Laser-diode interferometer with a photothermal modulation

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Laser-diode interferometerwith a photothermal modulation

Takamasa Suzuki, Mineki Matsuda, Osami Sasaki, and Takeo Maruyama

A laser-diode ~LD! interferometer that uses an accurate photothermal-modulating technique is proposed.Since this technique with the photothermal method modulates only a wavelength of the LD, measure-ment accuracy is not affected by an intensity modulation that usually appears in the current modulation.The fundamental characteristics of this technique are investigated in detail. The new setup is tested,and its accuracy is compared with that of a previous system. © 1999 Optical Society of America

OCIS codes: 120.3180, 120.3930, 120.5050, 120.5060, 140.2020, 140.6810.

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1. Introduction

We can modulate the wavelength of the laser diode~LD! by changing the injection current, a feature thats commonly used in the construction of a variety ofnterferometers. This technique is called the cur-ent modulation ~C modulation!. Unfortunately, the

injection current affects not only the wavelength butalso the optical power of the LD, which in turn affectsthe measurement accuracy.

A heterodyne LD interferometer1 and a phase-shifting LD interferometer2 use triangular and step-wise injection current, respectively, to modulate thewavelength of the LD. In such interferometers theintensity modulation that is introduced by the opticalpower change in the LD, the so-called intensity mod-ulation, always occurs. This undesired change hasto be normalized by a numerical calculation2 or by anelectrical circuit.3 Measurement error caused by theintensity modulation in a phase-shifting LD inter-ferometer has also been analyzed theoretically.4 Asinusoidal phase-modulating LD interferometer usessinusoidal injection current.5 Although the inter-ferometer does not require large phase shift and al-though the amplitude of the injection current issmall, the detected interference signal contains slighterrors caused by the power change in the LD.

A two-wavelength LD interferometer that is insen-

The authors are with the Faculty of Engineering, Niigata Uni-versity, 8050 Ikarashi 2, Niigata 950-2181, Japan. T. Suzuki’se-mail address is [email protected].

Received 26 May 1999; revised manuscript received 9 August1999.

0003-6935y99y347069-07$15.00y0© 1999 Optical Society of America

sitive to the LD’s optical power change has beenroposed. In this interferometer, phases in the twonterferograms are shifted in opposite directions toach other by use of the stepwise injection current.ince the amplitude of one interference signal in-reases, while the another decreases, the intensityhanges caused by the modulating current cancelach other in the sum of these two interference sig-als. If a single LD is used, however, this techniqueannot be used to eliminate the influence of the op-ical power change in the LD. In such a case thentensity-compensating processes mentioned abovere necessary.Another technique, however, which uses what is

alled the photothermal effect, in which a high-poweraser beam is directed at the active region of a secondD, is proposed7 and analyzed.8 The change of the

optical power is dramatically reduced in this photo-thermal modulation ~P modulation!. But suppress-ing the change of the optical power is not an idealtechnique, since laser-chip temperature variationsaffect optical output power even when the drivingcurrent is constant.

Our technique effectively unites the two methodsdescribed above; whereas the latter is used to modu-late the LD, the former functions as a means of com-pensating for photothermal modulation-inducedchanges in optical power. With this two-pronged ap-proach the current and the photothermal modulation~CP modulation! enable us to use a purely phase-modulated laser beam. Therefore the compensatingprocess for the intensity modulation is no longer nec-essary in the signal processing.

The modulating characteristics of both P and CPmodulation are investigated in detail. We estimatemeasurement errors caused by the optical power

1 December 1999 y Vol. 38, No. 34 y APPLIED OPTICS 7069

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change in the LD by means of surface-profile mea-surements with C, P, and CP modulation.

