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1
F equency modula ed op ical eedback
in e e ome y o nanome ic scale ib ome y
Aji Jha1,2, F ancisco J. Azcona1,S uden Membe , IEEE, San iago Royo1,Membe , IEEE,
Abs ac —We demons a e a no el me hod which makes e -
icien use o lase nonlinea dynamics when subjec o op ical
sel injec ion o sub-wa eleng h displacemen sensing pu poses.
The p oposed me hodology combines wo di e en phenomena
aking place inside he lase ca i y: op ical sel injec ion, which
esul s in op ical eedback in e e ence, and lase con inuous
wa e equency modula ion, gi ing ise o a wa eleng h sweeping
e ec in he lase ’s emission. We p esen a combina ion o hese
phenomena o measu e ib a ion ampli udes below λ/2wi h
esolu ions o a ew nanome e s, bandwid h dependen upon he
dis ance o ex e nal a ge , ampli ude and equency o cu en
modula ion. The basic heo e ical de ails and a ma hema ical
model a e p esen ed o he de eloped measu emen p inciple.
Expe imen al esul s, wi h he sys em wo king as a ib ome e
o measu e a a ge ib a ion o ampli ude λ/5(137.5 nm) wi h
mean peak o peak e o o 2.4 nm jus by poin ing he lase
diode on o he a ge and applying some signal p ocessing is also
demons a ed.
Index Te ms—Op ical eedback, Dopple equency, op ical
senso s, nano displacemen sensing, injec ion locking.
I. INTRODUCTION
AS desc ibed by Lang and Kobayashi [1], when he cohe -
en ligh e lec ed om an ex e nal a ge is sel -injec ed
in o he lase ’s ca i y, hen bea ing o ime delayed op ical ield
om dis an a ge and ield inside i s ca i y cause he lase o
en e in o mul i s able s a es. Depending upon he eedback
ield sel -injec ed in o he ca i y, se e al applica ions ha e
been de eloped in he las decade. When he eedback s eng h
is high, he lase diode (LD) eaches a chao ic egion, which
has been used o enc yp ed op ical communica ions [2]. On
he o he hand, unde mode a e o weak eedback condi ions,
he LD ou pu powe expe iences pe iodic luc ua ions wi h a
pe iod equi alen o hal emission wa eleng h (λ/2), which
can be associa ed o in e e ence inges, hus leading o he
concep o op ical eedback in e e ome y (OFI).
Classic OFI me hods a e limi ed o he measu emen o dis-
placemen s la ge han λ/2. In i s o igins, he inge coun ing
me hod enabled a λ/2 esolu ion, as desc ibed by Dona i in
[3]. Du ing he las wo decades, he inc ease o accu acy
and esolu ion has been a d i e o he esea ch in he ield
[4]–[6]. The capabili y o measu e ib a ion displacemen s
smalle han λ/2was ecen ly demons a ed o he i s ime
[7] using mechanical modula ion and a double lase se up.
1Cen e o Senso s, Ins umen s and Sys ems De elopmen , UPC-
Ba celonaTech, Rambla S . Neb idi 10, 08222, Te assa, Spain. 2Ins i u e o
Measu emen and Con ol Enginee ing, Ka ls uhe Ins i u e o Technology,
Engle -Bun e-Ring 21, 76131 Ka ls uhe, Ge many. Co esponding au ho -
[email p o ec ed].
This wo k is unded by Eu opean Union (G an No. 159224-1-2009-1-FR-
ERA MUNDUS-EMJD), Spanish Minis y o Science and Inno a ion (P ojec
no. DPI2014-56881-R) and Agau (G an no. 2012FI BI 00240).
Lase and
pho odiode
D i e
TIA
Piezo ( a ge )
Signal
gene a o
Powe
supply
Fig. 1: Expe imen al se -up o p oposed me hodology. (TIA:
T ans-Impedance Ampli ie ).
In ha app oach, he bandwid h o he senso was dependen
upon he p oduc o he equency and ampli ude o he linea
mechanical s age used o p oduce a e e ence OFI signal. The
use o a mechanical modula o wi h a linea esponse inc eased
he senso ’s cos and size while limi ing he measu emen
bandwid h.
To o e come hese p oblems, we p opose a no el app oach
ha akes ad an age o he ini e non-ze o linewid h en-
hancemen ac o (α) ha couples he lase ’s ampli ude and
equency modula ions, in o de o eplace he mechanical
modula ion depic ed in [7] by an elec onic modula ion. The
de eloped me hod in oduces wo main ad an ages o e [7].
