o cause minimal dis u bances. To achie e he
esul ing angula cha ac e is ic o he ansmi e assembly i mus be o a ed. The pi o poin
o all housing con igu a ions was he LED die, see Fig. 4.23. The whole assembly was o a ed in
s eps up o 90◦deg ee on bo h sides, while he in ensi y was eco ded. The measu ing dis ance
om LED o senso was kep cons an , bu he pa h leng h h ough he wa e was a ied by he
po con igu a ion. The sho es dis ance was he dome po and sou ce in he cen e , he longes
was he p essu e-neu al po ed e sion. The a enua ion coe icien o he basin wa e could only
be es ima ed, since no measu emen s we e a ailable. I was assumed o be low, maybe no he
same as pu e wa e , bu a alue o c= 0.15 1/m should oughly i o he used wa eleng h. The
esul ing a enua ions showed only mino di e ences o less han 1 %, hus he occu ing e ec
could be neglec ed.

4.4 To al Cha ac e is ics o Assembly 133
Figu e 4.24: Unde wa e goniome e se up in he es basin.
4.4.2 Compa ison o Measu emen s and Calcula ions o T ansmi e Side
To ensu e he measu emen s o he di e en con igu a ions emained as compa able as possible,
he condi ions mus be kep he same. This p ima ily conce ns he sou ce, he mechanical se up,
he measu ing equipmen used and he media. The co esponding common pa ame e s a e gi en
in Table 4.3.
Table 4.3: De ices and gene al pa ame e s used o measu emen s and calcula ions.
LED Sou ce Ledengin LZ4
Wa eleng h, cen e λ525 [nm]
De ec o Gigahe z Op ic RW3703WQ
Me e Gigahe z Op ic P9710-4
Dis ance dmeas 267 [mm]
Re ac ion index, ai n11.0
Re ac ion index, wa e n31.333
Angula Dis ibu ion o LED Sou ce and Fla Po
The diag am in Fig. 4.25 shows he no malized in ensi y as a unc ion o he esul ing angle θ
o he ansmi e assembly, and he cu es om measu ed alues o he la po con igu a ion
in ai and unde wa e . The measu ed cu e o he sou ce wi hou any po in ai is also gi en as
e e ence. Fu he mo e, he calcula ed g aph o he unde wa e case is shown o compa ison, and
he applied equa ions a e desc ibed in Appendix C.7. Addi ional con igu a ion- ela ed pa ame e s
can be ex ac ed om Table 4.4.
The measu ed cu e and he calcula ed cu e o he la po unde wa e show a easonably
good ag eemen . Any inaccu acies in he dis ance dsp and he po n2 alue can be uled ou as he
cause o de ia ions, as hese ha e no e ec . The wa e n3 alue changes wi hin a ealis ic ange
and would ha e ha dly any e ec , howe e imp ecise angle adjus men s and mino measu ing
dis ance a ia ions on he goniome e would be possible.
134 Chap e 4 UOWC Assemblies
Table 4.4: Fla po pa ame e s.
Manu ac u e , spec. unkown
Re ac ion index, supposed n21.475
Thickness, la po p 9 [mm]
Dis ance, sou ce o po dsp 15 [mm]
0 10 20 30 40 50 60 70 80 90
0
0.2
0.4
0.6
0.8
1
Re ac ed angle 𝜽 [°]
No malized in ensi y
Measu emen s:
no po , in ai
la po , in ai
la po , unde wa e
Calcula ion:
la po , unde wa e
Figu e 4.25: Measu emen s o an LED sou ce wi h and wi hou la po , in ai and
unde wa e , and a calcula ed cu e o la po unde wa e con igu a ion
is added o compa ison.
