Abstract

The unambiguous distance measurement range in two-color interferometry is generally understood to be limited to the equivalent or synthetic wavelength, which is inversely proportional to the wavelength separation of the two colors. Here it is shown that one may extend the unambiguous range well beyond this limit by using optical phase information to determine the synthetic-wavelength fringe order.

© 1994 Optical Society of America

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References

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  1. M. R. Benoît, “Application des phenomenes d'intérference a des déterminations métrologiques,” J. Phys. (Paris) 3, 57–68 (1898).
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987).
  3. S. P. Poole, J. H. Dowell, “Application of interferometry to the routine measurement of block gauges,” in Optics and Metrology, P. Mollet, ed. (Pergamon, New York, 1960).
  4. D. C. Barnes, M. J. Puttock, “National Physics Laboratory interferometer,” Engineer 196, 763–766 (1953).
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    [CrossRef]
  6. J. C. Wyant, “Testing aspherics using two-wavelength holography,” Appl. Opt. 10, 2113–2118 (1971).
    [CrossRef] [PubMed]
  7. C. R. Tilford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977).
    [CrossRef] [PubMed]
  8. T. A. Nussmeier, “Interferometric distance measurement method,” U.S. patent4,355,899 (26October1982).
  9. Y. Cheng, J. C. Wyant, “Two-wavelength phase shifting interferometry,” Appl. Opt. 23, 4539–4543 (1984).
    [CrossRef] [PubMed]
  10. N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).
    [CrossRef]
  11. P. de Groot, S. Kishner, “Synthetic wavelength stabilization of a two-color laser diode interferometer,” Appl. Opt. 30, 4026–4033 (1991).
    [CrossRef] [PubMed]
  12. E. B. Hochberg, “Single-exposure long-equivalent-wavelength interferometry,” NASA Tech. Brief 11, 52 (1991).
  13. K. Creath, J. C. Wyant, “Holographic and speckle tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 599–651.
  14. K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
    [CrossRef] [PubMed]
  15. C. C. Williams, H. K. Wickramasinghe, “Absolute optical ranging with 200-nm resolution,” Opt. Lett. 14, 542–544 (1989).
    [CrossRef] [PubMed]
  16. M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1991).
    [CrossRef]
  17. A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. V. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).
    [CrossRef]
  18. M. Hercher, “Ultra-high resolution interferometry,” Opt. Photon. News 2 (11), 24–29 (1991).
    [CrossRef]
  19. C. Steinmetz, R. Buroon, J. Herris, “Accuracy analysis and improvements to the Hewlett-Packard laser interferometer system,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 79–94 (1987).
    [CrossRef]
  20. R. A. Smythe, J. A. Soobitsky, B. E. Truax, “Recent advances in interferometry at Zygo,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 95–105 (1987).
    [CrossRef]
  21. A. F. Fercher, H. Z. Hu, U. Vry, “Rough surface interferometry with a two-wavelength heterodyne speckle interferometer,” Appl. Opt. 24, 2181–2188 (1985).
    [CrossRef] [PubMed]
  22. Z. Zoran, E. Fischer, T. Ittner, H. J. Tiziani, “Two-wavelength double heterodyne interferometry using a matched grating technique,” Appl. Opt. 30, 3139–3144 (1991).
    [CrossRef]
  23. P. de Groot, S. Kishner, “Synthetic wavelength stabilization of a two-color laser diode interferometer,” Appl. Opt. 30, 4026–4033 (1991).
    [CrossRef] [PubMed]

1991

1989

1987

1985

1984

1977

1971

1965

K. Haines, B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

1953

D. C. Barnes, M. J. Puttock, “National Physics Laboratory interferometer,” Engineer 196, 763–766 (1953).

1898

M. R. Benoît, “Application des phenomenes d'intérference a des déterminations métrologiques,” J. Phys. (Paris) 3, 57–68 (1898).

Barnes, D. C.

D. C. Barnes, M. J. Puttock, “National Physics Laboratory interferometer,” Engineer 196, 763–766 (1953).

Benoît, M. R.

