Abstract

I continue to analyze systematically the theory of optical frequency-modulated continuous-wave (FMCW) interference. Two special cases, multiple-beam optical FMCW interference and multiple-wavelength optical FMCW interference, are discussed in detail. Multiple-beam optical FMCW interference generates a signal with multiple frequencies because of mutual interference among the waves. Multiple-wavelength optical FMCW interference produces a signal whose amplitude is modulated by a synthetic wave. The applications of both types of optical FMCW interference are also discussed.

© 2005 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. A. J. Hymans, 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, New York, 1962).
  3. B. Culshaw, 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, 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, J. D. C. Jones, “All-fibre Michelson thermometer,” Electron. Lett. 19, 471–472 (1983).
    [CrossRef]
  6. 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, 971–976 (1985).
    [CrossRef]
  7. R. B. Franks, W. Torruellas, R. C. Youngquist, “Birefringent stress location sensor,” in Fiber Optic Sensors, H. J. Arditti, L. B. Jeunhomme, eds., Proc. SPIE586, 84–89 (1985).
  8. P. A. Leilabady, “Optical fiber point temperature sensor,” in Fiber Optic and Laser Sensors V, R. P. DePaula, E. Udd, eds., Proc. SPIE838, 231–237 (1987).
    [CrossRef]
  9. G. Zheng, M. Campbell, P. A. Wallace, “Reflectometric frequency-modulation continuous-wave distributed fiber-optic stress sensor with forward coupled beams,” Appl. Opt. 35, 5722–5726 (1996).
    [CrossRef] [PubMed]
  10. B. T. Meggitt, A. W. Palmer, “A fibre optic compatible signal-processing scheme for dual wavelength interferometry using Fourier harmonics,” Measurement 7, 50–54 (1989).
    [CrossRef]
  11. R. Onodera, Y. Ishii, “Two-wavelength laser-diode interferometer with fractional fringe techniques,” Appl. Opt. 34, 4740–4746 (1995).
    [CrossRef] [PubMed]
  12. J. Zheng, “Analysis of optical frequency-modulated continuous-wave interference,” Appl. Opt. 43, 4189–4198 (2004).
    [CrossRef] [PubMed]

2004 (1)

1996 (1)

1995 (1)

1989 (1)

B. T. Meggitt, A. W. Palmer, “A fibre optic compatible signal-processing scheme for dual wavelength interferometry using Fourier harmonics,” Measurement 7, 50–54 (1989).
[CrossRef]

1985 (1)

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, 971–976 (1985).
[CrossRef]

1983 (1)

M. Corke, A. D. Kersey, D. A. Jackson, J. D. C. Jones, “All-fibre Michelson thermometer,” Electron. Lett. 19, 471–472 (1983).
[CrossRef]

1982 (2)

B. Culshaw, 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, J. D. C. Jones, “Pseudoheterodyne detection scheme for optical interferometers,” Electron. Lett. 18, 1081–1083 (1982).
[CrossRef]

1960 (1)

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

Campbell, M.

Corke, M.

M. Corke, A. D. Kersey, D. A. Jackson, J. D. C. Jones, “All-fibre Michelson thermometer,” Electron. Lett. 19, 471–472 (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, 971–976 (1985).
[CrossRef]

B. Culshaw, 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, R. C. Youngquist, “Birefringent stress location sensor,” in Fiber Optic Sensors, H. J. Arditti, L. B. Jeunhomme, eds., Proc. SPIE586, 84–89 (1985).

Giles, I. P.

B. Culshaw, 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, J. Lait, “Analysis of a frequency-modulated continuous-wave ranging system,” Proc. IEEE 107, 365–372 (1960).

Ishii, Y.

Jackson, D. A.

M. Corke, A. D. Kersey, D. A. Jackson, J. D. C. Jones, “All-fibre Michelson thermometer,” Electron. Lett. 19, 471–472 (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.

M. Corke, A. D. Kersey, D. A. Jackson, J. D. C. Jones, “All-fibre Michelson thermometer,” Electron. Lett. 19, 471–472 (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]

Kersey, A. D.