Fi s , he se up is simpli ied since he use o a second lase
and o ex e nal mechanical elemen s o p o ide he modula ion
is no longe necessa y. This educes he cos and size o he
senso while making i compa able o classic OFI applica ions.
The use o only one lase also educes he possibili y o
bias in he measu emen in oduced by he di e ence o he
physical p ope ies be ween each LD o i s ci cui y. Second,
he bandwid h and esolu ion o he p oposed me hod a e
dependen only upon he LD elec onic and op ical pa ame e s,
in con as o he mechanical scheme desc ibed be o e. This,
in u n, allows o each la ge bandwid hs since he me hod is
no longe limi ed by mechanical cons ain s.
In he ollowing sec ions we desc ibe he wo king p inciple
o a p oposed op ical senso based on OFI e ec s induced by
con inuous wa e equency modula ion (CWFM-OFI), includ-
ing he me hodology o calcula e he a ge ib a ion wa e o m
- ampli ude and he equency bandwid h o senso .
II. SYSTEM DESCRIPTION AND THEORY
The p oposed concep o he expe imen is shown in Fig.1.
Fi s , a pe iodic cu en modula ion is applied while he a ge
is kep s a iona y. When he cu en eeding he lase is mod-
ula ed, no only he in ensi y o he emi ed signal is changed,
bu also i s emission wa eleng h, because o he coupling
be ween ampli ude and equency modula ion, deno ed by α
pa ame e . To a ain linea induced wa eleng h changes, a
2
iangula wa e is used as modula ion signal. Unde hese
condi ions, he lase can be hough as a mul i-wa eleng h
sou ce whose wa eleng h changes wi h ime p opo ionally o
he injec ed cu en . The ligh emi ed by he lase hen hi s he
s a iona y a ge and pa o he emi ed ligh is back e lec ed
in o he ca i y, whe e i in e e es wi h he s anding wa e al-
eady p esen in he ca i y, p oducing consecu i e in e e ence
inges in he emi ed powe wi h a phase di e ence o 2π
be ween hem.
The op ical eedback signal ob ained consis s o a se ies
o small ipples, caused by he bea ing o he ime delayed
e lec ed elec ic ield wi h he emi ed ield inside he ca i y,
supe imposed on o he amp o he powe signal modula ed by
he in ensi y as shown in Fig. 2(a). The signal is hen subjec ed
o a di e en ia ion which sepa a es he ipples caused by
in e e ence om he amp caused by modula ion. I has been
shown ha he numbe o inges which appea on he amp
depend upon he ound ip ime delay (dis ance be ween he
lase diode and he a ge ) and upon he wa eleng h peak o
peak change caused by he modula ion cu en [6]. We call his
he e e ence case and he inges p oduced e e ence inges.
In expe imen al signals, a e applying di e en ia ion, he ime
o occu ence o each inge will be no ed and eco ded.
We know ha each λ/2 a ge displacemen p oduces an
in e e ence inge in he signal [1], [3]. Thus, i he a ge
ib a ion ampli ude is smalle han λ/2, no addi ional inges
a e c ea ed as a esul o he a ge mo ion. E en hough he
o al numbe o inges emains cons an , he a ge mo ion
changes he equency seen by he lase due o he change in
op ical pa h di e ence, in he equi alen o a Dopple shi
in he equency domain. Thus, when compa ed o he o me
case, he new se o inges will be shi ed in ime p opo -
ionally o he op ical pa h change. F om his poin onwa d,
we e e o his case as ib a ion case, and o i s inges
as ib a ion inges. I will be shown ha i is possible o
ex ac he comple e in o ma ion o he a ge displacemen by
compa ing he e e ence and ib a ion cases. Ma hema ically,
all pa ame e s ela ed o he e e ence case will be deno ed by
subsc ip and he ib a ion case by subsc ip . The excess
phase φxand he emi ed powe Px(wi h x= [ , ]) equa ions
ha go e n bo h cases a e de ined by [8]
φ ( ) = 2πτex ( c −( h +im( )Ω ))
+Csin(2π c τex + an−1α) = 0,(1)
P ( ) = P ocos(2π c ( )τex ),(2)
φ ( ) = 2πτex ( )( c −( h +im( )Ω ))
+Csin(2π c τex ( ) + an−1α) = 0,(3)