M. R. Benoît, “Application des phenomenes d'intérference a des déterminations métrologiques,” J. Phys. (Paris) 3, 57–68 (1898).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987).

Buroon, R.

C. Steinmetz, R. Buroon, J. Herris, “Accuracy analysis and improvements to the Hewlett-Packard laser interferometer system,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 79–94 (1987).
[CrossRef]

Caulfield, H. J.

N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).
[CrossRef]

Cheng, Y.

Christenson, E.

M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1991).
[CrossRef]

Creath, K.

K. Creath, “Step height measurement using two-wavelength phase-shifting interferometry,” Appl. Opt. 26, 2810–2816 (1987).
[CrossRef] [PubMed]

K. Creath, J. C. Wyant, “Holographic and speckle tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 599–651.

Dandridge, A.

A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. V. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).
[CrossRef]

de Groot, P.

Dowell, J. H.

S. P. Poole, J. H. Dowell, “Application of interferometry to the routine measurement of block gauges,” in Optics and Metrology, P. Mollet, ed. (Pergamon, New York, 1960).

Fercher, A. F.

Fischer, E.

Haines, K.

K. Haines, B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Hercher, M.

M. Hercher, “Ultra-high resolution interferometry,” Opt. Photon. News 2 (11), 24–29 (1991).
[CrossRef]

Herris, J.

C. Steinmetz, R. Buroon, J. Herris, “Accuracy analysis and improvements to the Hewlett-Packard laser interferometer system,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 79–94 (1987).
[CrossRef]

Hildebrand, B. P.

K. Haines, B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Hochberg, E. B.

E. B. Hochberg, “Single-exposure long-equivalent-wavelength interferometry,” NASA Tech. Brief 11, 52 (1991).

Hu, H. Z.

Ittner, T.

Kersey, A. D.

A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. V. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).
[CrossRef]

Kishner, S.

Massie, N. A.

N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).
[CrossRef]

Nussmeier, T. A.

T. A. Nussmeier, “Interferometric distance measurement method,” U.S. patent4,355,899 (26October1982).

Poole, S. P.

S. P. Poole, J. H. Dowell, “Application of interferometry to the routine measurement of block gauges,” in Optics and Metrology, P. Mollet, ed. (Pergamon, New York, 1960).

Puttock, M. J.

D. C. Barnes, M. J. Puttock, “National Physics Laboratory interferometer,” Engineer 196, 763–766 (1953).

Smythe, R. A.

R. A. Smythe, J. A. Soobitsky, B. E. Truax, “Recent advances in interferometry at Zygo,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 95–105 (1987).
[CrossRef]

Soobitsky, J. A.

R. A. Smythe, J. A. Soobitsky, B. E. Truax, “Recent advances in interferometry at Zygo,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 95–105 (1987).
[CrossRef]

Steinmetz, C.

C. Steinmetz, R. Buroon, J. Herris, “Accuracy analysis and improvements to the Hewlett-Packard laser interferometer system,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 79–94 (1987).
[CrossRef]

Tilford, C. R.

Tiziani, H. J.

Truax, B. E.

R. A. Smythe, J. A. Soobitsky, B. E. Truax, “Recent advances in interferometry at Zygo,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 95–105 (1987).
[CrossRef]

Tucker, M.

M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1991).
[CrossRef]

Vry, U.

Wickramasinghe, H. K.

Williams, C. C.

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987).

Wyant, J. C.

Zoran, Z.

Appl. Opt.

Engineer

D. C. Barnes, M. J. Puttock, “National Physics Laboratory interferometer,” Engineer 196, 763–766 (1953).

J. Phys. (Paris)

M. R. Benoît, “Application des phenomenes d'intérference a des déterminations métrologiques,” J. Phys. (Paris) 3, 57–68 (1898).

NASA Tech. Brief

E. B. Hochberg, “Single-exposure long-equivalent-wavelength interferometry,” NASA Tech. Brief 11, 52 (1991).

Opt. Lett.

