E icien comp ession o F esnel ields o In e ne
ansmission o h ee-dimensional images
Thomas J. Naugh on,1John B. Mc Donald,1Bah am Ja idi2
1Depa men o Compu e Science, Na ional Uni e si y o I eland, Maynoo h,
Coun y Kilda e, I eland
2Depa men o Elec ical and Compu e Enginee ing, Uni e si y o Connec icu ,
U-157, S o s, CT 06269, USA
1
Abs ac . We comp ess phase-shi digi al holog ams (whole F esnel ields)
o he ansmission o h ee-dimensional images. Fo eal- ime ne wo king
applica ions, he ime equi ed o comp ess can be as c i ical as comp ession
a e. We achie e lossy comp ession h ough quan iza ion o bo h he eal and
imagina y s eams, ollowed by a bi packing ope a ion. Comp ession losses
in he econs uc ed objec s we e quan i ied. We de ine a speedup me ic
ha combines space gains due o comp ession wi h empo al o e heads
due o comp ession ou ine and ansmission se ializa ion. We empi ically
e i y ansmission speedup due o comp ession, using a special-pu pose
In e ne -based ne wo king applica ion. c
°2003 Op ical Socie y o Ame ica
OCIS codes: 90.1760 Compu e holog aphy, 100.6890 Th ee-dimensional image
p ocessing, 999.9999 Da a comp ession, 100.2000 Digi al image p ocessing, 100.0100
Image p ocessing
1. In oduc ion
Digi al holog aphy1–9 is one o se e al possible echniques o h ee-dimensional (3D)
imaging.10 Many exis ing 3D imaging and p ocessing echniques a e based on he
explici combina ion o se e al 2D pe spec i es (o ligh s ipes, e c.) h ough digi al
image p ocessing. Mul iple pe spec i es o a 3D objec can be combined op ically,
in pa allel, and s o ed oge he as a single complex- alued digi al holog am. Digi-
al holog aphy has seen enewed in e es wi h he ecen de elopmen o megapixel
digi al senso s wi h high spa ial esolu ion and dynamic ange. Thei digi al na u e
means ha hese holog ams a e in a sui able o m o p ocessing o ansmission.
2
We eco d in-line digi al holog ams, eco e he whole F esnel ield using a echnique
called phase-shi in e e ome y3,6,8 (PSI), and in oduce a hi d s ep, ha o dig-
i al comp ession and decomp ession.11 Each F esnel ield encodes mul iple iews o
he objec om a small ange o angles. Di e en pe spec i es o he objec can be
econs uc ed by ex ac ing app op ia e egions12, 13 om he ield and applying a nu-
me ical p opaga ion echnique.7–9 Real- ime op ical econs uc ion echniques ha e
also been demons a ed.14,15
Ou digi al F esnel ields ha e dimensions 2028 ×2044 pixels and in hei na-
i e o ma s o e 8 by es o ampli ude in o ma ion and 8 by es o phase in o ma ion
o each pixel. We would like o comp ess16 hese ields o mo e e icien s o age
and ansmission. Comp ession o F esnel ields (and digi al holog ams in gene al)
di e s o image comp ession p incipally because ou ields s o e 3D in o ma ion in
complex- alued pixels, and secondly because o he inhe en speckle con en which
gi es hem a whi e-noise appea ance. I is no a s aigh o wa d p ocedu e o emo e
he holog aphic speckle because i ac ually ca ies 3D in o ma ion. The noisy appea -
ance o digi al F esnel ields, and digi al holog ams in gene al, causes lossless da a
comp ession echniques (such as Lempel-Zi -Welch, Hu man, and Bu ows-Wheele )
o pe o m poo ly.11 The use o lossy comp ession echniques seems essen ial. Digi-
al holog am comp ession echniques based on Fou ie -domain p ocessing ha e been
demons a ed.11,17 These block-based echniques end o in oduce localized noise a
he bounda ies o nono e lapping blocks. A wa ele -based echnique migh be mo e
e ec i e. Ding e al.18 pe o m comp ession o digi al holog ams h ough wa ele de-
composi ion and selec ion o he p incipal wa ele basis componen s app op ia e o
3
hei pa e n ecogni ion applica ion. Liebling e al.19 ha e de eloped a wa ele -based
econs uc ion echnique o digi al holog ams. A cou se-scale econs uc ion o some
wa ele -domain quan iza ion in hei scheme could also o m he basis o a noise
emo al and/o comp ession echnique.
