Abstract

We describe a method for measuring submicrometer distances with an asymmetric fiber Michelson interferometer having an LED as a source of radiation. By measuring the phase slope of the Fourier components in the frequency domain, it is possible to locate the position of reflections with nanometer precision even in the presence of sample dispersion. The method is compatible with time domain sampling at the Nyquist rate which assures efficiency in data acquisition and processing.

© 1991 Optical Society of America

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References

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  1. K. Takada, K. Chida, J. Noda, S. Nakajima, “Trench Depth Measurement System for VLSI DRAM’s Capacitor Cells Using Optical Fiber and Michelson Interferometer,” IEEE/OSA J. Lightwave Technol. LT-5, 881–887 (1987).
    [CrossRef]
  2. T. H. Bosselmann, R. Ulrich, “High Accuracy Position Sensing with Fiber Coupled White-Light Interferometers,” in Proceedings, Second International Conference on Optical Fiber Sensors (VDE-Verlag, Berlin, 1984), pp. 361–364.
    [CrossRef]
  3. A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
    [CrossRef]
  4. L. M. Smith, C. C. Dobson, “Absolute Displacement Measurements Using Modulation of the Spectrum of White Light in a Michelson Interferometer,” Appl. Opt. 28, 3339–3342 (1989).
    [CrossRef] [PubMed]
  5. P. A. Fluornoy, R. W. McClure, G. Wyntjes, “White-Light Interferometric Thickness Gauge,” Appl. Opt. 11, 1907–1915 (1972).
    [CrossRef]
  6. K. Takada, N. Takato, J. Noda, Y. Noguchi, “Characterization of Silica-Based Waveguides with an Interferometric Optical Time-Domain Reflectometry System Using a 1.3-μm-Wavelength Superluminescent Diode,” Opt. Lett. 14, 706–708 (1989).
    [CrossRef] [PubMed]
  7. R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 8.
  8. J. R. Birch, T. J. Parkeer, “Dispersive Fourier Transform Spectroscopy,” in Infrared and Millimeter Waves. Vol.2: Instrumentation, K. J. Button, Ed. (Academic, New York, 1979), Chap. 3.
  9. P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, F. R. Alard, “Three Ways to Implement Interferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence, and Nonlinear Susceptibilities,” IEEE/OSA J. Lightwave Technol. LT-7, 500–513 (1989).
    [CrossRef]
  10. Ref. 8, p. 92.
  11. B. L. Danielson, C. D. Whittenberg, “Interferometric Dispersion Measurements on Small Guided-Wave Structures,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), pp. 360–361.
  12. R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).
  13. N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1981).
  14. W. L. Wolfe, “Properties of Optical Materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), Sec. 7.
  15. L. Thevenaz, J. P. Pellaux, J. P. von der Weid, “All-Fiber Interferometer for Chromatic Dispersion Measurements,” IEEE/OSA J. Lightwave Technol. LT-6, 1–7 (1988).
    [CrossRef]
  16. K. Okamoto, T. Hosaka, H. Itoh, “Measurement of Chromatic Dispersions in Ti-Diffused LiNbO3 Optical Waveguides,” Opt. Lett. 13, 65–67 (1988).
    [CrossRef] [PubMed]

1989 (3)

1988 (2)

L. Thevenaz, J. P. Pellaux, J. P. von der Weid, “All-Fiber Interferometer for Chromatic Dispersion Measurements,” IEEE/OSA J. Lightwave Technol. LT-6, 1–7 (1988).
[CrossRef]

K. Okamoto, T. Hosaka, H. Itoh, “Measurement of Chromatic Dispersions in Ti-Diffused LiNbO3 Optical Waveguides,” Opt. Lett. 13, 65–67 (1988).
[CrossRef] [PubMed]

1987 (2)

K. Takada, K. Chida, J. Noda, S. Nakajima, “Trench Depth Measurement System for VLSI DRAM’s Capacitor Cells Using Optical Fiber and Michelson Interferometer,” IEEE/OSA J. Lightwave Technol. LT-5, 881–887 (1987).
[CrossRef]

A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
[CrossRef]

1972 (1)

Alard, F. R.

