Abstract

A highly accurate method of optical path-length measurement is introduced by use of a scanning heterodyne optical interferometer with no moving parts. The instrument has demonstrated the potential to measure optical path length at angstrom resolution over continuous thickness in the micrometer range. This optical path length can be used to calculate the thickness of any material if the refractive index is known or to measure the refractive index of the material if the thickness is known. The instrument uses a single acousto-optic device in an in-line ultra-stable reflective geometry to implement rapid scanning in the microsecond domain for thickness measurements of the test medium.

© 2003 Optical Society of America

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References

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  1. P. Hariharan, Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995).
  2. P. K. Rastogi, ed., Holographic Interferometry, Vol. 68 of Springer Series in Optical Sciences (Springer, New York, 1994).
  3. J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
    [Crossref]
  4. R. Dandliker, Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1980), Vol. 17.
  5. S. Kim, I. Chang, D. Kim, T. Kim, S. Yoo, “Very large scale phase measuring interferometry for profile measurement of aspheric surfaces with nanometer accuracy,” in The Pacific Rim Conference on Lasers and Electro-Optics (IEEE, New York, 1999), pp. 70–71.
  6. J. E. Greaber, “Optical scanning interferometer for dynamic imaging of high-frequency surface motion,” in Ultrasonics Symposium, 2000 (IEEE, New York, 2000), pp. 733–736.
  7. Y. Watanable, I. Yamaguchi, “Digital Hilbert transform for separation measurement of thickness and refractive indices of layered objects by use of a wavelength-scanning heterodyneinterference confocal microscopes,” App. Opt. 41, 4497–4502 (2002).
    [Crossref]
  8. T. Fukano, I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
    [Crossref]
  9. N. A. Riza, “Scanning heterodyne optical interferometer,” Rev. Sci. Instrum. 67, 2466–2476 (1997).
    [Crossref]
  10. N. A. Riza, “Scanning heterodyne acousto-optical interferometers,” U.S. patent5,694,216 (2December1997).
  11. N. A. Riza, M. A. Arain, “Sub-micron range thickness measurements using a novel scanning heterodyne optical interferometer,” Proceedings of IEEE Sensors 2002 (IEEE, New York, 2002), Vol. 2, pp. 1080–1084.
    [Crossref]
  12. I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, N.J., 1993), Vol. 1.
    [Crossref]

2002 (1)

Y. Watanable, I. Yamaguchi, “Digital Hilbert transform for separation measurement of thickness and refractive indices of layered objects by use of a wavelength-scanning heterodyneinterference confocal microscopes,” App. Opt. 41, 4497–4502 (2002).
[Crossref]

1999 (1)

1997 (1)

N. A. Riza, “Scanning heterodyne optical interferometer,” Rev. Sci. Instrum. 67, 2466–2476 (1997).
[Crossref]

1974 (1)

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Arain, M. A.

N. A. Riza, M. A. Arain, “Sub-micron range thickness measurements using a novel scanning heterodyne optical interferometer,” Proceedings of IEEE Sensors 2002 (IEEE, New York, 2002), Vol. 2, pp. 1080–1084.
[Crossref]

Brangaccio, D. J.

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Chang, I.

S. Kim, I. Chang, D. Kim, T. Kim, S. Yoo, “Very large scale phase measuring interferometry for profile measurement of aspheric surfaces with nanometer accuracy,” in The Pacific Rim Conference on Lasers and Electro-Optics (IEEE, New York, 1999), pp. 70–71.

Dandliker, R.

R. Dandliker, Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1980), Vol. 17.

Fukano, T.

Gallagher, J. E.

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Greaber, J. E.

J. E. Greaber, “Optical scanning interferometer for dynamic imaging of high-frequency surface motion,” in Ultrasonics Symposium, 2000 (IEEE, New York, 2000), pp. 733–736.

Hariharan, P.

P. Hariharan, Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995).

Herriot, D. R.

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Khoo, I. C.

I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, N.J., 1993), Vol. 1.
[Crossref]

Kim, D.

S. Kim, I. Chang, D. Kim, T. Kim, S. Yoo, “Very large scale phase measuring interferometry for profile measurement of aspheric surfaces with nanometer accuracy,” in The Pacific Rim Conference on Lasers and Electro-Optics (IEEE, New York, 1999), pp. 70–71.

Kim, S.

S. Kim, I. Chang, D. Kim, T. Kim, S. Yoo, “Very large scale phase measuring interferometry for profile measurement of aspheric surfaces with nanometer accuracy,” in The Pacific Rim Conference on Lasers and Electro-Optics (IEEE, New York, 1999), pp. 70–71.

Kim, T.

S. Kim, I. Chang, D. Kim, T. Kim, S. Yoo, “Very large scale phase measuring interferometry for profile measurement of aspheric surfaces with nanometer accuracy,” in The Pacific Rim Conference on Lasers and Electro-Optics (IEEE, New York, 1999), pp. 70–71.

Riza, N. A.