Angula Dis ibu ion o LED Sou ce and Dome Po
The diag ams in Figs. 4.26 and 4.27 gi e he no malized in ensi y as a unc ion o he esul ing
angle θ o he ansmi e assembly, as cu es om measu ed alues o he dome po con ig-
u a ion in ai and unde wa e , and in each case o wo sou ce posi ions, one a he cen e as
well as one a he hal inne dome adius. The measu ed cu e o he sou ce wi hou any po
in ai is also p esen ed o e e ence. Fu he mo e, he calcula ed g aphs o he unde wa e case
a e shown o compa ison, and he applied equa ions a e desc ibed in Appendix C.8. Addi ional
con igu a ion- ela ed pa ame e s can be ga he ed om Table 4.5. The measu ed cu e and he
calcula ed cu e o he dome po unde wa e o a cen e ed sou ce a e almos iden ical, as well
as he cu es in ai .
The measu ed cu e and he calcula ed cu e o he dome po unde wa e including he sou ce
posi ioned on he hal inne adius a e ela i ely close o each o he . Inaccu acies o he h ee
e ac ion indices and he po hickness only exhibi mino e ec s. The mos p obable cause o
he de ia ions is he inaccu a e se ing o he dis ance dome cen e o he sou ce dcs. Imp ecise
angle adjus men s and mino measu ing dis ance a ia ions on he goniome e can also no be
excluded.
4.4 To al Cha ac e is ics o Assembly 135
Table 4.5: Dome po pa ame e s.
Manu ac u e , spec. Vi o ex, 8000m
Glass, ype Bo osilica e 3.3
Re ac ion index, 525 nm n21.475
Thickness, dome po dp 7 [mm]
Radius, inne dpi 50 [mm]
Dis ances, cen e o sou ce dcs 0, 25 [mm]
0 10 20 30 40 50 60 70 80 90
0
0.2
0.4
0.6
0.8
1
Re ac ed angle 𝜽 [°]
No malized in ensi y
Measu emen s:
no po , in ai
dome po , in ai
dome po , unde wa e
Calcula ion:
dome po , unde wa e
Figu e 4.26: Measu emen s o a cen e ed LED sou ce, wi h and wi hou a dome po ,
in ai and unde wa e , and a calcula ed cu e o dome po unde wa e
con igu a ion is added o compa ison.
0 10 20 30 40 50 60 70 80 90
0
0.2
0.4
0.6
0.8
1
Re ac ed angle 𝜽 [°]
No malized in ensi y
Measu emen s:
no po , in ai
dome po , in ai
dome po , unde wa e
Calcula ion:
dome po , unde wa e
Figu e 4.27: Measu emen s o an LED sou ce posi ioned on he hal adius o cen e ,
wi h and wi hou a dome po , in ai and unde wa e , and a calcula ed
cu e o dome po unde wa e con igu a ion is added o compa ison.
136 Chap e 4 UOWC Assemblies
Angula Dis ibu ion o LED Sou ce in P essu e-Neu al Cas
The diag ams in Figs. 4.28 and 4.29 gi e he no malized in ensi y as a unc ion o he esul ing
angle θ o he ansmi e assembly, as cu es om measu ed alues o he p essu e-neu al
cas ed con igu a ion wi h and wi hou he e lec o , and also in ai and unde wa e . The measu ed
cu es o he unpo ed sou ce in ai wi h and wi hou e lec o a e also p esen ed o e e ence.
Calcula ed cu es o compa ison a e omi ed. Addi ional con igu a ion- ela ed pa ame e s can
be ga he ed om Table 4.6.
Since a compa ison o measu ed and calcula ed cu es o he p essu e-neu al cas ed e sions
unde wa e is no possible, a leas i is possible o compa e he cu es in ai . In o de o
demons a e he in luence o he po ing, in addi ion o he ba e LED equipped ansmi e
measu emen s, some expe imen s we e also ca ied ou o a a ian equipped wi h a e lec o . A
sligh in luence o he cas ing can be seen, and i is mo e p onounced in he ba e LED e sion
han in he e lec o -equipped e sion. Based on he expe ience gained om he measu emen s o
many o he po ed LED- e lec o combina ions, hese wo examples can be conside ed ypical.
Table 4.6: P essu e-neu al cas pa ame e s.