Opt. Photon. News

M. Hercher, “Ultra-high resolution interferometry,” Opt. Photon. News 2 (11), 24–29 (1991).
[CrossRef]

Phys. Lett.

K. Haines, B. P. Hildebrand, “Contour generation by wavefront reconstruction,” Phys. Lett. 19, 10–11 (1965).
[CrossRef]

Other

T. A. Nussmeier, “Interferometric distance measurement method,” U.S. patent4,355,899 (26October1982).

N. A. Massie, H. J. Caulfield, “Absolute distance interferometry,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 149–157 (1987).
[CrossRef]

M. Tucker, E. Christenson, “Absolute interferometer for manufacturing applications,” in Fiber Optic and Laser Sensors VIII, R. P. DePaula, E. Udd, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1367, 289–299 (1991).
[CrossRef]

A. D. Kersey, A. Dandridge, “Dual-wavelength approach to interferometric sensing,” in Fiber Optic Sensors II, A. V. Scheggi, ed., Proc. Soc. Photo-Opt. Instrum. Eng.798, 176–181 (1987).
[CrossRef]

C. Steinmetz, R. Buroon, J. Herris, “Accuracy analysis and improvements to the Hewlett-Packard laser interferometer system,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 79–94 (1987).
[CrossRef]

R. A. Smythe, J. A. Soobitsky, B. E. Truax, “Recent advances in interferometry at Zygo,” in Interferometric Metrology, N. A. Massie, ed., Proc. Soc. Photo-Opt. Instrum. Eng.816, 95–105 (1987).
[CrossRef]

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1987).

S. P. Poole, J. H. Dowell, “Application of interferometry to the routine measurement of block gauges,” in Optics and Metrology, P. Mollet, ed. (Pergamon, New York, 1960).

K. Creath, J. C. Wyant, “Holographic and speckle tests,” in Optical Shop Testing, D. Malacara, ed. (Wiley, New York, 1992), pp. 599–651.

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Figures (2)

Fig. 1
Fig. 1

Michelson interferometer used for measuring the optical path difference between two mirrors.

Fig. 2
Fig. 2

Results of a computer simulation in which the extended unambiguous range and the restricted range of the conventional synthetic-wavelength methods are compared.

Tables (1)

Tables Icon

Table 1 Excess Fractions ϕ/2π and ϕ2/2π Corresponding to the Green and Red Wavelengths of Cadmium

Equations (24)

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

L = ( n + ϕ 2 π ) λ .
R n = n λ ,
Φ = ϕ ϕ 2 ,
L = ( N + Φ 2 π ) Λ ,
Λ = λ 2 λ λ λ 2 .
n = 1 2 π ( Φ Λ λ ϕ ) .
L = [ int ( n ) + ϕ 2 π ] λ ,
R N = N Λ .
Λ = n R N R λ ,
N = n int ( n ) Λ / λ int ( Λ / λ ) .
n = 1 2 π ( Φ Λ λ Φ ) + Λ λ int ( N ) .
L = [ int ( n ) + ϕ 2 π ] λ ,
L = L N R Λ int ( L N R Λ ) .
N R = | int [ 1 Λ / λ int ( Λ / λ ) ] | .
Δ L / L = Δ m ( λ / L ) + Δ λ / λ ,
n = Λ λ [ M + int ( N ) ] m .
δ Λ = Λ 2 ( δ λ λ 2 δ λ 2 λ 2 2 ) ,
L = [ M + int ( N ) ] Λ ,
δ n = ( L δ λ λ 2 + δ m ) ( Λ λ 1 ) ( L δ λ 2 λ 2 2 + δ m 2 ) ( Λ λ ) .
Δ n = ( 2 Λ λ 1 ) ( Δ λ λ L λ + Δ m ) .
Δ n < 0 . 5 .
N = n int ( n ) Λ / λ int ( Λ / λ ) .
n = M Λ λ m .
Δ N R N R Δ n .

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