P ( ) = P ocos(2π c ( )τex ( )),(4)
whe e Lex is he s a iona y dis ance om he lase o he
a ge , and Lex ( ) = Lex +a( ), wi h a( ) = A cos(2π )
desc ibes a a ge mo ion wi h peak ampli ude and equency
A and , espec i ely. τex = 2Lex /c is he ex e nal ound
ip ime o he e e ence case, τex ( ) = 2Lex ( )/c he
ound ip ime o he ib a ion case, c and c a e he
emission equency o he lase a e eedback o he e e ence
and ib a ion case espec i ely, h is he s andalone lase
equency a i s ope a ing poin when no eedback is p esen ,
TABLE I: Simula ion pa ame e s
Pa ame e s Value
Dis ance o ex e nal a ge om lase (Lex ) ( o wa d pa h) 0.3 m
Peak o peak modula ing cu en (Im(pp)) 1.5 mA
Modula ion equency ( m) 100 Hz
Ta ge ib a ion ampli ude (pp) (Am)λ
10
Ta ge ib a ion equency ( ) 200 Hz
F equency modula ion coe icien (Ω ) [8] -3 GHz/mA
Feedback s eng h (C) 0.9
Emission wa eleng h o lase (λ h) 692 nm
line wid h enhancemen ac o (α) 3
0 0.005 0.01
24
24.5
25
25.5
26
Ampli ude(mW)
ime (sec)
0 0.005 0.01
−4
−2
0
2
4x 10−3
ime (sec)
Ampli ude(a.u)
0 0.002 0.004 0.006 0.008 0.01
−0.1
−0.05
0
0.05
0.1
Ampli ude/λ
0 0.002 0.004 0.006 0.008 0.01
24
24.5
25
25.5
26
0 0.002 0.004 0.006 0.008 0.01
24
24.5
25
25.5
26
Powe (mW)
ime (sec)
2 2.5 3
x 10−3
24.8
25
ime (sec)
2 2.5
x 10−3
0
1
2
3
x 10−3
ime (sec)
m=100Hz
=200Hz
(a) (b)
(c)
Fig. 2: Simula ion esul s. (a) Emi ed powe a ia ions in
e e ence (blue solid) and ib a ion ( ed dash) cases (inse
gi es he magni ied iew). (b) Shi in inges in bo h cases.
(c) Ta ge wa e o m econs uc ed (black s a ) compa ed wi h
he e e ence ( ed squa e). A ows explains he o ma ion o
sampling poin s om inges. By symme y o modula ion
signal, p ocessing any one amp gi es in o ma ion abou a ge
ib a ion, making o he amp edundan .
im( )is he iangula AC modula ion cu en d i ing he lase ,
Ω is he equency coe icien o lase , Cis he eedback
s eng h, Pis he emission powe o he lase unde eedback,
wi h a o al ampli ude o P o and P o o he e e ence and
ib a ion cases.
Simula ions o pe o mance based on Eq. (1) - (4) we e
ca ied ou using he lase diode pa ame e s lis ed in Table
I. The goal o he simula ion was o p o e he appea ance o
powe shi s in ime be ween he e e ence and ib a ion cases.
Nonlinea equa ions Eq. (1) and Eq. (3) we e sol ed nume i-
cally o ind c and c espec i ely. Then he co esponding
powe luc ua ions we e calcula ed using Eq. (2) and Eq. (4).
Simula ion esul s a e p esen ed in Fig. 2(a) and 2(b), which
show a signi ican shi o he emission powe ela ed o he
a ge mo ion.
A. Displacemen Calcula ions
Now we will calcula e he a ge displacemen ou o he
he ime shi be ween ib a ion and e e ence inges. I is o
be no ed ha he phase di e ence be ween each consecu i e
inge is equi alen o a 2πphase change, which in OFI
can be ela ed o λ/2i a displacemen is p esen . Thus, he
ac ion o ime shi on he ib a ion inges ela i e o he
e e ence inges mul iplied by λ/2is equi alen o he a ge
displacemen . Le n
, n
, n
, n−1
be ec o s con aining he
eco ded alues o he ime o occu ence o he e e ence and
ib a ion inges, he ime di e ence be ween co esponding
3
inges, and he ime di e ence be ween consecu i e e e ence
inges ob ained in hal modula ion pe iod. whe e he supe -
sc ip is he numbe o elemen s in he conside ed ec o , xk
is he momen o occu ence o he k h inge. Thus, he a ge
displacemen A , ec can be compu ed simply using
A , ec = n−1
n−1
×λ/2(5)
Using Eq. (5), he a ge wa e o m is econs uc ed , shown in
Fig. 2(c). I is wo h no ing, ha , since he a ge ib a ion is
wice he modula ion equency, he en i e a ge wa e o m lie
in one amp (hal pe iod) o he modula ion signal wi h a ow
illus a ing ha each inge co esponds o a measu emen
poin . So i is desi able o p ocess one o he amp o a ge
ib a ion ela ed in o ma ion.