Manu ac u e , ype In e col 5435
Ma e ial Polyu e hane
Re ac ion index n1.48
Thickness, es im. pnc 1 [mm]
0 10 20 30 40 50 60 70 80 90
0
0.2
0.4
0.6
0.8
1
Re ac ed angle 𝜽 [°]
No malized in ensi y
Measu emen s:
LED wi hou e lec o
unpo ed, in ai
po ed, in ai
po ed, unde wa e
Figu e 4.28: Measu emen s o a ba e LED, wi h and wi hou p essu e-neu al cas ,
and in ai and unde wa e .
4.4 To al Cha ac e is ics o Assembly 137
0 10 20 30 40 50 60 70 80 90
0
0.2
0.4
0.6
0.8
1
Re ac ed angle 𝜽 [°]
No malized in ensi y
Measu emen s:
LED including e lec o
Ca clo 10255
unpo ed, in ai
po ed, in ai
po ed, unde wa e
Figu e 4.29: Measu emen s o an LED including e lec o , wi h and wi hou p essu e-
neu al cas , and in ai and unde wa e .
In ensi y Ra ios o he Examined Combina ions
The sou ce adiance L1and he ansmi ed adiance L3o he po equipped housings a e loca ed
in di e en media, in ai and in wa e . The e o e absolu e measu emen s would need di e en ly
calib a ed senso s. As hese we e no a ailable, and only an uncalib a ed senso modi ied o
adiance could be applied, i was necessa y o swi ch o he use o a ios. The measu emen s
o he la po , he dome po wi h sou ce a hal inne adius, and he p essu e-neu al po ed
e sion we e no malized o he measu emen o he cen e ed dome po con igu a ion. The easons
o his a e he ideal p ope ies wi hou angula e ac ion and a cons an magni ude o e lec ion.
Fo compa ison, he ela i e ansmi ed adiances o he po e sions we e also calcula ed, based
on he ela i e angula in ensi y dis ibu ion o he LED in ai and he pa ame e s p e iously used.
Due o he magni ica ion e ec o he la po and he dome po wi h a non-cen e ed sou ce,
a calcula ion o he appa en shi o he sou ce posi ion is needed, c . Appendices C.7 and C.8.
This shi and he measu ing dis ance p o ide he co ec ion ac o ia he in e se squa e law. The
calcula ed adiance alues a e also subjec o no maliza ion o alues om he cen e ed dome po
con igu a ion. The cu es in Fig. 4.30 depic he adiance a ios as a unc ion o he esul ing angle
θ om ansmi e assemblies in di e en e sions o unde wa e ope a ion. Measu ed a ios a e
compa ed o calcula ed a ios in he meaning ul ange o θ om 0◦ o 25◦. The measu ed and
calcula ed cu es ha e he expec ed o de o magni ude and show easonable ag eemen . The cause
o he de ia ions a e p obably ela ed o unce ain ies in he se ing o he dis ances, mainly he
sou ce o po posi ioning and he dis ance om he sou ce o he de ec o . As wi h he p e ious
measu emen s in his sec ion, impac s o angula inaccu acies and inco ec e ac ion indices a e
es ima ed o be mino . Non-linea i y o he senso and supply o empe a u e- ela ed d i e ec s
o he LED should be negligible.
Due o he high ele ance o he dome po and he good ans e abili y o many p ac ical
applica ions, a se o cu es o adially a ied sou ce posi ions om he cen e o nea he dome
inne su ace is gi en in Fig. 4.31. The espec i e calcula ions a e based on same sou ce and dome
po pa ame e s as used p e iously, including an LED Ledengin LZ4 wi hou e lec o and alues
gi en in Table 4.5. The cu es a e no malized o he ini ial adiance o he LED a 0◦. I is clea ly
isible ha he LED pa e n becomes na owe and he in ensi y inc eases wi h g owing dis ance
o he sou ce om he cen e . The cha ac e is ic changes om he ideal dome po o he la

138 Chap e 4 UOWC Assemblies
0 5 10 15 20 25
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Re ac ed angle 𝜽 [°]
Radiance a io
Fla po
calcula ed
measu ed
Dome po
(sou ce a hal inne adius)
calcula ed
measu ed
P essu e neu al cas
measu ed
Radiance a ios ela i e o
dome po wi h cen e ed
sou ce
Figu e 4.30: Radiance a ions o ansmi e assemblies in di e en con igu a ions,
including measu ed and calcula ed cu es.
po .