2. Principle

A. Current Modulation

Schematics of C, P, and CP modulation are shown inFig. 1. A LD’s wavelength and optical power varyaccording to the amount of injection current supplied,as shown in Fig. 2, because the cavity length of theLD changes according to the heat generated by theinjection current.3 The C modulation illustrated in

ig. 1~a!, which uses the tunability of the LD’s wave-ength shown in Fig. 2~a!, simplifies realization ofavelength modulation and is widely used in inter-

Fig. 1. Schematic of ~a! C modulation, ~b! P modulation, and ~c! Clight source; LD2, heating laser; M, mirror.

Fig. 2. Characteristics of LD’s ~a! wavelength tunability and~b!optical power change with injection current.

070 APPLIED OPTICS y Vol. 38, No. 34 y 1 December 1999

erometers. At this point, however, undesirablehange occurs in the optical power as shown in Fig.~b!. When both dc bias current I1 and modulating

current

i1~t! 5 a1 cos~vmt 1 u1! (1)

are injected into LD1 as shown in Fig. 1~a!, the wave-length varies by

lc1~t! 5 @Dlc1yDi1#i1~t! ; b1i1~t! (2)

around the central wavelength l0, where subscript 1means that the variable is mainly related to LD1.At the same time the optical power changes by

Pc1~t! 5 @DPc1yDi1#i1~t! ; g1i1~t!, (3)

here b1 and g1 are LD1’s modulating efficiency andcoefficient of the optical power change, respectively,that are illustrated in Fig. 2. The square bracketsenclosing this parameter indicate the gradient of theline in Fig. 2 or Fig. 3, and the brackets serve thesame purpose throughout. Next the interferencesignal in the Twyman–Green interferometer is givenby

Sc~x, t! 5 @1 1 g1a1 cos~vmt 1 u1!#

3 $Sc1 1 Sc2 cos@zc cos~vmt 1 u1! 1 a~x!#%, (4)

where

zc 5 2pa1b1 lyl02 (5)

is modulation depth, l is optical path difference, anda~x! is phase distribution. Sc1 and Sc2 are the dccomponent and the amplitude of the ac component ofthe interference signal, respectively. The secondterm of the coefficient @1 1 g1a1 cos~vmt 1 u1!# in Eq.4! gives the intensity modulation and is identified ashe source of the measurement error.

B. Photothermal Modulation

As stated above, and as shown in Fig. 3, wavelengthand optical power vary according to temperature.Their coefficients are denoted by DlpyDT and DPpyDTs shown in Figs. 3~a! and 3~b!, respectively. The

wavelength tunability with temperature is applicable

odulation. BS, beam splitter; I, dc bias current; LD1, laser for a
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to the P modulation as well. In the P modulationshown in Fig. 1~b! we use intensity-modulated LD2whereas LD1 is injected with dc bias current I1 only.When both dc bias current I2 and modulating current

i2~t! 5 a2 cos~vmt 1 u2! (6)

are injected into LD2, its optical power varies by

Pc2~t! 5 @DPc2yDi2#i2~t!, (7)

according to the characteristic shown in Fig. 2~b!.his intensity-modulated laser beam is fed into LD1

hrough the exit pupil, and it heats the laser chip inD1. The temperature change influences the wave-

ength of LD1. Consequently the wavelength of LD1n Fig. 1~b! varies by

lp1~t! 5 FDlp1

DT1G FDT1

DPc2G FDPc2

Di2Gi2~t! ; b2i2~t!, (8)

where b2 is a modulating efficiency in the P modula-tion. DT1yDPc2, the conversion efficiency from opti-cal power to temperature, depends on the opticalsetup and especially on the alignment of the opticalaxis. In the same way the optical power change inLD1 is represented by

Pp1~t! 5 FDPp1

DT1G FDT1

DPc2G FDPc2

Di2Gi2~t! ; g2i2~t!, (9)

Fig. 3. Characteristics of LD’s ~a! wavelength tunability and ~b!optical power change with temperature. DPpyDT is negative.

where g2 is a coefficient of the optical power change inthe P modulation and its sign is opposite to g1. The

odulated interference signal is given by

Sp~x, t! 5 @1 1 g2a2 cos~vmt 1 u2!#

3 $Sp1 1 Sp2 cos@zp cos~vmt 1 u2! 1 a~x!#%,(10)

where

zp 5 2pa2b2 lyl02. (11)

Although g2 is small compared with g1, the modu-lated interference signal still has a change in its am-plitude. Compensation of this intensity modulation,however, is important when a precise measurementis called for.