B. F equency Bandwid h
Le m=1
Tm
be he modula ion equency o cu en o he
lase . In ime Tm/2(conside ing only one amp o modula ion
signal; u he explained in sec ion III), we ha e N inges
gi ing N−1sample poin s. Thus he sampling a e o a ge
econs uc ion is gi en by s, ec = (2N m−1). F om Nyquis
heo em, he maximum equency ha can be econs uc ed
is hal he sampling a e and using 2N m>> 1, can be
app oxima ed as , ec ≃N m. We see ha he maximum
equency o a ge ib a ion ha can be econs uc ed using
he p oposed senso is dependen upon he p oduc o modula-
ion equency and he numbe o inges. Hence keeping he
numbe o inges Ncons an , he equency o a ge ib a ion
ha can be de ec ed is di ec ly p opo ional o he modula ion
equency i.e. , ec ∝ m. Since, a lase can be modula ed
a la ge equencies (MHz) keeping signi ican equency
de ia ion [9] as compa ed o mechanical ib a ion o lase
in [7], his me hod gi es wide bandwid h as compa ed o [7].
This also demons a es he ac ha he senso ’s bandwid h
ha was limi ed by he bandwid h o piezo in o me is now
solely de e mined by he p ope ies (maximum modula ion
equency) o lase used and hence ex ending he bandwid h
o senso as compa ed o o me .
III. EXPERIMENT AND RESULTS
Expe imen ally, a Hi achi HL6501 0.65 µm band AlGaAsP
lase diode (LD) wi h a mul i-quan um well (MQW) s uc u e
was used o es he me hod. The emission wa eleng h was
measu ed wi h Ins umen Sys em’s SPECTRO 320(D) R5
uni . The lase was hen di ec ly modula ed o ob ain he
desi ed equency chi p. Since unde his ope a ing condi ions
he LD may show mode hopping, a de ailed analysis o i s
spec al cha ac e is ics as a unc ion o he injec ion cu en
was pe o med o loca e he op imal ope a ing poin as shown
in Fig. 3, whose measu emen s we e pe o med epe i i ely
in s able wo king condi ions. The LD ope a ing poin was
selec ed as I h = 48 mA wi h λ h = 692.5 nm. The lase
is kep powe ed on and unde s able wo king condi ions
when acqui ing he e e ence and ib a ion measu emen s. To
p oduce he equency chi p, he LD is ed using a iangula
cu en modula ion wi h alue a he ope a ing poin (I h)
peak o peak ampli ude o 250 mV (0.2 mA) and a equency
o m= 100 Hz. The LD is ocused on he a ge using a
45 50 55 60
692
692.5
693
693.5
694
694.5
bias,(mA)
Wa eleng h,(nm)
Linea , egion
Linea , egion
Ope a ing
poin ,48,mA,
692.5nm
Mode,hop
Linea , egion
Mode,hop
Fig. 3: Va ia ion o emission wa eleng h wi h bias cu en .
Tho labs lens 352240 wi h ocal leng h o 8 mm and nume ical
ape u e o 0.5 placed a a dis ance o 3.5 mm om he lase .
A piezoelec ic linea s age PI-LISA (P-753.3CD) placed a
a dis ance ( o wa d pa h) o 12 cm om he lase is used as
a ge ; he s age includes an embedded capaci i e senso wi h
a esolu ion o 0.2 nm [10] which is used o compa ing he
ob ained esul s. P e ious o each measu emen , he lase is
se o wo k in he weak eedback egion and i is allowed o
a ain a s able s a e. To dissipa e he hea p oduced by he LD,
he lase is moun ed on an aluminium pla o m.
In a i s s ep, a measu emen o he e e ence case is
acqui ed and denoised using a sym6 wa ele ans o m [11]
and, hen, he ime o occu ence o he inges is no ed.
