Abstract

A fiber optic Fourier transform spectrometer capable of coherent interferogram averaging is constructed, for the first time to our knowledge. One fiber arm of the interferometer is periodically stretched, and the amplitudes of the fundamental and second harmonics of the modulation frequency in the photocurrent output are simultaneously detected. Successful operation results from the generation of an external clock for sampling the interferogram from the detected outputs varying in phase quadrature. Even when the moving mirror in the interferometer translates nonlinearly and two fiber arms receive random perturbations independently, sampling can be uniformly performed along the interferogram. From the experiments, variation of sampling start position on each interferogram was limited within 100 nm during one hundred repetitive scans. For 100 coherent averages, therefore, the SNR increased by ~10 without deformation.

© 1990 Optical Society of America

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References

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  1. R. J. Bell, Introductory Fourier-Transform Spectroscopy (Academic, New York, 1972), Chap. 1.
  2. As a method of achieving uniform sampling of an interferogram based on polarization, see, for an example, K. Takada, K. Chida, J. Noda, S. Nakajima, “Development of a Trench Depth Measurement System for VLSI Dynamic Random Access Memory Vertical Capacitor Cells Using an Interferometric Technique With a Michelson Interferometer,” Appl. Opt. 28, 3373–3381 (1989).
    [CrossRef] [PubMed]
  3. D. A. Jackson, A. Dandridge, S. K. Sheem, “Measurement of Small Phase Shifts Using a Single-Mode Optical-Fiber Interferometer,” Opt. Lett. 5, 139–141 (1980).
    [CrossRef] [PubMed]
  4. M. Imai, T. Ohashi, Y. Ohtsuka, “Fiber-Optic Michelson Interferometer Using an Optical Power Divider,” Opt. Lett. 5, 418–420 (1980).
    [CrossRef] [PubMed]
  5. S. K. Sheem, “Fiber-Optic Gyroscope With [3 × 3] Directional Coupler,” Appl. Phys. Lett. 37, 869–871 (1980).
    [CrossRef]
  6. M. Imai, T. Ohashi, Y. Ohtsuka, “High-Sensitive All-fiber Michelson Interferometer by Use of Differential Output Configuration,” Opt. Commun. 39, 7–10 (1981).
    [CrossRef]
  7. Th. Niemeier, R. Ulrich, “Quadrature Outputs from Fiber Interferometer with 4 × 4 Coupler,” Opt. Lett. 11, 677–679 (1986).
    [CrossRef] [PubMed]
  8. A. D. Kersey, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Single-mode Fiber Fourier Transform Spectrometer,” Electron. Lett. 21, 463–464 (1985).
  9. A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE J. Quantum Electron. QE-18, 1647–1653 (1982).
    [CrossRef]
  10. D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
    [CrossRef]
  11. N. Shibata, S. Shibata, T. Edahiro, “Refractive Index Dispersion of Lightguide Glasses at High Temperature,” Electron. Lett. 17, 310–311 (1981).
    [CrossRef]
  12. E. O. Brigham, The Fast Fourier Transform, (Prentice-Hall, Englewood Cliffs, NJ, 1974), pp. 140–146.

1989 (1)

1986 (1)

1985 (2)

A. D. Kersey, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Single-mode Fiber Fourier Transform Spectrometer,” Electron. Lett. 21, 463–464 (1985).

D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
[CrossRef]

1982 (1)

A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE J. Quantum Electron. QE-18, 1647–1653 (1982).
[CrossRef]

1981 (2)

M. Imai, T. Ohashi, Y. Ohtsuka, “High-Sensitive All-fiber Michelson Interferometer by Use of Differential Output Configuration,” Opt. Commun. 39, 7–10 (1981).
[CrossRef]

N. Shibata, S. Shibata, T. Edahiro, “Refractive Index Dispersion of Lightguide Glasses at High Temperature,” Electron. Lett. 17, 310–311 (1981).
[CrossRef]

1980 (3)

Bell, R. J.

R. J. Bell, Introductory Fourier-Transform Spectroscopy (Academic, New York, 1972), Chap. 1.

Brigham, E. O.

E. O. Brigham, The Fast Fourier Transform, (Prentice-Hall, Englewood Cliffs, NJ, 1974), pp. 140–146.

Chida, K.

Dandridge, A.

A. D. Kersey, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Single-mode Fiber Fourier Transform Spectrometer,” Electron. Lett. 21, 463–464 (1985).