In his pape , we apply quan iza ion di ec ly o he complex- alued pixels. Quan-
iza ion and phase quan iza ion ha e been applied success ully o Fou ie and holo-
g aphic da a in he pas .11, 17, 20, 21 We apply a wo-s age comp ession echnique based
on complex-domain quan iza ion and bi packing. This in oduces a hi d eason why
comp ession o F esnel ields (and digi al holog ams in gene al) di e s o comp es-
sion o digi al images; a change locally in a F esnel ield will, in heo y, a ec he
whole econs uc ed objec . We a e no in e es ed in how comp ession noise a ec s
he decomp essed F esnel ield i sel , only how comp ession noise a ec s subsequen
objec econs uc ion. In his pape , we use a econs uc ed-objec -plane RMS me ic
o quan i y he quali y o ou decomp essed F esnel ields.
Comp ession will pe mi F esnel ields o be s o ed mo e e icien ly. In e ms o
hei ansmission, howe e , he e is a leas one o he p ope y ha should be e al-
ua ed when compa ing comp ession s a egies. We need o know he ime i akes,
ela i e o he ansmission ime, o comp ess and uncomp ess he ield in o de o
decide on a comp ession mechanism o ansmission. In pa icula , i migh no e en
be ad an ageous o comp ess he da a p io o ansmission i he la ency caused
by he comp ession ou ine is signi ican ela i e o he a e age uncomp essed ans-
mission ime. We conside he case whe e i is no possible o comp ess he da a in
ad ance, o example in a eal- ime imaging and ansmission applica ion. We use a
4
measu e called speedup o quan i y he e ec i eness o ou comp ession echnique in
e ms o bo h space and ime esou ces. Ou da a is ob ained using a special-pu pose
eely-accessible In e ne applica ion ha , h ough he in eg a ion o comp ession and
ansmission ou ines in o a single applica ion, was able o eliably measu e comp es-
sion ime ela i e o ansmission ime.
In Sec . 2, we desc ibe how he ully-complex F esnel ields a e cap u ed using
PSI. The ne wo king sys em is de ailed in Sec . 3, and he comp ession algo i hm
and comp ession pe o mance in Sec . 4. Finally, in Sec . 5, we p esen he esul s o
speedup expe imen s pe o med wi h an implemen a ion o he ne wo king sys em.
2. Phase-shi digi al holog aphy
We eco d F esnel ields wi h an op ical sys em based on a Mach-Zehnde in e e om-
e e (see Fig. 1). A linea ly pola ized A gon ion (514.5 nm) lase beam is expanded
and collima ed, and di ided in o objec and e e ence beams. The objec beam illu-
mina es a e e ence objec placed a a dis ance o app oxima ely d= 350 mm om a
10-bi 2028 ×2044 pixel Kodak Megaplus CCD came a. Le U0(x, y) be he complex
ampli ude dis ibu ion immedia ely in on o he 3D objec . The linea ly pola ized
e e ence beam passes h ough hal -wa e pla e RP1and qua e -wa e pla e RP2. This
beam can be phase-modula ed by o a ing he wo e a da ion pla es. Th ough pe -
mu a ion o he as and slow axes o he pla es we can achie e phase shi s o 0,
−π/2, −π, and −3π/2. The e e ence beam combines wi h he ligh di ac ed om
he objec and o ms an in e e ence pa e n in he plane o he came a. A each o
he ou phase shi s we eco d an in e e og am. We use hese ou eal- alued im-
5

ages o compu e he came a-plane complex ield by PSI.3,8 We call he came a-plane
complex ield he F esnel ield, and deno e i H0(x, y). F esnel ields cap u ed using
his a chi ec u e ha e hemsel es been e e ed o as digi al holog ams,9,22–24 gi en a
gene alized de ini ion o he e m holog am.
A F esnel ield H0(x, y) con ains su icien ampli ude and phase in o ma ion o
econs uc he complex ield U(x, y, z) in a plane in he objec beam a any dis ance
z om he came a. This can be calcula ed om he F esnel app oxima ion13 as
U(x, y, z) = −i
λz exp µi2π
λz¶H0(x, y)?exp "iπ(x2+y2)
λz #,(1)
whe e λis he wa eleng h o he illumina ion and ?deno es a con olu ion ope a ion.
A z=d, and igno ing e o s in digi al p opaga ion due o disc e e space (pixela ion)
and ounding, he disc e e econs uc ion U(x, y, z) closely app oxima es he physical
con inuous ield U0(x, y).