C. Current and Photothermal Modulation

Note that the coefficients b1 and b2 share the samesign but those of g1 and g2 are opposite. When weemploy C and P modulation simultaneously, the in-tensity modulation derived from the latter can becompensated by the former. Then the interferencesignal is given by

Scp~x, t! 5 @1 1 g1a1 cos~vmt 1 u1! 1 g2a2 cos~vmt 1 u2!#

3 $Scp1 1 Scp2 cos@zcp cos~vmt 1 u3! 1 a~x!#%,(12)

where

zcp 5 2p~a1b1 1 a2b2!lyl02. (13)

Fig. 4. Experimental setup of the CP-modulating system with afeedback control. CPMS, current and photothermal modulatingsystem; FBC, feedback controller; LD1, laser for a light source;LD2, heating laser; PBS, polarizing beam splitter; BS, beam split-ter; M, mirror; AMP, amplifier; INT, integrator; ATT, attenuator.


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If the conditions of ug1a1u 5 ug2a2u and u1 5 u2 hold,by adjustment of amplitude a1 and phase u1 in themodulating or the compensating current i1~t!, thenntensity modulation is assumed to have no effect.

oreover, fortunately, Eq. ~13! indicates that theodulation depth in CP modulation becomes larger

than that in P modulation alone.

3. Experimental Setup

Our experimental setup is shown in Fig. 4. LD1 is alight source for the interferometer. The laser beamemitted from LD2 is injected into LD1 from its exitface. The central wavelengths and the maximum

Fig. 5. Optical power changes in the LD with respect to theinjection current ~a! for LD1 and ~b! for LD2.

Fig. 6. Phase lags in the C- and the P-modulated interferencesignals with respect to the frequency of the injection current.


output powers of the LD’s are shown in Fig. 4. LDmodulators LM1 and LM2 generate the LD’s drivingcurrents that are correspond to the input voltages.Their gains are 22.9 and 62.6 mAyV, respectively.The optical path difference l is 60 mm. The polar-izations of the LD’s are perpendicular to each other toavoid the interference between LD1 and LD2. Un-desired light radiated by LD2 is removed with a po-larizing filter. Any changes in the output intensityof LD1 are monitored by photodetector 2 ~PD2!.

emporal changes in the interference signal are de-ected by PD1 and relayed to the feedback controllero eliminate external disturbance.9 The sinusoidal

signal Vm~t! and the feedback signal are added andre injected into the heating laser LD2.The modulating signal Vm~t! is also transmitted to

the feedforward controller to compensate for the in-tensity modulation in the interference signal. Am-plitude a1 and phase u1 of LD1’s injection current areadjusted by the feedforward controller to satisfy theconditions described in Section 2. The spatialchange of the interference signal is detected by the

Fig. 7. Interference signals obtained by ~a! C modulation, ~b! Pmodulation, and ~c! CP modulation. Modulation frequency is 2kHz. Dashed curve, distortion introduced by the intensity mod-ulation.

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one-dimensional CCD image sensor and is processedby a computer.

4. Experimental Results

A. Characteristics of the Modulating Methods

First, the characteristics of the C and the P modula-tion were examined in detail. Figure 5 shows theoptical power changes detected by PD2 in the exper-imental setup, in which the LD1 is sinusoidally mod-ulated with C or P modulation, respectively. Themodulation frequency was 2 kHz. In the C modula-tion the output power of LD1 varies with injectioncurrent as shown in Fig. 5~a!. In this figure thechange has the same phase as the injection current.But in the P modulation shown in Fig. 5~b! the outputpower of LD1 is inversely proportional to the injectioncurrent of LD2. These two results can be explainedby the LD’s characteristics as shown in Figs. 2~b! and~b!, respectively.

