Abstract

I discuss optical frequency-modulated continuous-wave (FMCW) interferometers, including their principles, characteristics, specific requirements, procedure for their construction, optical configurations, primary applications, optical sources, resolution, measurement range, and stability.

© 2006 Optical Society of America

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References

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  1. A. J. Hymans and J. Lait, " Analysis of a frequency-modulated continuous-wave ranging system," Proc. IEEE 107, 365- 372 ( 1960).
  2. M. I. Skolnik, Introduction to Radar Systems (McGraw Hill, 1962).
  3. B. Culshaw and I. P. Giles, " Frequency modulated heterodyne optical Sagnac interferometer," IEEE J. Quantum Electron. QE-18, 690- 693 ( 1982).
    [CrossRef]
  4. D. A. Jackson, A. D. Kersey, M. Corke, and J. D. C. Jones, " Pseudoheterodyne detection scheme for optical interferometers," Electron. Lett. 18, 1081- 1083 ( 1982).
    [CrossRef]
  5. M. Corke, A. D. Kersey, D. A. Jackson, and J. D. C. Jones, " All-fiber Michelson thermometer," Electron. Lett. 19, 471- 472 ( 1983).
    [CrossRef]
  6. R. B. Franks, W. Torruellas, and R. C. Youngquist, " Birefringent stress location sensor," in Fiber Optic Sensors, H.J.Arditti and L.B.Jeunhomme, eds., Proc. SPIE 586, 84- 89 ( 1985).
  7. P. A. Leilabady, " Optical fiber point temperature sensor," in Fiber Optic and Laser Sensors V, R.P.DePaula and E.Udd, eds., Proc. SPIE 838, 231- 237 ( 1987).
  8. J. Zheng, " Analysis of optical frequency-modulated continuous-wave interference," Appl. Opt. 43, 4189- 4198 ( 2004).
    [CrossRef] [PubMed]
  9. J. Zheng, " Continued analysis of optical frequency-modulated continuous-wave interference," Appl. Opt. 44, 765- 769 ( 2005).
    [CrossRef] [PubMed]
  10. J. Zheng, " Coherence analysis of optical frequency-modulated continuous-wave interference," Appl. Opt. (to be published).
    [PubMed]

2005 (1)

2004 (1)

1983 (1)

M. Corke, A. D. Kersey, D. A. Jackson, and J. D. C. Jones, " All-fiber Michelson thermometer," Electron. Lett. 19, 471- 472 ( 1983).
[CrossRef]

1982 (2)

B. Culshaw and I. P. Giles, " Frequency modulated heterodyne optical Sagnac interferometer," IEEE J. Quantum Electron. QE-18, 690- 693 ( 1982).
[CrossRef]

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

1960 (1)

A. J. Hymans and J. Lait, " Analysis of a frequency-modulated continuous-wave ranging system," Proc. IEEE 107, 365- 372 ( 1960).

Corke, M.

M. Corke, A. D. Kersey, D. A. Jackson, and J. D. C. Jones, " All-fiber Michelson thermometer," Electron. Lett. 19, 471- 472 ( 1983).
[CrossRef]

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

Culshaw, B.

B. Culshaw and I. P. Giles, " Frequency modulated heterodyne optical Sagnac interferometer," IEEE J. Quantum Electron. QE-18, 690- 693 ( 1982).
[CrossRef]

Franks, R. B.

R. B. Franks, W. Torruellas, and R. C. Youngquist, " Birefringent stress location sensor," in Fiber Optic Sensors, H.J.Arditti and L.B.Jeunhomme, eds., Proc. SPIE 586, 84- 89 ( 1985).

Giles, I. P.

B. Culshaw and I. P. Giles, " Frequency modulated heterodyne optical Sagnac interferometer," IEEE J. Quantum Electron. QE-18, 690- 693 ( 1982).
[CrossRef]

Hymans, A. J.

A. J. Hymans and J. Lait, " Analysis of a frequency-modulated continuous-wave ranging system," Proc. IEEE 107, 365- 372 ( 1960).

Jackson, D. A.

M. Corke, A. D. Kersey, D. A. Jackson, and J. D. C. Jones, " All-fiber Michelson thermometer," Electron. Lett. 19, 471- 472 ( 1983).
[CrossRef]

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

Jones, J. D. C.

M. Corke, A. D. Kersey, D. A. Jackson, and J. D. C. Jones, " All-fiber Michelson thermometer," Electron. Lett. 19, 471- 472 ( 1983).
[CrossRef]

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

Kersey, A. D.

M. Corke, A. D. Kersey, D. A. Jackson, and J. D. C. Jones, " All-fiber Michelson thermometer," Electron. Lett. 19, 471- 472 ( 1983).
[CrossRef]

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

Lait, J.

A. J. Hymans and J. Lait, " Analysis of a frequency-modulated continuous-wave ranging system," Proc. IEEE 107, 365- 372 ( 1960).

Leilabady, P. A.

P. A. Leilabady, " Optical fiber point temperature sensor," in Fiber Optic and Laser Sensors V, R.P.DePaula and E.Udd, eds., Proc. SPIE 838, 231- 237 ( 1987).

Skolnik, M. I.

M. I. Skolnik, Introduction to Radar Systems (McGraw Hill, 1962).

Torruellas, W.

R. B. Franks, W. Torruellas, and R. C. Youngquist, " Birefringent stress location sensor," in Fiber Optic Sensors, H.J.Arditti and L.B.Jeunhomme, eds., Proc. SPIE 586, 84- 89 ( 1985).

Youngquist, R. C.