Fu he mo e, as wi h con en ional holog aphy,12,13 a windowed subse o he F es-
nel ield can be used o econs uc a pa icula iew o he objec . As he window
explo es he ield a di e en angle o iew o he objec can be econs uc ed. The
ange o iewing angles is de e mined by he a io o he window size o he ull CCD
senso dimensions. Ou CCD senso has app oxima e dimensions o 18.5×18.5 mm
and so a 1024 ×1024 pixel window has a maximum la e al shi o 9 mm ac oss he
ace o he senso . Wi h an objec posi ioned d= 350 mm om he came a, iewing
angles in he ange ±0.74◦a e pe mi ed. Smalle windows will pe mi a la ge ange
o iewing angles a he expense o image quali y a each iewpoin .
6
3. Ne wo k
We can e alua e comp ession algo i hms in e ms o bo h space and ime esou ce
usage by using a measu e called speedup. Speedup sis de ined as s=Pu/Pcwhe e Pu
is he ime equi ed o p ocess and ansmi he uncomp essed F esnel ield and Pcis
he ime equi ed o p ocess, and ansmi he comp essed ield. In o de o measu e
speedup o a comp ession sys em ha esides o e a public wide-a ea ne wo k we
ha e ound ha he ollowing h ee equi emen s should be me . Fi s ly, due o he
empo al luc ua ions in bandwid h o e wide-a ea ne wo ks, i is necessa y o a e age
o e a la ge numbe o iming measu emen s. Secondly, in o de o accu a ely measu e
comp ession and decomp ession imes, he comp ession ou ines should be emo ed
om hei con olled p o o yping en i onmen and execu ed in a eal-wo ld se ing.
Finally, bo h he ne wo king so wa e and comp ession so wa e should be in eg a ed
so ha meaning ul conclusions can be d awn om he ela i e pe o mance o he
ansmission and comp ession componen s o he sys em.
We ha e cons uc ed an In e ne -based F esnel ield comp ession applica ion in
o de o measu e eliably and accu a ely he in e ac ion be ween comp ession imes
and ansmission imes. This clien -se e applica ion and associa ed comp ession
algo i hms we e w i en wi h Ja aTM (Sun Mic osys ems, Inc). This allowed us o
de elop a pla o m-independen en i onmen o expe imen a ion o e he In e ne .
Pla o m-independence ensu es ha he sys em suppo s any a chi ec u e ha uns
a Ja a i ual machine, and is sui able o he e ogeneous en i onmen s ( he se e
needs no knowledge o a clien ’s compu e a chi ec u e o ope a ing sys em o com-
7
munica e). As such, we ensu e as much as possible he epea abili y and ele ance o
ou esul s o a wide ange o In e ne se -ups.
An o e iew o he ope a ion o he ne wo king applica ion is shown in Fig. 2.
Mul iple clien s, h ough hei use in e aces, access he se e and eques pa icu-
la iews o 3D objec s s o ed as F esnel ields. The se e esponds by p o iding he
app op ia e window o pixels, and he clien s econs uc iews o he 3D objec s lo-
cally. To build he communica ion componen o he clien -se e applica ion we used
Ja a’s emo e me hod in oca ion (RMI) acili ies. RMI allows applica ions unning
on di e en machines o communica e wi h each o he in an e icien and anspa en
manne . Cen al o p o iding his ease o communica ion is Ja a se ializa ion. The
e m se ializa ion e e s o he packaging o ola ile da a-s uc u es in o pe sis en
bi -s eams which can hen be w i en o pe manen s o age o ansmi ed ac oss
a communica ions link. Ou clien -se e sys em unc ions o e any ne wo k (local,
wide, wi eless) ha suppo s IP (In e ne P o ocol).
The in e nal ope a ion o he clien s and se e om Fig. 2 a e shown in Fig. 3.
A eques o a pa icula iew o a pa icula 3D objec is passed om he use
in e ace, h ough he clien , o he se e (s age 0 in Fig. 3). The se e ex ac s he
app op ia e window om he F esnel ield s o ed on disk (s age 1), and o ma s he
ield o ansmission (s age 2). Ja a is an objec -o ien ed language. As such, F esnel
ields a e s o ed as gene alized holog am objec s, in a da a o ma ha allows e icien
manipula ion by specialized complex- alued digi al holog am p ocessing algo i hms,
and comple e wi h he unc ionali y o ead/w i e hem om/ o disk, display hem,
and econs uc hei 3D objec s. Fo ma ing is equi ed o s eamline he holog am
8
objec o ansmission, by emo ing all unc ionali y and con e ing he ield da a
in o wo compac 1D a ays o eal and imagina y alues. The ield is comp essed
(s age 3) o a s eam o by es as explained in Sec . 4. The pa icula comp ession
algo i hm and comp ession pa ame e s o be employed by he se e a e speci ied by
he clien a s age 0.