Nex , he a ge is se in o ib a ion by applying o he AC
sinusoidal signal wi h ampli ude 55 mV and equency 200
Hz (so ha en i e a ge ib a ion wa e o m lie in one amp
o modula ion signal) o he piezoelec ic s age using a signal
gene a o , esul ing in a 137.5 nm displacemen measu ed by
he embedded capaci i e senso [10]. The choice o a ge
ib a ion equency o 200 Hz was chosen as a p oo o
concep accompanied by simula ions and heo e ical p oo and
limi ed by he piezo. Due o he a ge mo ion, he op ical
pa h di e ence be ween lase and a ge changes esul ing in
a shi o he inges when compa ed o he e e ence case.
As in he e e ence case, he signal is acqui ed, denoised and
he ime o occu ence o he inges is eco ded. An example
o ypical expe imen al esul s is shown in Fig. 4. The inge
shi is easily app ecia ed and will be used o eco e he a ge
ampli ude and equency o ib a ion.
Once he ime o occu ence o each inge is compu ed o
he e e ence and ib a ion cases, he a ge displacemen is
calcula ed using Eq. (5). Fig. 5 shows he expe imen al a ge
displacemen e ie ed co esponding o he de ec ed inges
esul ing om a single oscilla ion o he a ge p esen ed in
Fig. 4, compa ed wi h he da a ob ained om he embedded
capaci i e senso . I should be no ed ha only one amp
is p ocessed o ge he ull pe iod o a ge wa e o m (as
he a ge ib a ion equency is wice ha o modula ion
equency). The expe imen was pe o med nine imes unde
equi alen condi ions. The mean e o (pp) was 2.4 nm. Fo
conciseness, only i e measu emen s a e lis ed in Table II.
Howe e , he - es was ca ied on Ns= 9 samples wi h he
deg ee o eedom d = 2Ns−2= 16 and signi icance
le el αs= 0.05. Unde hese condi ions, he p obabili y o
ob aining sample da a i null hypo hesis we e ue is p= 0.92.
4
0 2 4 6
x 10−3
0
0.02
0.04
ime(sec)
Ampli ude(V)
0 2 4 6
x 10−3
0
0.02
0.04
ime(sec)
Ampli ude(V)
0 2 4 6
x 10−3
0
0.02
0.04
ime(sec)
Ampli ude(V)
0 2 4 6
x 10−3
0
0.5
1
ime(sec)
Ampli ude(a.u)
(d)
(b)
(c)
(a)
Fig. 4: Expe imen al esul s. (a) OFI signal, e e ence case,
a e di e en ia ion o sepa a ing he inges om he amp
in he acqui ed signal; (b) OFI signal, ib a ion case, also a e
di e en ia ion (c) Denoised and di e en ia ed OFI inges o
e e ence (solid line) and ib a ion (b oken line) cases; (d)
Shi in ime occu ence o inges in he ib a ion cases wi h
espec o e e ence case ha o ms he basis o displacemen
calcula ion.
1 1.5 2 2.5 3 3.5 4 4.5 5
x 10−3
−80
−60
−40
−20
0
20
40
60
80
ime (sec)
Ampli ude (nm)
e e ence i
OFI i
e e ence measu ed
OFI measu ed
Fig. 5: Expe imen al esul s (Exp . 1 in Table II). P oposed
OFI based a ge displacemen compa ed agains piezoelec ic
s age embedded capaci i e senso .
Since p > αs, we conclude ha he da a samples in OFI
and Re (Table II) ha e same mean a 95% con idence le el.
Fo illus a ion pu poses, he i s case, which had an e o
(pp) o 1.5 nm is shown in Fig. 5. In o de o u he p o e
he easibili y o he p oposed me hodology, i was applied o
de ec a bi a y wa e o m shapes. Resul s o expe imen s o
measu e Gaussian pulse shapes o wid h 4 ms and ampli ude
63.8 nm a e p esen ed in Fig. 6, showing an a e age e o
(pp) o 4.05 nm measu ed unde compa able condi ions o
ha o Fig. 5. The ela i ely high e o in Gaussian wa e o m
is due o he limi ed numbe o sample poin s o ollow apid
changes in he slope o he displacemen gi ing ise o apid
phase changes (as compa ed o o me ).
