Abstract

An optical heterodyne interferometer with a frequency-ramped laser diode has been constructed. The effect of the beat frequency on the measured phase has been theoretically investigated in the frequency domain and experimentally verified. Phase errors caused by the difference between the ramp frequency and the beat frequency alter sinusoidally in accordance with the π periodicity of the interferogram. The error can be eliminated by the electronic calibration technique of the beat frequency.

© 1996 Optical Society of America

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References

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  1. Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Lasers Eng. 14, 293–309 (1991).
    [CrossRef]
  2. D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
    [CrossRef]
  3. A. D. Kersey, D. A. Jackson, M. Corke, “Demodulation scheme fibre interferometric sensors employing laser frequency switching,” Electron. Lett. 19, 102–103 (1983).
    [CrossRef]
  4. D. Uttam, B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. LT-3, 971–977 (1985).
    [CrossRef]
  5. G. Economou, R. C. Youngquist, D. E. N. Davies, “Limitations and noise in interferometric systems using frequency ramped single-mode diode lasers,” J. Lightwave Technol. LT-4, 1601–1608 (1986).
    [CrossRef]
  6. G. Beheim, “Fiber-optic interferometer using frequency-modulated laser diodes,” Appl. Opt. 25, 3469–3472 (1986).
    [CrossRef] [PubMed]
  7. K. Hotate, D.-T. Jong, “Quasi-heterodyne optical fiber sensor with automated adjustment of the driving wave parameter,” Appl. Opt. 26, 2956–2961 (1987).
    [CrossRef] [PubMed]
  8. J. Ohtsubo, T. Aoshima, “A new method to separate the Doppler signal from the drift component using a laser diode frequency change,” Opt. Commun. 73, 101–105 (1989).
    [CrossRef]
  9. M. Imai, K. Kawakita, “Optical-heterodyne displacement measurement using a frequency-ramped laser diode,” Opt. Commun. 78, 113–117 (1990).
    [CrossRef]
  10. P.-Y. Chien, C. L. Pan, “Multiplexed fiber-optic sensors using a dual-slope frequency-modulated source,” Opt. Lett. 16, 872–874 (1991).
    [CrossRef] [PubMed]
  11. K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization of light,” J. Mod. Opt. 38, 1567–1580 (1991).
    [CrossRef]
  12. M. Takeda, M. Kitoh, “Spatiotemporal frequency multiplex heterodyne interferometry,” J. Opt. Soc. Am. A 9, 1607–1614 (1992).
    [CrossRef]
  13. R. Onodera, Y. Ishii, “Selective imaging with a frequency-modulated laser-diode interferometer,” Opt. Lett. 20, 761–763 (1995).
    [CrossRef] [PubMed]
  14. I. Yamaguchi, K. Hamano, “Multiplexed heterodyne fiber interferometer that uses laser-diode modulation,” Opt. Lett. 20, 1661–1663 (1995).
    [CrossRef] [PubMed]
  15. R. Onodera, Y. Ishii, “Two-wavelength laser-diode interferometer with fractional fringe techniques,” Appl. Opt. 34, 4740–4746 (1995).
    [CrossRef] [PubMed]
  16. Y. Otani, A. Tanahashi, T. Yoshizawa, “Light source with orthogonally linear polarized two-frequency beam from laser diode and its application,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 293–298 (1995).
  17. R. Onodera, Y. Ishii, “Two-wavelength laser-diode heterodyne interferometry with one phasemeter,” Opt. Lett. 20, 2502–2504 (1995).
    [CrossRef] [PubMed]
  18. R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” J. Lightwave Technol. 13, 675–681 (1995).
    [CrossRef]

1995

1992

1991

P.-Y. Chien, C. L. Pan, “Multiplexed fiber-optic sensors using a dual-slope frequency-modulated source,” Opt. Lett. 16, 872–874 (1991).
[CrossRef] [PubMed]

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization of light,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Lasers Eng. 14, 293–309 (1991).
[CrossRef]

1990

M. Imai, K. Kawakita, “Optical-heterodyne displacement measurement using a frequency-ramped laser diode,” Opt. Commun. 78, 113–117 (1990).
[CrossRef]

1989

J. Ohtsubo, T. Aoshima, “A new method to separate the Doppler signal from the drift component using a laser diode frequency change,” Opt. Commun. 73, 101–105 (1989).
[CrossRef]

1987

1986

G. Economou, R. C. Youngquist, D. E. N. Davies, “Limitations and noise in interferometric systems using frequency ramped single-mode diode lasers,” J. Lightwave Technol. LT-4, 1601–1608 (1986).
[CrossRef]

G. Beheim, “Fiber-optic interferometer using frequency-modulated laser diodes,” Appl. Opt. 25, 3469–3472 (1986).
[CrossRef] [PubMed]

1985

D. Uttam, B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. LT-3, 971–977 (1985).
[CrossRef]

1983

A. D. Kersey, D. A. Jackson, M. Corke, “Demodulation scheme fibre interferometric sensors employing laser frequency switching,” Electron. Lett. 19, 102–103 (1983).
[CrossRef]

1982

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

Aoshima, T.