A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE J. Quantum Electron. QE-18, 1647–1653 (1982).
[CrossRef]

D. A. Jackson, A. Dandridge, S. K. Sheem, “Measurement of Small Phase Shifts Using a Single-Mode Optical-Fiber Interferometer,” Opt. Lett. 5, 139–141 (1980).
[CrossRef] [PubMed]

Edahiro, T.

N. Shibata, S. Shibata, T. Edahiro, “Refractive Index Dispersion of Lightguide Glasses at High Temperature,” Electron. Lett. 17, 310–311 (1981).
[CrossRef]

Giallorenzi, T. G.

A. D. Kersey, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Single-mode Fiber Fourier Transform Spectrometer,” Electron. Lett. 21, 463–464 (1985).

A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE J. Quantum Electron. QE-18, 1647–1653 (1982).
[CrossRef]

Imai, M.

M. Imai, T. Ohashi, Y. Ohtsuka, “High-Sensitive All-fiber Michelson Interferometer by Use of Differential Output Configuration,” Opt. Commun. 39, 7–10 (1981).
[CrossRef]

M. Imai, T. Ohashi, Y. Ohtsuka, “Fiber-Optic Michelson Interferometer Using an Optical Power Divider,” Opt. Lett. 5, 418–420 (1980).
[CrossRef] [PubMed]

Jackson, D. A.

Kersey, A. D.

A. D. Kersey, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Single-mode Fiber Fourier Transform Spectrometer,” Electron. Lett. 21, 463–464 (1985).

Mortimore, D. B.

D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
[CrossRef]

Nakajima, S.

Niemeier, Th.

Noda, J.

Ohashi, T.

M. Imai, T. Ohashi, Y. Ohtsuka, “High-Sensitive All-fiber Michelson Interferometer by Use of Differential Output Configuration,” Opt. Commun. 39, 7–10 (1981).
[CrossRef]

M. Imai, T. Ohashi, Y. Ohtsuka, “Fiber-Optic Michelson Interferometer Using an Optical Power Divider,” Opt. Lett. 5, 418–420 (1980).
[CrossRef] [PubMed]

Ohtsuka, Y.

M. Imai, T. Ohashi, Y. Ohtsuka, “High-Sensitive All-fiber Michelson Interferometer by Use of Differential Output Configuration,” Opt. Commun. 39, 7–10 (1981).
[CrossRef]

M. Imai, T. Ohashi, Y. Ohtsuka, “Fiber-Optic Michelson Interferometer Using an Optical Power Divider,” Opt. Lett. 5, 418–420 (1980).
[CrossRef] [PubMed]

Sheem, S. K.

Shibata, N.

N. Shibata, S. Shibata, T. Edahiro, “Refractive Index Dispersion of Lightguide Glasses at High Temperature,” Electron. Lett. 17, 310–311 (1981).
[CrossRef]

Shibata, S.

N. Shibata, S. Shibata, T. Edahiro, “Refractive Index Dispersion of Lightguide Glasses at High Temperature,” Electron. Lett. 17, 310–311 (1981).
[CrossRef]

Takada, K.

Tveten, A. B.

A. D. Kersey, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Single-mode Fiber Fourier Transform Spectrometer,” Electron. Lett. 21, 463–464 (1985).

A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE J. Quantum Electron. QE-18, 1647–1653 (1982).
[CrossRef]

Ulrich, R.

Appl. Opt. (1)

Appl. Phys. Lett. (1)

S. K. Sheem, “Fiber-Optic Gyroscope With [3 × 3] Directional Coupler,” Appl. Phys. Lett. 37, 869–871 (1980).
[CrossRef]

Electron. Lett. (3)

A. D. Kersey, A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Single-mode Fiber Fourier Transform Spectrometer,” Electron. Lett. 21, 463–464 (1985).

D. B. Mortimore, “Wavelength-Flattened Fused Couplers,” Electron. Lett. 21, 742–743 (1985).
[CrossRef]

N. Shibata, S. Shibata, T. Edahiro, “Refractive Index Dispersion of Lightguide Glasses at High Temperature,” Electron. Lett. 17, 310–311 (1981).
[CrossRef]

IEEE J. Quantum Electron. (1)

A. Dandridge, A. B. Tveten, T. G. Giallorenzi, “Homodyne Demodulation Scheme for Fiber Optic Sensors Using Phase Generated Carrier,” IEEE J. Quantum Electron. QE-18, 1647–1653 (1982).
[CrossRef]

Opt. Commun. (1)

M. Imai, T. Ohashi, Y. Ohtsuka, “High-Sensitive All-fiber Michelson Interferometer by Use of Differential Output Configuration,” Opt. Commun. 39, 7–10 (1981).
[CrossRef]