0 10 20 30 40 50 60 70 80 90
0
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
Re ac ed angle 𝜽 [°]
Rela i e adiance
Dome po
dpi = 50 mm, dp = 7 mm
LED LZ4 sou ce
(sou ce nea po )
dcs = 0.95 dpi
dcs = 0.85 dpi
dcs = 0.70 dpi
dcs = 0.50 dpi
dcs = 0.25 dpi
dcs = 0
(sou ce in cen e )
Figu e 4.31: Calcula ed angula adiance p og ession, o an LED sou ce in dome po
con igu a ion unde wa e , wi h he sou ce posi ion a ied om he cen e
o he nea po inne su ace.
4.4 To al Cha ac e is ics o Assembly 139
4.4.3 Implica ions o Measu emen s, Design and Implemen a ion
Imp o emen P oposals o Measu emen s
The conduc ed expe imen s ha e shown good ag eemen o he calcula ions. Howe e , ce ain
simpli ica ions we e no applied, such as he hin po assump ion, omi ing he shi o an appa -
en posi ion, and he use o gene al e ac ion indices. Con e sely, his means ha he pa ame e s
mus be known and he p inciples mus be applied in-dep h. Accu a ely acqui ing dimensions
and p ope ies such as nea ield cha ac e is ic can be associa ed wi h di icul ies. The e o e,
measu emen s a e an essen ial elemen in addi ion o calcula ions.
Based on he expe ience gained, a numbe o imp o emen s can be de i ed. This includes
an o e all highe p ecision o he goniome e se up, exac o a ional adjus abili y, and co ec
dis ance se ings and igid ca ie s. Since o a ional symme y canno always be assumed, an
axial o a abili y o he assembly unde es is essen ial o h ee-dimensional measu emen s o
de e mine he ansi ion zones in mul iple segmen ed se ups. Fu he mo e, access o calib a ed
senso s o absolu e measu emen s in ai and unde wa e would be desi able. To ex end he
capabili ies o he measu emen s o ecei e assemblies, an unde wa e e e ence ligh sou ce is
necessa y. In addi ion, a la ge-dimensioned basin is desi able o p o ide inc eased measu emen
dep hs and dis ances, including wa e pa ame e con ol.
Conside a ions o Assembly Design
Unde wa e housings o op ical applica ions a e subjec o many selec ion c i e ia as gi en in
Sec ion 4.1.1, and one o he majo c i e ia is he op ical usable ield, which depends on he
in ended applica ion. In he case o UOWC, we ind a ce ain beam angle on he ansmi e side
and a ce ain FOV on he ecei e side, and bo h conically shaped as solid angles. The equi ed
size o hese angles can be de i ed om unde wa e ope a ion scena ios. Besides he di ec ion,
he communica ion dis ance and he wa e p ope ies a e also o signi icance. Since ehicles a e
in ol ed in mos scena ios, as p esen ed in Fig. 1.1, he e a e cons ain s associa ed wi h his.
These include: minimum dis ances o a oid collision damage o ge ing caugh , minimum speeds
o non-ho e ing ehicles, and posi ioning accu acy. The UOWC echnique, moun ed on ixed
s uc u es, mainly ep esen s only one side o he communica ion pa ne . F om he abo e sec ion,
i can be concluded ha na ow angles, o a he solid angles, which can be ela ed o poin ing
and acking p oblems, should only a ely be used. Wide (solid) angles, s a ing om a ew ens
o deg ees up o hemisphe es o sphe es, a e equi ed o many applica ions. This indica es ha
he la po is sui able o ewe applica ions compa ed o he dome po . The ideal p ope ies
o he dome po a e inc easingly los as he size o he op ical and elec onic componen s g ows.