P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, F. R. Alard, “Three Ways to Implement Interferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence, and Nonlinear Susceptibilities,” IEEE/OSA J. Lightwave Technol. LT-7, 500–513 (1989).
[CrossRef]

Bell, R. J.

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 8.

Birch, J. R.

J. R. Birch, T. J. Parkeer, “Dispersive Fourier Transform Spectroscopy,” in Infrared and Millimeter Waves. Vol.2: Instrumentation, K. J. Button, Ed. (Academic, New York, 1979), Chap. 3.

Bosselmann, T. H.

T. H. Bosselmann, R. Ulrich, “High Accuracy Position Sensing with Fiber Coupled White-Light Interferometers,” in Proceedings, Second International Conference on Optical Fiber Sensors (VDE-Verlag, Berlin, 1984), pp. 361–364.
[CrossRef]

Bracewell, R. N.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).

Chida, K.

K. Takada, K. Chida, J. Noda, S. Nakajima, “Trench Depth Measurement System for VLSI DRAM’s Capacitor Cells Using Optical Fiber and Michelson Interferometer,” IEEE/OSA J. Lightwave Technol. LT-5, 881–887 (1987).
[CrossRef]

Danielson, B. L.

B. L. Danielson, C. D. Whittenberg, “Interferometric Dispersion Measurements on Small Guided-Wave Structures,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), pp. 360–361.

Dobson, C. C.

Draper, N. R.

N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1981).

Durteste, Y.

P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, F. R. Alard, “Three Ways to Implement Interferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence, and Nonlinear Susceptibilities,” IEEE/OSA J. Lightwave Technol. LT-7, 500–513 (1989).
[CrossRef]

Farah, F.

A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
[CrossRef]

Fluornoy, P. A.

Francois, P.-L.

P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, F. R. Alard, “Three Ways to Implement Interferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence, and Nonlinear Susceptibilities,” IEEE/OSA J. Lightwave Technol. LT-7, 500–513 (1989).
[CrossRef]

Gerges, A. S.

A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
[CrossRef]

Hosaka, T.

Itoh, H.

Jackson, D. A.

A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
[CrossRef]

Jones, J. D. C.

A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
[CrossRef]

McClure, R. W.

Monerie, M.

P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, F. R. Alard, “Three Ways to Implement Interferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence, and Nonlinear Susceptibilities,” IEEE/OSA J. Lightwave Technol. LT-7, 500–513 (1989).
[CrossRef]

Nakajima, S.

K. Takada, K. Chida, J. Noda, S. Nakajima, “Trench Depth Measurement System for VLSI DRAM’s Capacitor Cells Using Optical Fiber and Michelson Interferometer,” IEEE/OSA J. Lightwave Technol. LT-5, 881–887 (1987).
[CrossRef]

Newson, T. P.

A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
[CrossRef]

Noda, J.

K. Takada, N. Takato, J. Noda, Y. Noguchi, “Characterization of Silica-Based Waveguides with an Interferometric Optical Time-Domain Reflectometry System Using a 1.3-μm-Wavelength Superluminescent Diode,” Opt. Lett. 14, 706–708 (1989).
[CrossRef] [PubMed]

K. Takada, K. Chida, J. Noda, S. Nakajima, “Trench Depth Measurement System for VLSI DRAM’s Capacitor Cells Using Optical Fiber and Michelson Interferometer,” IEEE/OSA J. Lightwave Technol. LT-5, 881–887 (1987).
[CrossRef]

Noguchi, Y.

Okamoto, K.

Parkeer, T. J.

J. R. Birch, T. J. Parkeer, “Dispersive Fourier Transform Spectroscopy,” in Infrared and Millimeter Waves. Vol.2: Instrumentation, K. J. Button, Ed. (Academic, New York, 1979), Chap. 3.