Opt. Lett. (3)

Other (2)

E. O. Brigham, The Fast Fourier Transform, (Prentice-Hall, Englewood Cliffs, NJ, 1974), pp. 140–146.

R. J. Bell, Introductory Fourier-Transform Spectroscopy (Academic, New York, 1972), Chap. 1.

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Figures (8)

Fig. 1
Fig. 1

Experimental setup of a fiber optic Fourier transform spectrometer with quadrature outputs: PZT MOD, cylindrical PZT modulator; PSD, phase sensitive detector; OSC, oscillator; TRG, up/down pulse descriminator circuit; ADC, A–D converer; HOST, host computer.

Fig. 2
Fig. 2

Schematic diagram of change in optical phase difference between two arms of the interferometer (upper trace), and a histogram of sampling number at each memory (lower trace).

Fig. 3
Fig. 3

(a) Output signals V f and V2 f displayed as a function of phase change ϕ r ; (b) Lissajous’s figure of V f vs V2 f ; and (c) change in output signal V f near the turning point, and up and down pulses generated by the up/down pulse discriminator.

Fig. 4
Fig. 4

Amplitudes of V f and V2 f vs RMS value of voltage applied to the PZT modulator.

Fig. 5
Fig. 5

(a) Two interferograms sequentially sampled and written on memories during first (forward) and second (backward) scans, and (b) results of overwriting all interferograms stored in memories in the same figure.

Fig. 6
Fig. 6

Interferograms acquired (a) before and (b) after coherent averaging.

Fig. 7
Fig. 7

(a) Interferogram of DFB laser diode acquired during 4.1-cm long total scan, and (b) its light spectrum calculated by FFT with Hanning window.

Fig. 8
Fig. 8

(a) Interferogram of SLD acquired of path change ranged from −150 to 150 μm, and (b) its light spectrum calculated by FFT with uniform window.

Equations (13)

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ϕ ˜ r ( t ) = ϕ r - Δ ϕ r sin ( 2 π f t ) .
ϕ r = 2 π ν r ( ν r ) c , Δ ϕ r = 2 π ν r Δ ( ν r ) c ,
E 1 E 2 cos [ ϕ ˜ r ( t ) ] = E 1 E 2 cos ( ϕ r ) cos [ Δ ϕ r sin ( 2 π f t ) ] + E 1 E 2 sin ( ϕ r ) sin [ Δ ϕ r sin ( 2 π f t ) ] .
E 1 E 2 cos ( ϕ r ) { J 0 ( Δ ϕ r ) + 2 n = 1 J 2 n ( Δ ϕ r ) cos ( 4 π n f t ) } + 2 E 1 E 2 sin ( ϕ r ) n = 0 J 2 n + 1 ( Δ ϕ r ) sin [ 2 π ( 2 n + 1 ) f t ] ,
I f ( t ) = 2 E 1 E 2 J 1 ( Δ ϕ r ) sin ( ϕ r ) sin ( 2 π f t ) , I 2 f ( t ) = 2 E 1 E 2 J 2 ( Δ ϕ r ) cos ( ϕ r ) cos ( 4 π f t ) .
V f = V 0 J 1 ( Δ ϕ r ) sin ( ϕ r ) , V 2 f = V 0 J 2 ( Δ ϕ r ) cos ( ϕ r ) ,
( ν ) = n 1 ( ν ) L 1 + x - n 2 ( ν ) L 2 ,
( ν r ) = n 1 ( ν r ) L 1 + x - n 2 ( ν r ) L 2 .
( ν ) = { n 1 ( ν r ) L 1 + x - n 2 ( ν r ) L 2 } + { Δ n 1 L 1 - Δ n 2 L 2 } = ( ν r ) + ( Δ n 1 L 1 - Δ n 2 L 2 ) .
ϕ ( ν ) = 2 π ν ( ν r ) c + ϕ 0 ( ν ) , Δ ϕ ( ν ) = 2 π ν Δ ( ν r ) c ,
V ( x ) = 2 0 J 2 [ Δ ϕ ( ν ) ] G ( ν ) cos [ ϕ ( ν ) ] d ν ,
V ( τ ) = 2 0 J 2 [ Δ ϕ ( ν ) ] G ( ν ) cos [ 2 π ν τ + ϕ 0 ( ν ) ] d ν .
δ ( Δ n 1 L 1 - Δ n 2 L 2 ) = { δ n 1 ( ν ) δ T - δ n 1 ( ν r ) δ T } δ T L 1 .

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