The p essu e-neu al cas o e s many possibili ies in op ical aspec s, bu has limi a ions in o he
a eas.
Finally, he housing including he op ical po o al e na i ely any po ed o m ha a e me ged
wi h he LED, o espec i ely he PD, a e combined wi h addi ional op ical elemen s in an as-
sembly esul ing in i s own cha ac e is ics. The e o e, no only he ini ial p ope ies o he LED
and PD a e impo an , bu also hose o he componen s in he op ical pa h. These il e s and
concen a o s o a ious kinds and numbe s may gene a e addi ional media ansi ions. La ge
changes in he e ac i e index should be a oided, as hese can lead o o al e lec ion depending
on he di ec ion. A glass-ai ansi ion, as wi h a la po in on o a PD o example, can
esul in a o al e lec ion a an inciden angle o 45◦. Special angula cha ac e is ics o il e s in
e ms o he AOI, o e lec o s in e ms o he nea - ield, and o lenses o ecei e s in e ms o
wande ing ocal poin s also need o be conside ed. Gene al in o ma ion and new app oaches o
concen a o s concep s a e gi en in [79, 205, 206, 207], and he il e s a e discussed in Sec ion 3.2.
In addi ion o he cons ain s wi h espec o shape and olume o single-colo LEDs, concen a-
o s, la ge-a ea pho ode ec o s and op ical bandpass il e s, he e is ano he aspec o a gene al
140 Chap e 4 UOWC Assemblies
na u e, he selec ion is comp omised by a limi ed p oduc ange in hese segmen s.
Implemen a ion o Mul iple Segmen ed T ansduce s
Based on a gene al need o la ge solid angles, his equi emen can be oughly di ided in o wo
ca ego ies. The i s is a hemisphe ical space in he UOWC zone, as wi h ships and buoys di ec ed
downwa ds om he su ace, and complemen a y o lande s and c awle s di ec ed upwa ds om
he sea loo . The second is an in o al sphe ical cha ac e is ic in he case o AUVs and nodes in he
middle o he wa e column. A he same ime, he e a e limi a ions on bo h he ansmi e and
he ecei e sides. The e a e powe cons ain s ega ding he LED ansmi e due o he igh
ene gy budge o ba e y powe ed sys ems such as AUVs, which a e di ec ly linked o he c ucial
ope a ing du a ion. Pho ode ec o s used on he ecei e side equi e ambien ligh supp ession
il e s, hese can ha e la ge in luence on he ield o iew. In summa y, i leads o he di ision
in o a numbe o segmen s ha indi idually yield es ic ions and in o al mee he demand.
Implemen a ion o he UOWC ansmi e in o o as a sphe e is possible in p inciple, bu has
disad an ages in he ield such as pa ial blocking by he ehicles hull o shadowing o ins o
an ennas. Fu he mo e, a aised moun ed o owed UOWC de ice would be exposed o a g ea e
isk o collision du ing ope a ion and would be imp ac ical o deploymen and eco e y. A solu ion
o his is spli ing he sys em in o on - ea , uppe -lowe , o le - igh uni s.
The simul aneous use o sepa a e neighbo ing sec o s enables he possibili y o applying MIMO
echnology o one o he sub- ypes, see Sec ion 2.1.6. C ea ing mul iple channels also equi es
mo e ha dwa e, hus mo e olume is needed, and an ins alla ion in o nea he swee spo o he
dome po is becoming inc easingly di icul . Ene ge ically, he main ad an age is ha unused
ansmi ing sec o s can be swi ched o . In he composi ion o a de ined sphe e segmen om
se e al solid angles, gaps o minima a e o med. Fo example, o achie e a ela i ely uni o m
hemisphe ical cha ac e is ic by combining a numbe o conical sec o s, whe he om ansmi ing
elemen s bounded by he beam angle, o om ecei ing elemen s bounded by he FOV, dis inc
o e lapping zones would be c ea ed au oma ically. An example: o o m a hemisphe ical co e age
om solid angles o 0.842 s each, which co esponds o 60◦, including an o e lap o 30 % esul s
in 10 elemen s.