Pellaux, J. P.

L. Thevenaz, J. P. Pellaux, J. P. von der Weid, “All-Fiber Interferometer for Chromatic Dispersion Measurements,” IEEE/OSA J. Lightwave Technol. LT-6, 1–7 (1988).
[CrossRef]

Smith, H.

N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1981).

Smith, L. M.

Takada, K.

K. Takada, N. Takato, J. Noda, Y. Noguchi, “Characterization of Silica-Based Waveguides with an Interferometric Optical Time-Domain Reflectometry System Using a 1.3-μm-Wavelength Superluminescent Diode,” Opt. Lett. 14, 706–708 (1989).
[CrossRef] [PubMed]

K. Takada, K. Chida, J. Noda, S. Nakajima, “Trench Depth Measurement System for VLSI DRAM’s Capacitor Cells Using Optical Fiber and Michelson Interferometer,” IEEE/OSA J. Lightwave Technol. LT-5, 881–887 (1987).
[CrossRef]

Takato, N.

Thevenaz, L.

L. Thevenaz, J. P. Pellaux, J. P. von der Weid, “All-Fiber Interferometer for Chromatic Dispersion Measurements,” IEEE/OSA J. Lightwave Technol. LT-6, 1–7 (1988).
[CrossRef]

Ulrich, R.

T. H. Bosselmann, R. Ulrich, “High Accuracy Position Sensing with Fiber Coupled White-Light Interferometers,” in Proceedings, Second International Conference on Optical Fiber Sensors (VDE-Verlag, Berlin, 1984), pp. 361–364.
[CrossRef]

Vassallo, C.

P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, F. R. Alard, “Three Ways to Implement Interferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence, and Nonlinear Susceptibilities,” IEEE/OSA J. Lightwave Technol. LT-7, 500–513 (1989).
[CrossRef]

von der Weid, J. P.

L. Thevenaz, J. P. Pellaux, J. P. von der Weid, “All-Fiber Interferometer for Chromatic Dispersion Measurements,” IEEE/OSA J. Lightwave Technol. LT-6, 1–7 (1988).
[CrossRef]

Whittenberg, C. D.

B. L. Danielson, C. D. Whittenberg, “Interferometric Dispersion Measurements on Small Guided-Wave Structures,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), pp. 360–361.

Wolfe, W. L.

W. L. Wolfe, “Properties of Optical Materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), Sec. 7.

Wyntjes, G.

Appl. Opt. (2)

Electron. Lett. (1)

A. S. Gerges, F. Farah, T. P. Newson, J. D. C. Jones, D. A. Jackson, “Interferometric Fiber-Optic Sensor Using a Short-Coherence Length Source,” Electron. Lett. 23, 1110–1111 (1987).
[CrossRef]

IEEE/OSA J. Lightwave Technol. (3)

K. Takada, K. Chida, J. Noda, S. Nakajima, “Trench Depth Measurement System for VLSI DRAM’s Capacitor Cells Using Optical Fiber and Michelson Interferometer,” IEEE/OSA J. Lightwave Technol. LT-5, 881–887 (1987).
[CrossRef]

L. Thevenaz, J. P. Pellaux, J. P. von der Weid, “All-Fiber Interferometer for Chromatic Dispersion Measurements,” IEEE/OSA J. Lightwave Technol. LT-6, 1–7 (1988).
[CrossRef]

P.-L. Francois, M. Monerie, C. Vassallo, Y. Durteste, F. R. Alard, “Three Ways to Implement Interferencial Techniques: Application to Measurements of Chromatic Dispersion, Birefringence, and Nonlinear Susceptibilities,” IEEE/OSA J. Lightwave Technol. LT-7, 500–513 (1989).
[CrossRef]

Opt. Lett. (2)

Other (8)

T. H. Bosselmann, R. Ulrich, “High Accuracy Position Sensing with Fiber Coupled White-Light Interferometers,” in Proceedings, Second International Conference on Optical Fiber Sensors (VDE-Verlag, Berlin, 1984), pp. 361–364.
[CrossRef]

R. J. Bell, Introductory Fourier Transform Spectroscopy (Academic, New York, 1972), Chap. 8.

J. R. Birch, T. J. Parkeer, “Dispersive Fourier Transform Spectroscopy,” in Infrared and Millimeter Waves. Vol.2: Instrumentation, K. J. Button, Ed. (Academic, New York, 1979), Chap. 3.