J. Ohtsubo, T. Aoshima, “A new method to separate the Doppler signal from the drift component using a laser diode frequency change,” Opt. Commun. 73, 101–105 (1989).
[CrossRef]

Beheim, G.

Chien, P.-Y.

Corke, M.

A. D. Kersey, D. A. Jackson, M. Corke, “Demodulation scheme fibre interferometric sensors employing laser frequency switching,” Electron. Lett. 19, 102–103 (1983).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

Culshaw, B.

D. Uttam, B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. LT-3, 971–977 (1985).
[CrossRef]

Davies, D. E. N.

G. Economou, R. C. Youngquist, D. E. N. Davies, “Limitations and noise in interferometric systems using frequency ramped single-mode diode lasers,” J. Lightwave Technol. LT-4, 1601–1608 (1986).
[CrossRef]

Economou, G.

G. Economou, R. C. Youngquist, D. E. N. Davies, “Limitations and noise in interferometric systems using frequency ramped single-mode diode lasers,” J. Lightwave Technol. LT-4, 1601–1608 (1986).
[CrossRef]

Hamano, K.

Hotate, K.

Imai, M.

M. Imai, K. Kawakita, “Optical-heterodyne displacement measurement using a frequency-ramped laser diode,” Opt. Commun. 78, 113–117 (1990).
[CrossRef]

Ishii, Y.

Jackson, D. A.

A. D. Kersey, D. A. Jackson, M. Corke, “Demodulation scheme fibre interferometric sensors employing laser frequency switching,” Electron. Lett. 19, 102–103 (1983).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

Jones, J. D. C.

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

Jong, D.-T.

Kawakita, K.

M. Imai, K. Kawakita, “Optical-heterodyne displacement measurement using a frequency-ramped laser diode,” Opt. Commun. 78, 113–117 (1990).
[CrossRef]

Kersey, A. D.

A. D. Kersey, D. A. Jackson, M. Corke, “Demodulation scheme fibre interferometric sensors employing laser frequency switching,” Electron. Lett. 19, 102–103 (1983).
[CrossRef]

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

Kitoh, M.

Ohde, N.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

Ohtsubo, J.

J. Ohtsubo, T. Aoshima, “A new method to separate the Doppler signal from the drift component using a laser diode frequency change,” Opt. Commun. 73, 101–105 (1989).
[CrossRef]

Ohtsuka, Y.

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization of light,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

Oka, K.

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization of light,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

Onodera, R.

Otani, Y.

Y. Otani, A. Tanahashi, T. Yoshizawa, “Light source with orthogonally linear polarized two-frequency beam from laser diode and its application,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 293–298 (1995).

Pan, C. L.

Takahashi, Y.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

Takeda, M.

Takeda, T.

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization of light,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

Tanahashi, A.

Y. Otani, A. Tanahashi, T. Yoshizawa, “Light source with orthogonally linear polarized two-frequency beam from laser diode and its application,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 293–298 (1995).

Uttam, D.

D. Uttam, B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. LT-3, 971–977 (1985).
[CrossRef]

Yamaguchi, I.

Yoshino, T.

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

Yoshizawa, T.

Y. Otani, A. Tanahashi, T. Yoshizawa, “Light source with orthogonally linear polarized two-frequency beam from laser diode and its application,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 293–298 (1995).

Youngquist, R. C.

G. Economou, R. C. Youngquist, D. E. N. Davies, “Limitations and noise in interferometric systems using frequency ramped single-mode diode lasers,” J. Lightwave Technol. LT-4, 1601–1608 (1986).
[CrossRef]

Appl. Opt.

Electron. Lett.