M. Corke, A. D. Kersey, D. A. Jackson, J. D. C. Jones, “All-fibre Michelson thermometer,” Electron. Lett. 19, 471–472 (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]

Lait, J.

A. J. Hymans, 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, E. Udd, eds., Proc. SPIE838, 231–237 (1987).
[CrossRef]

Meggitt, B. T.

B. T. Meggitt, A. W. Palmer, “A fibre optic compatible signal-processing scheme for dual wavelength interferometry using Fourier harmonics,” Measurement 7, 50–54 (1989).
[CrossRef]

Onodera, R.

Palmer, A. W.

B. T. Meggitt, A. W. Palmer, “A fibre optic compatible signal-processing scheme for dual wavelength interferometry using Fourier harmonics,” Measurement 7, 50–54 (1989).
[CrossRef]

Skolnik, M. I.

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

Torruellas, W.

R. B. Franks, W. Torruellas, R. C. Youngquist, “Birefringent stress location sensor,” in Fiber Optic Sensors, H. J. Arditti, L. B. Jeunhomme, eds., Proc. SPIE586, 84–89 (1985).

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, 971–976 (1985).
[CrossRef]

Wallace, P. A.

Youngquist, R. C.

R. B. Franks, W. Torruellas, R. C. Youngquist, “Birefringent stress location sensor,” in Fiber Optic Sensors, H. J. Arditti, L. B. Jeunhomme, eds., Proc. SPIE586, 84–89 (1985).

Zheng, G.

Zheng, J.

Appl. Opt. (3)

Electron. Lett. (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]

M. Corke, A. D. Kersey, D. A. Jackson, J. D. C. Jones, “All-fibre Michelson thermometer,” Electron. Lett. 19, 471–472 (1983).
[CrossRef]

IEEE J. Quantum Electron. (1)

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

J. Lightwave Technol. (1)

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, 971–976 (1985).
[CrossRef]

Measurement (1)

B. T. Meggitt, A. W. Palmer, “A fibre optic compatible signal-processing scheme for dual wavelength interferometry using Fourier harmonics,” Measurement 7, 50–54 (1989).
[CrossRef]

Proc. IEEE (1)

A. J. Hymans, 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, New York, 1962).

R. B. Franks, W. Torruellas, R. C. Youngquist, “Birefringent stress location sensor,” in Fiber Optic Sensors, H. J. Arditti, L. B. Jeunhomme, eds., Proc. SPIE586, 84–89 (1985).

P. A. Leilabady, “Optical fiber point temperature sensor,” in Fiber Optic and Laser Sensors V, R. P. DePaula, E. Udd, eds., Proc. SPIE838, 231–237 (1987).
[CrossRef]

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 (4)

Fig. 1
Fig. 1

Real signals from the triple-beam sawtooth-wave Michelson FMCW interferometer.

Fig. 2
Fig. 2

Signal of double-wavelength sawtooth-wave FMCW interference.

Fig. 3
Fig. 3

Contrast of the signal of double-wavelength sawtooth-wave FMCW interference (when α1 = α2 and ω01 ≠ ω02).

Fig. 4
Fig. 4

Contrast of the signal from the practical double-wavelength sawtooth-wave FMCW interferometer [when α1 = α2 and ω01 ≠ ω02, the dashed curve represents the degree of temporal coherence |γ(τ)| of the optical FMCWs].

Equations (23)