Ref. 8, p. 92.

B. L. Danielson, C. D. Whittenberg, “Interferometric Dispersion Measurements on Small Guided-Wave Structures,” in Technical Digest, Conference on Lasers and Electro-Optics (Optical Society of America, Washington, DC, 1988), pp. 360–361.

R. N. Bracewell, The Fourier Transform and Its Applications (McGraw-Hill, New York, 1978).

N. R. Draper, H. Smith, Applied Regression Analysis (Wiley, New York, 1981).

W. L. Wolfe, “Properties of Optical Materials,” in Handbook of Optics, W. G. Driscoll, W. Vaughan, Eds. (McGraw-Hill, New York, 1978), Sec. 7.

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Figures (4)

Fig. 1
Fig. 1

Block diagram of a fiber scanning Michelson interferometer. A transparent sample is inserted in the test arm so that the Fresnel reflection from the front surface at (a) occurs at the point of equal path difference. Scanning mirror M generates a second interferogram from the back surface at (b) and involves radiation propagating a distance z through the sample. The LED source is unmodulated.

Fig. 2
Fig. 2

Oversampled interferograms from the front (a) and back (b) surfaces of a silica etalon 19 mm thick.

Fig. 3
Fig. 3

Interferograms of Fig. 2 sampled at the Nyquist rate.

Fig. 4
Fig. 4

Experimental values for the phase slope at various time-shifted computational origins around the position of stationary phase. The zero crossing occurs near the maximum of the interferogram in Fig. 3(b). The sample number is arbitrarily labeled so that m = 0 is nearest the zero crossing. The phase slope is plotted in dimensionless units of k−1, where k is the FFT array dimension (see text).

Equations (14)

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m ( ω ) = - + M ( t ) exp ( i ω t ) d t ,
m ( ω ) = B ( ω ) exp [ - i ϕ ( ω ) ] .
ϕ ( ω ) = ω c z n ( ω ) ,
ϕ ( ω ) = ϕ ( ω 0 ) + d ϕ d ω ( ω 0 ) · ( ω - ω 0 ) + 1 2 d 2 ϕ d ω 2 ( ω 0 ) · ( ω - ω 0 ) 2 + 1 6 d 3 ϕ d ω 3 ( ω 0 ) · ( ω - ω 0 ) 3 + .
T ( ω ) = d ϕ d ω ( ω ) · = z c [ N g ( ω 0 ) + d N g d ω ( ω 0 ) · ( ω - ω 0 ) + 1 2 d 2 N g d ω 2 ( ω 0 ) · ( ω - ω 0 ) 2 + ] ,
N g ( ω ) = n ( ω ) + ω d n d ω ( ω ) · .
z = c N g ( ω 0 ) d ϕ d ω ( ω 0 ) · .
ϕ s ( ω ) = z c ω n ( ω ) - ω m Δ T ,
z = c N g ( ω 0 ) [ d ϕ s d ω ( ω 0 ) + m Δ T ] .
M ( t ) = 1 2 π - + B ( ω ) exp [ - i ϕ ( ω ) ] exp ( - i ω t ) d ω .
B ( ω ) = exp [ - ( ω - ω 0 ) 2 / 2 σ ω 2 ] .
M ( t ) = exp ( - t 2 / 2 σ t 2 ) g ( t ) .
σ t = σ t o { 1 + [ d 2 ϕ ( ω 0 ) d ω 2 ] σ ω 4 } 1 / 2 ,
D ( ω 0 ) = - ω 0 2 2 π z c d 2 ϕ ( ω ) d ω 2 .

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