R. B. Franks, W. Torruellas, and R. C. Youngquist, " Birefringent stress location sensor," in Fiber Optic Sensors, H.J.Arditti and L.B.Jeunhomme, eds., Proc. SPIE 586, 84- 89 ( 1985).

Zheng, J.

Appl. Opt. (3)

Electron. Lett. (2)

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

M. Corke, A. D. Kersey, D. A. Jackson, and J. D. C. Jones, " All-fiber Michelson thermometer," Electron. Lett. 19, 471- 472 ( 1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

B. Culshaw and I. P. Giles, " Frequency modulated heterodyne optical Sagnac interferometer," IEEE J. Quantum Electron. QE-18, 690- 693 ( 1982).
[CrossRef]

Proc. IEEE (1)

A. J. Hymans and J. Lait, " Analysis of a frequency-modulated continuous-wave ranging system," Proc. IEEE 107, 365- 372 ( 1960).

Other (3)

M. I. Skolnik, Introduction to Radar Systems (McGraw Hill, 1962).

R. B. Franks, W. Torruellas, and R. C. Youngquist, " Birefringent stress location sensor," in Fiber Optic Sensors, H.J.Arditti and L.B.Jeunhomme, eds., Proc. SPIE 586, 84- 89 ( 1985).

P. A. Leilabady, " Optical fiber point temperature sensor," in Fiber Optic and Laser Sensors V, R.P.DePaula and E.Udd, eds., Proc. SPIE 838, 231- 237 ( 1987).

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Figures (9)

Fig. 1
Fig. 1

Spatial dependency of the OPD on the sensing surface of a photodetector.

Fig. 2
Fig. 2

Contrast of beat signals under different conditions: a, ideal optical source, I 1 = I 2, θ = 0; b, ideal optical source, I 1 = I 2∕4, θ = 0; c, ideal optical source, I 1 = I 2∕4, θ = λ0∕2L; d, practical optical source, I 1 = I 2, θ = 0; e, practical optical source, I 1 = I 2∕4, θ = 0; f, practical optical source, I 1 = I 2∕4, θ = λ0∕2L.

Fig. 3
Fig. 3

Waveforms of the beat signals of sawtooth-wave FMCW interference with three beat frequencies: (a) vb < vm , (b) vb = vm , (c) vb vm.

Fig. 4
Fig. 4

Michelson FMCW interferometer.

Fig. 5
Fig. 5

Michelson FMCW interferometer with retroreflectors.

Fig. 6
Fig. 6

Mach–Zehnder FMCW interferometer.

Fig. 7
Fig. 7

Fabry–Perot FMCW interferometer.

Fig. 8
Fig. 8

Waveforms of the real beat signal under several conditions.

Fig. 9
Fig. 9

Experimental results of the Fabry–Perot FMCW interferometer.

Equations (35)

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I ( τ , t ) = I 1 + I 2 + 2 I 1 I 2 cos ( α τ t + ω 0 τ )
= I 0 [ 1 + V cos ( ω b t + ϕ b 0 ) ] ,
α = Δ ω / T m ,
ω b = α τ ,
ϕ b 0 = ω 0 τ .
I ( OPD,   t ) = I 0 [ 1 + V cos ( 2 π Δ v v m OPD c t + 2 π λ 0 OPD ) ]
= I 0 [ 1 + V cos ( 2 π v b t + ϕ b 0 ) ] ,
v b = α OPD 2 π c = Δ v v m OPD c ,
ϕ b 0 = ω 0 OPD c = 2 π OPD λ 0 .
OPD = c Δ v v m v b ,
δ ( OPD ) = λ 0 2 π δ ϕ b 0 .
v D ¯ = 1 2 ( v br ¯ | v bf ¯ | ) .
v D ¯ = 1 λ 0 dOPD ( t ) d t .
s = λ 0 2 n v D ¯ ,
Δ ( OPD ) = n x sin θ
x θ ,
I ( t ) = 0 L ( i 1 + i 2 ) [ 1 + 2 i 1 i 2 i 1 + i 2 × cos ( ω b t + ϕ b + 2 π θ λ 0 x ) ] d x
= ( i 1 + i 2 ) [ L + 2 i 1 i 2 i 1 + i 2 λ 0 π θ sin ( π L λ 0 θ ) cos ( ω b t + ϕ b + π L λ 0 θ ) ]
= ( i 1 + i 2 ) L [ 1 + 2 i 1 i 2 i 1 + i 2   sinc ( π L λ 0 θ ) cos ( ω b t + ϕ b + π L λ 0 θ ) ]
= ( I 1 + I 2 ) [ 1 + 2 I 1 I 2 I 1 + I 2   sinc ( π L λ 0 θ ) × cos ( ω b t + ϕ b + π L λ 0 θ ) ]
= I 0 [ 1 + V cos ( ω b t + ϕ b + π L λ 0 θ ) ] ,
V = 2 I 1 I 2 I 1 + I 2   sinc ( π L λ 0 θ ) .
V = 2 I 1 I 2 I 1 + I 2 .
V = 0.
V = 2 I 1 I 2 I 1 + I 2 | sinc ( π l c  OPD ) | sinc ( π L λ 0 θ ) ,
OPD c / Δ v .
OPD = 2 n ( l 2 l 1 ) ,
ϕ b 0 = 4 π n ( l 2 l 1 ) λ 0 .
Δ l 2 = λ 0 4 π n Δ ϕ b 0 .
OPD = n ( l 2 l 1 ) ,
OPD = 2 n d ,
v b = 2 n d Δ v v m c ,
ϕ b 0 = 4 π n d λ 0 .
d = c 2 n Δ v v m v b ,
Δ d = λ 0 4 π n Δ ϕ b 0 .

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