Fig. 8. Dependency of modulation depth z on modulation fre-uency.

Fig. 9. Wavelength shift corresponding to amplitude of i2~t!. Inthe CP modulation, wavelength shifts by lp and lc with the P

odulation and the C modulation, respectively. Total wave-ength shift lcp. becomes the sum of lp and lc in CP modulation.

Figure 5 shows that the phase of the output powers delayed slightly with respect to the injection cur-ent of LD2. We measured this phase lag by chang-ng the frequency of the injection current. Resultsre shown in Fig. 6. The phase lag in the P modu-ation is larger than that in the C modulation. This

shows that we have to apply appropriate phase delayto the compensating current in the CP modulation.

We measured the modulation efficiencies b1 and b2denoted in Eqs. ~2! and ~8!. The amplitudes of the

odulating current were 0.8 and 21.5 mA in the Codulation and the P modulation, respectively, when

he modulation depths zc and zp were set at py2.herefore b1 and b2 are calculated as 4.676 3 1023

nmymA and 1.740 3 1024 nmymA, respectively, byuse of Eqs. ~5! and ~11!. b2 varies, of course, depend-ing on the optical alignment; it is small comparedwith b1.

Next we discuss the advantages of CP modulationas compared with the modulating methods men-tioned above. Interference signals obtained by thethree kinds of method are shown in Fig. 7. Figures7~a! and 7~b! are obtained by means of C modulationand P modulation, respectively. The effect that in-tensity modulation exerts on the P modulation ismuch smaller than that in the C modulation. But its difficult to make a precise measurement with thisntensity-modulated interference signal. The tracebtained by the CP modulation is shown in Fig. 7~c!.odulating conditions on the P modulation in Fig.

~c! are the same as those in Fig. 7~b!. The effect ofntensity modulation is completely eliminated in theP modulation.

Fig. 10. Deviations of the phase extracted from the intensity-modulated interference signal with visibility of 100%. g, the co-efficient of the optical power changes, are ~a! 0.1 and ~b! 0.5.


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Dependency of the modulation depth z on themodulating frequency is shown in Fig. 8. The cut-off frequency at the 23-dB level of the modulationdepth z reaches 50 kHz in the C modulationwhereas that in P modulation is 1 kHz. It is, how-ever, improved to 4 kHz in the CP modulation, asexplained in Eq. ~13!.

Moreover, wavelength shift in the CP modulationas measured. The wavelength shift shown in Fig.is calculated with the interference signal that isodulated by a sinusoidal current. Data plotted by

quares are wavelength shift Dlp corresponding tohe amplitude of modulating current i2~t!. At this

time, intensity modulation is simultaneously com-pensated by the modulating current i1~t! generated inhe feedforward controller. Then the wavelength isaried by i1~t! as well. Wavelength shift is plottedith triangles as Dlc in Fig. 9. Exact wavelength

shift in LD1 is then measured and plotted with cir-cles. We can find that the wavelength shift Dlcp inCP modulation is given as the sum of Dlp and Dlc.

bm


B. Application for the Surface-Profile Measurement

First, by means of simulation, we estimated the mea-surement error that is introduced by the intensitymodulation. In this case the error appears as a non-linear distortion in the measurement results. In thesimulation the interference signal was generatedwith Eq. ~4! for a linear phase distribution a~x!.

hen we extracted a~x! from the interference signaly using the bucket method. Simulations wereade by variation of the visibility Sc2ySc1 and g1, the

coefficient of the optical power change. Major re-sults with a visibility of 100% are shown schemati-cally in Fig. 10, in which ~a! and ~b! are obtained at g15 0.1 and 0.5, respectively. As g1 increases, devia-tion in the extracted phase becomes large even if theinterference signal has a maximum visibility of 100%.Deviations, which are denoted by the rms error withrespect to the given phase, were calculated for vari-ous g1 by changing of the visibility V. Results areplotted in Fig.11. Although the deviation reduces asthe visibility increases, considerable error still re-mains.