Fac ually, his leads o dome po s wi h a diame e in he o de o 100 mm. An own ansduce
model and a ansmi e head a e shown in Fig. 4.32. Comme cial p oduc s, al hough a e, exhibi
he same o m ac o , see Table 1.2. O cou se, his opic can also be ound in he li e a u e; one o
he i s implemen a ions including a hemispe ical LED emi e and PMT is desc ibed by Fa e
al. [157]. Baiden in oduced an omni-di ec ional op ical ansmi e in [208]. An UOWC ci cula
anscei e and a node concep a e shown in [40]. Simpson e al. demons a ed segmen ed sma
UOWC ansmi e s and ecei e s in [30]. An FSO ecei e wi h o e lapping FOV is discussed in
[209], and a hemispe ical ee o m lens o UOWC is p oposed in [210].
4.5 Chap e Summa y 141
Figu e 4.32: Le : Model o ansduce u ilizing a 100 mm dome po and comp ising
9 pcs. la ge a ea PD and 9 LED elemen s. Righ : P essu e-neu al po ed
ansmi e head o 95 mm diame e , including 4 segmen s o each 4 powe
LEDs and d i e ci cui s.
4.5 Chap e Summa y
In his chap e , assemblies o UOWC ha e been examined in e ms o hei op ical p ope ies.
The main concep s behind housings as indispensable componen s ha e been p esen ed, including
gene al selec ion c i e ia. Rela ed hea and in eg a ion issues ha e been indica ed. The op ical
window is an in eg al pa o he housing, and in mos cases so-called la po s o dome po s
a e applied. The ma e ial o hese po s is ypically glass o syn he ics, which leads o e ac ion
indices o 1.4 o 1.6, hus signi ican ly di e en han he indices o 1.0 o ai and 1.34 o wa e .
Independen o sou ce o ecei e side, ligh ays ha e o pass a leas wo media bounda ies,
which esul s in e ac ion. Snell’s law mus be applied he e, and he F esnel’s equa ions o
ansmi ance and e lec ance. To exp ess he di ec ion and he amoun o ligh , he adiance
concep is u ilized, including he ’n2law o adiance’. Calcula ions in his espec ha e been
execu ed o la and dome po s, bo h o he ansmi e and he ecei e sides. The la and he
dome po s exhibi signi ican ly di e en cha ac e is ics, and a ia ions o he e ac ion indices
and he po hickness show only mino e ec s. The posi ion o a sou ce o de ec o wi hin he
dome po plays a c ucial ole. Placemen in he cen e , in he so-called ’swee spo ’, leads o an
almos ideal neu al beha io . Radial displacemen owa ds he dome inne su ace esul s in a
ansi ion o la po cha ac e is ics.
T anspa en embedded componen s can ep esen an al e na i e o he common p essu e hous-
ing and po combina ions. This special design has ad an ages and disad an ages, bu allows o
a a ie y o makes, so i is di icul o gene alize.
The o al cha ac e is ic o eal assemblies has also been examined. Fo his pu pose, goniome ic
measu emen s in a es basin we e execu ed. The same powe LED including a p ima y op ic was
ope a ed in a la po housing, in a dome po housing a di e en posi ions, and as a po ed
de ice. The measu ed angula dis ibu ions o hese cases, each unde wa e and in ai , we e
compa ed o calcula ions. Fo he dome and la po s he ou comes we e as expec ed and showed
good ag eemen . Fo he cas ed LED, wi h and wi hou a e lec o , i was seen ha he cas
caused only mino changes. The di e ence be ween measu ed and calcula ed adiance a ios a e
small.
Conce ning he assembly design in he UOWC, he ollowing can be ex ac ed: in mos cases a
hemisphe ical cha ac e is ic is a o ed, bu he a ainable beam angels o FOVs o single elemen s