In s ages 4 and 5 he comp essed F esnel ield da a is se ialized and ansmi ed.
The se e collec s iming in o ma ion ( ime o ead om disk, o ma , and comp ess)
and ansmi s his wi h he ield. The se e esponds o he clien h ough a dedica ed
communica ion channel ha is se up h ough RMI, and closed immedia ely a e -
wa ds. The clien , on eceip o he ield da a, pe o ms a dese ializa ion ope a ion
(s age 6) and decomp esses he by e s eam as explained in Sec . 4. The un o ma -
ing ope a ion con e s he sepa a e eal and imagina y a ays o ield da a in o a
holog am objec ha has he unc ionali y o be p opaga ed nume ically and/o dis-
played as an in ensi y image a he use in e ace (s ages 7 h ough 10). Once again,
imings a e aken by he clien o each o i s ope a ions. The clien -side in e ace o
he iming applica ion is shown in Fig. 4. Ou In e ne -based F esnel ield/holog am
comp ession and iming applica ion is accessible online.25
4. Comp ession
In ou expe imen s, he F esnel ield window was comp essed by he se e (s age 3
in Fig. 3) using a wo-s ep p ocess. The ield da a was i s quan ized a a pa icula
esolu ion and hen comp essed using a bi packing echnique. Each pixel o he ield
da a equi ed wo da a alues ( eal, imagina y). Quan iza ion le els we e chosen o be
9
Technologies, Sp inge , Be lin, 2002.
11. T. J. Naugh on, Y. F auel, B. Ja idi, and E. Tajahue ce, “Comp ession o digi al
holog ams o h ee-dimensional objec econs uc ion and ecogni ion,” Appl.
Op . 41, 4124–4132, 2002.
12. H. J. Caul ield, ed., Handbook o Op ical Holog aphy, Academic P ess, New Yo k,
1979.
13. J. W. Goodman, In oduc ion o Fou ie Op ics, McG aw-Hill, New Yo k, sec-
ond ed., 1996.
14. M. Su kowski and M. Kujawinska, “Applica ion o liquid c ys al (LC) de ices o
op oelec onic econs uc ion o digi ally s o ed holog ams,” Op ics and Lase s
in Enginee ing 33, 191–201, 2000.
15. O. Ma oba, T. J. Naugh on, Y. F auel, N. Be aux, and B. Ja idi, “Real- ime
h ee-dimensional objec econs uc ion by use o a phase-encoded digi al holo-
g am,” Appl. Op . 41, 6187–6192, 2002.
16. M. Rabbani, ed., Selec ed Pape s on Image Coding and Comp ession, SPIE Mile-
s one Se ies ol. MS48, SPIE P ess, Bellingham, Washing on, 1992.
17. T. Nomu a, A. Okazaki, M. Kameda, Y. Mo imo o, and B. Ja idi, “Digi al holo-
g aphic da a econs uc ion wi h da a comp ession,” Algo i hms and Sys ems o
Op ical In o ma ion P ocessing V, P oceedings o SPIE ol. 4471, 235–242, (San
Diego, Cali o nia), 2001.
18. L. Ding, Y. Yan, Q. Xue, and G. Jin, “Wa ele packe comp ession o olume
holog aphic image ecogni ion,” Op . Comm. 216, 105–113, 2003.
16

19. M. Liebling, T. Blu, and M. Unse , “F esnele s: new mul i esolu ion wa ele bases
o digi al holog aphy,” IEEE T ansac ions on Image P ocessing 12, 29–43, 2003.
20. J. W. Goodman and A. M. Sil es i, “Some e ec s o Fou ie domain phase quan-
iza ion,” IBM J. Res. De elop. 14, 478–484, 1970.
21. W. J. Dallas and A. W. Lohmann, “Phase quan iza ion in holog ams,” Appl. Op .
11, 192–194, 1972.
22. E. Tajahue ce, O. Ma oba, and B. Ja idi, “Shi -in a ian h ee-dimensional ob-
jec ecogni ion by means o digi al holog aphy,” Appl. Op . 40, 3877–3886, 2001.