D. A. Jackson, A. D. Kersey, M. Corke, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

A. D. Kersey, D. A. Jackson, M. Corke, “Demodulation scheme fibre interferometric sensors employing laser frequency switching,” Electron. Lett. 19, 102–103 (1983).
[CrossRef]

J. Lightwave Technol.

D. Uttam, B. Culshaw, “Precision time domain reflectometry in optical fiber systems using a frequency modulated continuous wave ranging technique,” J. Lightwave Technol. LT-3, 971–977 (1985).
[CrossRef]

G. Economou, R. C. Youngquist, D. E. N. Davies, “Limitations and noise in interferometric systems using frequency ramped single-mode diode lasers,” J. Lightwave Technol. LT-4, 1601–1608 (1986).
[CrossRef]

R. Onodera, Y. Ishii, N. Ohde, Y. Takahashi, T. Yoshino, “Effect of laser-diode power change on optical heterodyne interferometry,” J. Lightwave Technol. 13, 675–681 (1995).
[CrossRef]

J. Mod. Opt.

K. Oka, T. Takeda, Y. Ohtsuka, “Optical heterodyne polarimeter for studying space- and time-dependent state of polarization of light,” J. Mod. Opt. 38, 1567–1580 (1991).
[CrossRef]

J. Opt. Soc. Am. A

Opt. Commun.

J. Ohtsubo, T. Aoshima, “A new method to separate the Doppler signal from the drift component using a laser diode frequency change,” Opt. Commun. 73, 101–105 (1989).
[CrossRef]

M. Imai, K. Kawakita, “Optical-heterodyne displacement measurement using a frequency-ramped laser diode,” Opt. Commun. 78, 113–117 (1990).
[CrossRef]

Opt. Lasers Eng.

Y. Ishii, “Recent developments in laser-diode interferometry,” Opt. Lasers Eng. 14, 293–309 (1991).
[CrossRef]

Opt. Lett.

Other

Y. Otani, A. Tanahashi, T. Yoshizawa, “Light source with orthogonally linear polarized two-frequency beam from laser diode and its application,” in International Conference on Optical Fabrication and Testing, T. Kasai, ed., Proc. SPIE2576, 293–298 (1995).

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Figures (7)

Fig. 1
Fig. 1

Experimental setup for a LD heterodyne interferometer. The tested phase is measured with the lock-in amplifier by the heterodyne method.

Fig. 2
Fig. 2

Numerical calculation of the average amplitude D ave of a bandpass-filtered signal as a function of b r . The beat signal of the LD-heterodyne interferometer has the same spectrum component as the modulation frequency.

Fig. 3
Fig. 3

Tested phases measured for (top) b r = 0.7, (middle) b r = 1.0, and (bottom) b r = 1.3. The phase errors with π periodicity can be seen in the top and bottom figures. The errors are caused by the difference between the beat frequency ω b and the modulation frequency ω s .

Fig. 4
Fig. 4

Block diagram of the electronic calibration method for equalizing the beat frequency with the modulation frequency.

Fig. 5
Fig. 5

Timing chart for the calibration circuit in Fig. 4 of the beat frequency.

Fig. 6
Fig. 6

(Upper traces) sawtooth modulation currents and (lower traces) beat signals when the feedback loop is off and on.

Fig. 7
Fig. 7

Reduction in phase errors obtained by performing the electronic calibration technique. The actual phase being tested can be measured during the feedback operation.

Equations (17)

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Δ ω = 2 πβ i m ,
ω b = Δ ω τ T ,
ω b = ω s β l c i m .
s 0 ( t ) = I M [ 1 + γ cos ( ω b t + ϕ ) ] ,
ϕ = ω c τ + Δ ω 2 T τ 2 ,
ϕ = 2 π l λ c ,
s ( t ) = [ rect ( t T ) × s 0 ( t ) ] * [ 1 T × comb ( t T ) ] ,
rect ( t T ) = { 1 for | t | T / 2 , 0 for otherwise ,
1 T × comb ( t T ) = n = δ ( t n T ) ,
s f ( t ) = 1 2 π S ( ω ) [ rect ( ω + ω s 2 B ) + rect ( ω ω s 2 B ) ] exp ( j ω t ) = 1 2 π ω s B ω s + B S ( ω ) exp ( j ω t ) + 1 2 π ω s B ω s + B S ( ω ) exp ( j ω t ) .
S ( ω ) = F [ s ( t ) ] = [ 2 π I M sinc ( ω ω s ) + πγ I M exp ( j ϕ ) sinc ( ω ω b ω s ) + πγ I M exp ( j ϕ ) sinc ( ω + ω b ω s ) ] × comb ( ω ω s ) ,
s f ( t ) D γ I M cos ( ω s t + ϕ ) ,
D = 2 1 + b r | sin [ π ( 1 b r ) ] π ( 1 b r ) | [ ( b r cos ϕ ) 2 + sin 2 ϕ ] , 1 / 2
ϕ = tan 1 ( 1 b r tan ϕ ) ,
b r = ω b ω s .
s f ( t ) = γ I M cos ( ω s t + ϕ ) .
Δ ϕ ϕ ϕ 1 b r 2 b r sin 2 ϕ .

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