Abstract

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, measurement 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

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. J. Chen, Y. Ishii, K. Murata, “Heterodyne interferometry with a frequency-modulated laser diode,” Appl. Opt. 27, 124–128 (1988).
    [CrossRef] [PubMed]
  2. Y. Ishii, J. Chen, K. Murata, “Digital phase-measuring interferometry with a tunable laser diode,” Opt. Lett. 12, 233–235 (1987).
    [CrossRef] [PubMed]
  3. K. Tatsuno, Y. Tsunoda, “Diode laser direct modulation heterodyne interferometer,” Appl. Opt. 26, 37–40 (1987).
    [CrossRef] [PubMed]
  4. P. Hariharan, “Phase-stepping interferometry with laser diodes: effect of changes in laser power with output wavelength,” Appl. Opt. 28, 27–29 (1989).
    [CrossRef] [PubMed]
  5. T. Suzuki, O. Sasaki, K. Higuchi, T. Maruyama, “Real-time displacement measurement in sinusoidal phase modulating interferometry,” Appl. Opt. 28, 5270–5274 (1989).
    [CrossRef] [PubMed]
  6. R. Onodera, Y. Ishii, “Two-wavelength phase-shifting interferometry insensitive to the intensity modulation of dual laser diodes,” Appl. Opt. 33, 5052–5061 (1994).
    [CrossRef] [PubMed]
  7. C. M. Kiimcak, J. C. Camparo, “Photothermal wavelength modulation of a diode laser,” J. Opt. Soc. Am. B 5, 211–214 (1988).
    [CrossRef]
  8. R. D. Esman, D. L. Rode, “Semiconductor-laser thermal time constant,” J. Appl. Phys. 59, 407–409 (1986).
    [CrossRef]
  9. O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
    [CrossRef]

1994

1990

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

1989

1988

1987

1986

R. D. Esman, D. L. Rode, “Semiconductor-laser thermal time constant,” J. Appl. Phys. 59, 407–409 (1986).
[CrossRef]

Camparo, J. C.

Chen, J.

Esman, R. D.

R. D. Esman, D. L. Rode, “Semiconductor-laser thermal time constant,” J. Appl. Phys. 59, 407–409 (1986).
[CrossRef]

Hariharan, P.

Higuchi, K.

Ishii, Y.

Kiimcak, C. M.

Maruyama, T.

Murata, K.

Onodera, R.

Rode, D. L.

R. D. Esman, D. L. Rode, “Semiconductor-laser thermal time constant,” J. Appl. Phys. 59, 407–409 (1986).
[CrossRef]

Sasaki, O.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

T. Suzuki, O. Sasaki, K. Higuchi, T. Maruyama, “Real-time displacement measurement in sinusoidal phase modulating interferometry,” Appl. Opt. 28, 5270–5274 (1989).
[CrossRef] [PubMed]

Suzuki, T.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

T. Suzuki, O. Sasaki, K. Higuchi, T. Maruyama, “Real-time displacement measurement in sinusoidal phase modulating interferometry,” Appl. Opt. 28, 5270–5274 (1989).
[CrossRef] [PubMed]

Takahashi, K.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Tatsuno, K.

Tsunoda, Y.

Appl. Opt.

J. Appl. Phys.

R. D. Esman, D. L. Rode, “Semiconductor-laser thermal time constant,” J. Appl. Phys. 59, 407–409 (1986).
[CrossRef]

J. Opt. Soc. Am. B

Opt. Eng.

O. Sasaki, K. Takahashi, T. Suzuki, “Sinusoidal phase modulating laser diode interferometer with a feedback control system to eliminate external disturbance,” Opt. Eng. 29, 1511–1515 (1990).
[CrossRef]

Opt. Lett.

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (13)

Fig. 1
Fig. 1

Schematic of (a) C modulation, (b) P modulation, and (c) CP modulation. BS, beam splitter; I, dc bias current; LD1, laser for a light source; LD2, heating laser; M, mirror.

Fig. 2
Fig. 2

Characteristics of LD’s (a) wavelength tunability and (b)optical power change with injection current.

Fig. 3
Fig. 3

Characteristics of LD’s (a) wavelength tunability and (b) optical power change with temperature. ΔP p T is negative.

Fig. 4
Fig. 4

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

Fig. 5
Fig. 5

Optical power changes in the LD with respect to the injection current (a) for LD1 and (b) for LD2.

Fig. 6
Fig. 6

Phase lags in the C- and the P-modulated interference signals with respect to the frequency of the injection current.

Fig. 7
Fig. 7

Interference signals obtained by (a) C modulation, (b) P modulation, and (c) CP modulation. Modulation frequency is 2 kHz. Dashed curve, distortion introduced by the intensity modulation.

Fig. 8
Fig. 8

Dependency of modulation depth z on modulation frequency.

Fig. 9
Fig. 9

Wavelength shift corresponding to amplitude of i 2 (t). In the CP modulation, wavelength shifts by λ p and λ c with the P modulation and the C modulation, respectively. Total wavelength shift λ cp. becomes the sum of λ p and λ c in CP modulation.

Fig. 10
Fig. 10

Deviations of the phase extracted from the intensity-modulated interference signal with visibility of 100%. γ, the coefficient of the optical power changes, are (a) 0.1 and (b) 0.5.

Fig. 11
Fig. 11

Dependency of deviations on coefficient γ1. Although the deviation reduces as the visibility increases, considerable error still remains.

Fig. 12
Fig. 12

Schematic of calculation method for σ, which is denoted by the rms value of the difference between the linear fitting line and the polynomial fitting curve of degree three.

Fig. 13
Fig. 13

Surface profile of flat mirror measured with (a) C modulation, (b) P modulation, and (c) CP modulation. σ’s are the differences between the fitting line and the fitting curve, and they indicate that CP modulation is useful for reducing the deviation caused by the intensity modulation.

Equations (13)

Equations on this page are rendered with MathJax. Learn more.

i1t=a1 cosωmt+θ1
λc1t=Δλc1/Δi1i1tβ1i1t
Pc1t=ΔPc1/Δi1i1tγ1i1t,
Scx, t=1+γ1a1 cosωmt+θ1×Sc1+Sc2 coszc cosωmt+θ1+αx,
zc=2πa1β1 l/λ02
i2t=a2 cosωmt+θ2
Pc2t=ΔPc2/Δi2i2t,
λp1t=Δλp1ΔT1ΔT1ΔPc2ΔPc2Δi2i2tβ2i2t,
Pp1t=ΔPp1ΔT1ΔT1ΔPc2ΔPc2Δi2i2tγ2i2t,
Spx, t=1+γ2a2 cosωmt+θ2×Sp1+Sp2 coszp cosωmt+θ2+αx,
zp=2πa2β2 l/λ02.
Scpx, t=1+γ1a1 cosωmt+θ1+γ2a2 cosωmt+θ2×Scp1+Scp2 coszcp cosωmt+θ3+αx,
zcp=2πa1β1+a2β2l/λ02.

Metrics