23. Y. F auel, E. Tajahue ce, M.-A. Cas o, and B. Ja idi, “Dis o ion- ole an h ee-
dimensional objec ecogni ion wi h digi al holog aphy,” Appl. Op . 40, 3887–
3893, 2001.
24. Y. F auel and B. Ja idi, “Neu al ne wo k o h ee-dimensional objec ecogni ion
based on digi al holog aphy,” Op . Le . 26, 1478–1480, 2001.
25. h p://holog am.cs.may.ie/online/jao2003/holog am.h ml .
17
Lis o Figu e Cap ions
Fig. 1 Expe imen al se up o PSI: BE, beam expande ; BS, beam spli e ; RP, e-
a da ion pla e; M, mi o .
Fig. 2 Illus a ion o he ne wo k-independen mul iple-clien sys em; U.I., use in e -
ace.
Fig. 3 In e nal ope a ion o (a) se e and (b) clien p ocesses.
Fig. 4 Sc eensho o clien -side o imings applica ion. Top ow (l o ): ull F esnel
ield wi h window indica ed, uncomp essed F esnel ield window da a, uncomp essed
imings, and uncomp essed econs uc ion. Bo om ow (l o ): con ol panel, com-
p essed window, comp essed iming in o ma ion, and comp essed econs uc ion.
Fig. 5 NRMS di e ence in he econs uc ed in ensi y plo ed agains numbe o
bi s in each o he F esnel ield’s eal and imagina y alues, o a ious deg ees o
subsampling.
Fig. 6 Recons uc ed iews (wi h 4×4 subsampling) om a 1024×1024-pixel window
om he F esnel ield s o ed wi h di e en quan iza ion esolu ions: (a) no quan iza-
ion, (b) 4 bi s, (c) 3 bi s, (d) 2 bi s o esolu ion in each eal and imagina y alue.
Fig. 7 Speedup as a unc ion o inc easing comp ession, o a ious F esnel ield win-
dow sizes.
18
λ/2 λ/4
BE M
A lase
CCD
BS
BS
M
M
RP1RP2
d
Fig. 1. Expe imen al se up o PSI: BE, beam expande ; BS, beam spli e ;
RP, e a da ion pla e; M, mi o . jnF1.eps
19
Se e
...
Local,
wi eless, o
wide-a ea
ne wo k
Clien
Clien
Clien
Holog am da abase
U.I.
U.I.
U.I.
Fig. 2. Illus a ion o he ne wo k-independen mul iple-clien sys em; U.I.,
use in e ace. jnF2.eps
20
Fo ma Comp ess T ansmi
Se e p ocess
Dese ialize Decomp ess Un o ma Image
Recons uc
Clien p ocess
(b)
2 3 5
6 7 8 10
9
Reques holog am window
0
(a)
Read
1
Reques om clien
Se ialize
4
Fig. 3. In e nal ope a ion o (a) se e and (b) clien p ocesses. jnF3.eps
21

Fig. 4. Sc eensho o clien -side o imings applica ion. Top ow (l o ): ull
F esnel ield wi h window indica ed, uncomp essed F esnel ield window da a,
uncomp essed imings, and uncomp essed econs uc ion. Bo om ow (l o
): con ol panel, comp essed window, comp essed iming in o ma ion, and
comp essed econs uc ion. jnF4.eps
22
2 3 4 5 6 7 8 9 10
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Quan iza ion esolu ion (bi s pe alue)
No malized RMS di e ence
no subsampling, RM ene gy = 0.13394
[2 2], RM ene gy = 0.46764
[4 4], RM ene gy = 1.6359
[16 16], RM ene gy = 23.5195
Fig. 5. NRMS di e ence in he econs uc ed in ensi y plo ed agains numbe
o bi s in each o he F esnel ield’s eal and imagina y alues, o a ious
deg ees o subsampling. jnF5.eps
23
(a) (b)
(c) (d)
Fig. 6. Recons uc ed iews (wi h 4×4 subsampling) om a 1024×1024-pixel
window om he F esnel ield s o ed wi h di e en quan iza ion esolu ions:
(a) no quan iza ion, (b) 4 bi s, (c) 3 bi s, (d) 2 bi s o esolu ion in each eal
and imagina y alue. jnF6.eps
24
2345678
1
3
5
7
9
11
13
Quan iza ion esolu ion (bi s pe alue)
Speedup in ansmission
512x512
256x256
128x128
64x64
32x32
16x16
Fig. 7. Speedup as a unc ion o inc easing comp ession, o a ious F esnel
ield window sizes. jnF7.eps
25