IV. CONCLUSION
We ha e p oposed and expe imen ally demons a ed a
me hodology o make e icien use o di ec lase injec ion
cu en modula ion o induce CWFM and nonlinea dynamics
e ec s in a LD subjec ed o op ical eedback o measu e
nanome ic ampli ude displacemen s. The key con ibu ion
o his wo k is he use o single lase diode o de ec sub
TABLE II: Expe imen al esul s.
Exp . Re (nm) OFI (nm) E o (nm)
1 137.5 139.0 1.5
2 155.55 155.18 0.37
3 126.08 124.58 1.5
4 132.95 132.41 0.54
5 159.1 156.3 2.8
0 0.002 0.004 0.006 0.008 0.01 0.012
−10
0
10
20
30
40
50
60
70
ime (sec)
Ampli ude (nm)
e e ence i
OFI i
e e ence measu ed
OFI measu ed
Fig. 6: Expe imen al esul s. Gaussian pulse de ec ed com-
pa ed agains piezoelec ic s age embedded capaci i e senso .
wa eleng h a ge ib a ions wi h nanome ic accu acies, using
he modula ion o he injec ion cu en and expanding he
bandwid h o o me DSMI senso s [7] o a leas he MHz
equency ange in de ec ion. The mean peak o peak e o
o he p oposed senso ou o nine di e en measu emen o
a single oscilla ion is 2.4 nm; a Gaussian pulse o wid h 4
ms and ampli ude 63.8 nm is also de ec ed wi h mean e o
(pp) o 4.08 nm. The maximum a ge ib a ion de ec able is
limi ed o λ/2, and he bandwid h o he senso is p opo ional
o he numbe o inges and equency o he lase cu en
modula ion.
REFERENCES
[1] R. Lang and K. Kobayashi, “Ex e nal op ical eedback e ec s on
semiconduc o injec ion lase p ope ies,” IEEE J. Quan um Elec on.,
ol. 16, pp. 347–355, Ma ch 1980.
[2] N. Jiang, W. Pan, B. Luo, L. Yan, S. Xiang, L. Yang, D. Zheng,
and N. Li, “In luence o injec ion cu en on he synch oniza ion
and communica ion pe o mance o closed-loop chao ic semiconduc o
lase s,” Op . Le ., ol. 36, pp. 3197–3199, Aug 2011.
[3] S. Dona i, G. Giuliani, and S. Me lo, “Lase diode eedback in e e -
ome e o measu emen o displacemen s wi hou ambigui y,” IEEE J.
Quan um Elec on., ol. 31, pp. 113–119, 1995.
[4] N. Se agen , F. Gouaux, and T. Bosch, “Measu emen o displacemen
using sel mixing in e e ence in a lase diode,” J.op , ol. 29, pp. 168–
173, Aug 1998.
[5] C. Bes, G. Plan ie , and T. Bosch, “Displacemen measu emen s using a
sel -mixing lase diode unde mode a e eedback,” IEEE T ans. Ins um.
Meas., ol. 55, pp. 1101–1105, Aug 2006.
[6] D. M. Guo, M. Wang, and S. Q. Tan, “Sel -mixing in e e ome e
based on sinusoidal phase modula ing echnique,” Op .Exp ess, ol. 13,
pp. 1537–1543, Aug 2005.
[7] F. Azcona, R. A ashkhooei, S. Royo, J. As udillo and A. Jha, “A
nanome ic displacemen measu emen sys em using di e en ial op-
ical eedback in e e ome y,” IEEE Pho on. Technol. Le ., ol. 25,
pp. 2074–2077, 2013.
[8] E. Gagnon and J.F. Ri es , “Lase ange imaging using he sel -mixing
e ec in a lase diode,” IEEE T ans. Ins um. Meas., ol. 48, pp. 693–
699, June 1999.
[9] S. Kobayashi,Y. Yamamo o, M. I o, T. Kimu a,“Di ec equency mod-
ula ion in AlGaAs semiconduc o lase s, IEEE J. Quan um Elec on.,
ol.18, pp. 582-595, Ap 1982.
[10] h p://www.physikins umen e.com/p oduc -de ail-page/p-753-
200900.h ml.
[11] D. Zhigang, Z. Jingxuan, and J. Chun ong, “An imp o ed wa ele h esh-
old denoising algo i hm,” P oc. In e na ional Con e ence on In elligen
Sys em Design and Enginee ing Applica ions, pp. 297–299, China 2013.