N. A. Riza, “Scanning heterodyne optical interferometer,” Rev. Sci. Instrum. 67, 2466–2476 (1997).
[Crossref]

N. A. Riza, “Scanning heterodyne acousto-optical interferometers,” U.S. patent5,694,216 (2December1997).

N. A. Riza, M. A. Arain, “Sub-micron range thickness measurements using a novel scanning heterodyne optical interferometer,” Proceedings of IEEE Sensors 2002 (IEEE, New York, 2002), Vol. 2, pp. 1080–1084.
[Crossref]

Rosenfeld, D. P.

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Schwider, J.

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Watanable, Y.

Y. Watanable, I. Yamaguchi, “Digital Hilbert transform for separation measurement of thickness and refractive indices of layered objects by use of a wavelength-scanning heterodyneinterference confocal microscopes,” App. Opt. 41, 4497–4502 (2002).
[Crossref]

White, A. D.

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Wu, S. T.

I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, N.J., 1993), Vol. 1.
[Crossref]

Yamaguchi, I.

Y. Watanable, I. Yamaguchi, “Digital Hilbert transform for separation measurement of thickness and refractive indices of layered objects by use of a wavelength-scanning heterodyneinterference confocal microscopes,” App. Opt. 41, 4497–4502 (2002).
[Crossref]

T. Fukano, I. Yamaguchi, “Separation of measurement of the refractive index and the geometrical thickness by use of a wavelength-scanning interferometer with a confocal microscope,” Appl. Opt. 38, 4065–4073 (1999).
[Crossref]

Yoo, S.

S. Kim, I. Chang, D. Kim, T. Kim, S. Yoo, “Very large scale phase measuring interferometry for profile measurement of aspheric surfaces with nanometer accuracy,” in The Pacific Rim Conference on Lasers and Electro-Optics (IEEE, New York, 1999), pp. 70–71.

App. Opt. (2)

J. Schwider, D. R. Herriot, J. E. Gallagher, D. P. Rosenfeld, A. D. White, D. J. Brangaccio, “Digital wavefront measuring interferometer for testing optical surfaces and lenses,” App. Opt. 13, 2693–2703 (1974).
[Crossref]

Y. Watanable, I. Yamaguchi, “Digital Hilbert transform for separation measurement of thickness and refractive indices of layered objects by use of a wavelength-scanning heterodyneinterference confocal microscopes,” App. Opt. 41, 4497–4502 (2002).
[Crossref]

Appl. Opt. (1)

Rev. Sci. Instrum. (1)

N. A. Riza, “Scanning heterodyne optical interferometer,” Rev. Sci. Instrum. 67, 2466–2476 (1997).
[Crossref]

Other (8)

N. A. Riza, “Scanning heterodyne acousto-optical interferometers,” U.S. patent5,694,216 (2December1997).

N. A. Riza, M. A. Arain, “Sub-micron range thickness measurements using a novel scanning heterodyne optical interferometer,” Proceedings of IEEE Sensors 2002 (IEEE, New York, 2002), Vol. 2, pp. 1080–1084.
[Crossref]

I. C. Khoo, S. T. Wu, Optics and Nonlinear Optics of Liquid Crystals (World Scientific, N.J., 1993), Vol. 1.
[Crossref]

R. Dandliker, Progress in Optics, E. Wolf, ed. (North-Holland, New York, 1980), Vol. 17.

S. Kim, I. Chang, D. Kim, T. Kim, S. Yoo, “Very large scale phase measuring interferometry for profile measurement of aspheric surfaces with nanometer accuracy,” in The Pacific Rim Conference on Lasers and Electro-Optics (IEEE, New York, 1999), pp. 70–71.

J. E. Greaber, “Optical scanning interferometer for dynamic imaging of high-frequency surface motion,” in Ultrasonics Symposium, 2000 (IEEE, New York, 2000), pp. 733–736.

P. Hariharan, Handbook of Optics, 2nd ed., M. Bass, ed. (McGraw-Hill, New York, 1995).

P. K. Rastogi, ed., Holographic Interferometry, Vol. 68 of Springer Series in Optical Sciences (Springer, New York, 1994).

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Figures (5)

Fig. 1
Fig. 1

Geometry for calculating the phase shift introduced in the two components of the optical beam by a material when it is (a) transmissive material or (b) reflective material for optical path-length measurement.

Fig. 2
Fig. 2

Top view and side views of the reflective design of the novel scanning heterodyne optical interferometer: (a) top view and (b) two views at V1 and V2 planes shown in (a). V, View; CC, calibration cell; BS, beam splitter; PBS, polarization beam splitter; PD, photodetector.

Fig. 3
Fig. 3

Measured data for the OPL difference produced by a parallel-rub NLC cell when its drive voltage is varied. Δn is the birefringence, and d is the cell thickness.

Fig. 4
Fig. 4

Oscilloscope traces of the output from the photoreceivers when our test material, i.e., a NLC cell is inserted in the scan beam with a 70-MHz drive signal and when the voltage amplitude level corresponds to optical phase shifts of (a) 90°, (b) 180°, (c) 270°, and (d) 360°.

Fig. 5
Fig. 5

Experimental data of relative thickness of the test plate inserted in the interferometer relative to a 70-MHz center frequency position with scanning performed by a frequency-sweep signal of 52 to 90 MHz.

Equations (3)

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ϕ=2π/λOPL=2π/λnt=2πnt/λ,
φ=2πn-1t/λ.
ϕ=4πt/λ.

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