Next we measured the surface profile of a flat mir-ror by using a one-dimensional CCD image sensor

Fig. 13. Surface profile of flat mirror measured with ~a! C mod-ulation, ~b! P modulation, and ~c! CP modulation. s’s are thedifferences between the fitting line and the fitting curve, and theyindicate that CP modulation is useful for reducing the deviationcaused by the intensity modulation.

Fig. 11. Dependency of deviations on coefficient g1. Althoughthe deviation reduces as the visibility increases, considerable errorstill remains.

Fig. 12. Schematic of calculation method for s, which is denotedby the rms value of the difference between the linear fitting lineand the polynomial fitting curve of degree three.

sT

mtis

t

and estimated the deviations influenced by the inten-sity modulation. To execute numerical comparisonin the deviations, we calculate the first-order approx-imate line and the third-order approximate curve byusing the measured data. The deviation s is de-noted by the rms value of the difference between thefitting line and the curve as shown in Fig. 12. Re-sults obtained by the C, P, and CP modulations arehown in Figs. 13~a!, 13~b!, and 13~c!, respectively.hen the deviations were calculated as 1.91 3 1021,

5.45 3 1022, and 1.01 3 1022 for the C, P, and CPodulations, respectively. It was confirmed that

he CP modulation is useful for generating the idealnterference signal, and it enables us to reduce mea-urement error caused by the intensity modulation.

5. Conclusions

We have proposed a mechanically simple yet highlyaccurate modulating technique that uses both cur-rent modulation and photothermal modulation, si-multaneously, to remove undesirable intensitymodulation from the interference signal. We haveformularized each modulating method, including con-ventional current modulation. The current ~C! andhe photothermal ~P! modulations use the difference

between the dependencies of the LD’s output poweron the injection current and on the temperature.We have shown these characteristics in the experi-ment. The interference signals modulated by threekinds of method have been observed and compared.Those observations enable us to confirm the advan-

tage of the current and photothermal ~CP! modula-tion that is free from intensity modulation. Thistechnique is simple, easy to realize, and useful forgenerating a purely phase-modulated laser beam.

References1. J. Chen, Y. Ishii, and K. Murata, “Heterodyne interferometry

with a frequency-modulated laser diode,” Appl. Opt. 27, 124–128 ~1988!.

2. Y. Ishii, J. Chen, and K. Murata, “Digital phase-measuringinterferometry with a tunable laser diode,” Opt. Lett. 12, 233–235 ~1987!.

3. K. Tatsuno and Y. Tsunoda, “Diode laser direct modulationheterodyne interferometer,” Appl. Opt. 26, 37–40 ~1987!.

4. P. Hariharan, “Phase-stepping interferometry with laser di-odes: effect of changes in laser power with output wave-length,” Appl. Opt. 28, 27–29 ~1989!.

5. T. Suzuki, O. Sasaki, K. Higuchi, and T. Maruyama, “Real-time displacement measurement in sinusoidal phase modulat-ing interferometry,” Appl. Opt. 28, 5270–5274 ~1989!.

6. R. Onodera and Y. Ishii, “Two-wavelength phase-shifting in-terferometry insensitive to the intensity modulation of duallaser diodes,” Appl. Opt. 33, 5052–5061 ~1994!.

7. C. M. Kiimcak and J. C. Camparo, “Photothermal wavelengthmodulation of a diode laser,” J. Opt. Soc. Am. B 5, 211–214~1988!.

8. R. D. Esman and D. L. Rode, “Semiconductor-laser thermaltime constant,” J. Appl. Phys. 59, 407–409 ~1986!.

9. O. Sasaki, K. Takahashi, and T. Suzuki, “Sinusoidal phasemodulating laser diode interferometer with a feedback controlsystem to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 ~1990!.


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Laser-diode interferometer with a photothermal modulation