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

E ( τ , t ) = E 0 exp [ j ϕ ( t - τ p ) ] ,
I ( τ 1 ,     τ m , t ) = [ i = 1 m E i ( τ i , t ) ] 2 | i = 1 m E i ( τ i , t ) | 2 ,
I ( τ 1 , τ 2 , τ 3 , t ) = E 1 ( τ 1 , t ) + E 2 ( τ 2 , t ) + E 3 ( τ 3 , t ) 2 = [ E 1 ( τ 1 , t ) + E 2 ( τ 2 , t ) + E 3 ( τ 3 , t ) ] [ E 1 ( τ 1 , t ) + E 2 ( τ 2 , t ) + E 3 ( τ 3 , t ) ] * = E 1 ( τ 1 , t ) E 1 * ( τ 1 , t ) + E 2 ( τ 2 , t ) E 2 * ( τ 2 , t ) + E 3 ( τ 3 , t ) E 3 * ( τ 3 , t ) + E 1 ( τ 1 , t ) E 2 * ( τ 2 , t ) + E 1 * ( τ 1 , t ) E 2 ( τ 2 , t ) + E 2 ( τ 2 , t ) E 3 * ( τ 3 , t ) + E 2 * ( τ 2 , t ) E 3 ( τ 3 , t ) + E 1 ( τ 1 , t ) E 3 * ( τ 3 , t ) + E 1 * ( τ 1 , t ) E 3 ( τ 3 , t ) = I 1 + I 2 + I 3 + 2 I 1 I 2 cos [ ϕ 1 ( t - τ 1 ) - ϕ 2 ( t - τ 2 ) ] + 2 I 2 I 3 cos [ ϕ 2 ( t - τ 2 ) - ϕ 3 ( t - τ 3 ) ] + 2 I 1 I 3 cos [ ϕ 1 ( t - τ 1 ) - ϕ 3 ( t - τ 3 ) ] ,
ω ( t ) = α t + ω 0 ,
α = Δ ω / T m ,
ϕ ( τ p , t ) = ½ α ( t - τ p ) 2 + ω 0 ( t - τ p ) + ϕ 0 ,
I ( τ 1 , τ 2 , τ 3 , t ) = I 1 + I 2 + I 3 + 2 I 1 I 2 cos [ α ( τ 2 - τ 1 ) t - ω 0 ( τ 2 - τ 1 ) ] + 2 I 2 I 3 cos × [ α ( τ 3 - τ 2 ) t - ω 0 ( τ 3 - τ 2 ) ] + 2 I 1 I 3 cos [ α ( τ 3 - τ 1 ) t - ω 0 ( τ 3 - τ 1 ) ] ,
τ 2 - τ 1 = ω b 1 / α , τ 3 - τ 2 = ω b 2 / α , τ 3 - τ 1 = ω b 3 / α ,
Δ τ 2 = Δ ω b 1 / α , Δ ( τ 3 - τ 2 ) = Δ ω b 2 / α , Δ τ 3 = Δ ω b 3 / α .
I ( τ , t ) = i = 1 m I 0 λ i { 1 + V λ i cos [ ϕ λ i ( t ) - ϕ λ i ( t - τ ) ] } ,
I ( τ , t ) = I 0 λ 1 { 1 + V λ 1 cos [ ϕ λ 1 ( t ) - ϕ λ 1 ( t - τ ) ] } + I 0 λ 2 { 1 + V λ 2 cos [ ϕ λ 2 ( t ) - ϕ λ 2 ( t - τ ) ] } ,
I ( τ , t ) = I 01 [ 1 + V 1 cos ( α 1 τ t + ω 01 τ ) ] + I 02 [ 1 + V 2 cos ( α 2 τ t + ω 02 ] ,
I ( τ , t ) = I 0 { 1 + V 2 [ cos ( α 1 τ t + ω 01 τ ) + cos ( α 2 τ t + ω 02 τ ) ] } = I 0 { 1 + V [ cos ( α 1 - α 2 2 τ t + ω 01 - ω 02 2 τ ) × cos ( α 1 + α 2 2 τ t + ω 01 + ω 02 2 τ ) ] } = I 0 { 1 + V [ cos ( Δ α 2 τ t + Δ ω 0 2 τ ) × cos ( α ¯ τ t + ω 0 ¯ τ ] } ,
Δ α = α 1 - α 2 ,
Δ ω 0 = ω 01 - ω 02 ,
α ¯ = α 1 + α 2 2 ,
ω 0 ¯ = ω 01 + ω 02 2 .
ω s = Δ α τ 2 = Δ α OPD 2 c ,
T s = 4 π Δ α τ = 4 π c Δ α OPD .
ϕ s 0 = Δ ω 0 τ 2 = Δ ω 0 OPD 2 c .
λ s = λ 01 λ 02 λ 01 - λ 02 ,
OPD c ω m Δ α ,
I ( τ , t ) = I 0 { 1 + V [ cos ( Δ ω 0 τ / 2 ) cos ( α τ t + ω 0 ¯ τ ) ] } .

Metrics