Abstract

The combined optical spectrum of a pair of multimode laser diodes is composed of a large number of well-defined wavelengths. This work reports the use of three of these wavelengths in a phase-modulated interferometer to measure absolute distance over 360-μm intervals with a resolution of 0.5 nm. The laboratory demonstration system is composed of a three-wavelength source coupled by single-mode fiber to a compact interferometric probe. This system has been used for displacement measurement and profiling of optical surfaces.

© 1991 Optical Society of America

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References

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  1. A. A. Michelson, J. R. Benoit, Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).
  2. M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).
  3. C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).
  4. Y.-Y. Cheng, J. C. Wyant, “Multiple-wavelength phase-shifting interferometry,” Appl. Opt. 24, 804–807 (1985).
    [CrossRef] [PubMed]
  5. C. C. Williams, H. K. Wickramasinghe, “Absolute optical ranging with 200-nm resolution,” Opt. Lett. 14, 542–544 (1989).
    [CrossRef] [PubMed]
  6. C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
    [CrossRef]
  7. A. J. den Boef, “Two-wavelength scanning spot interferometer using single-frequency diode lasers,” Appl. Opt. 27, 306–311 (1988).
    [CrossRef]
  8. A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
    [CrossRef]
  9. P. de Groot, S. Kishner, “Synthetic wavelength stabilization of a two-color laser diode interferometer,” Appl. Opt. (to be published).
  10. P. J. de Groot, “Laser diode technologies for in-process metrology,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 195–203 (1900).
  11. P. de Groot, “Interferometric laser profilometer for rough surfaces,” Opt. Lett. 16, 357–359 (1991).
    [CrossRef] [PubMed]
  12. C. R. Telford, “Analytical procedure for determining lengths from fractional fringes,” Appl. Opt. 16, 1857–1860 (1977).
    [CrossRef]
  13. Y. Ning, K. T. V. Grattan, B. T. Meggitt, A. W. Palmer, “Characteristics of laser diodes for interferometric use,” Appl. Opt. 28, 3657–3661 (1989).
    [CrossRef] [PubMed]
  14. P. de Groot, “Range dependent optical feedback effects on the multimode spectrum of laser diodes,” J. Mod. Opt. 37, 1199–1214 (1990).
    [CrossRef]
  15. P. Hariharan, B. F. Oreb, T. Eiju, “Digital phase-shifting interferometry: a single error-compensating phase calculation algorithm,” Appl. Opt. 26, 2504–2506 (1987).
    [CrossRef] [PubMed]

1991 (1)

1990 (1)

P. de Groot, “Range dependent optical feedback effects on the multimode spectrum of laser diodes,” J. Mod. Opt. 37, 1199–1214 (1990).
[CrossRef]

1989 (3)

1988 (1)

1987 (1)

1986 (1)

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

1985 (1)

1983 (1)

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

1977 (1)

1895 (1)

A. A. Michelson, J. R. Benoit, Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Benoit, J. R.

A. A. Michelson, J. R. Benoit, Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Born, M.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Buholz, N. E.

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

Cheng, Y.-Y.

de Groot, P.

P. de Groot, “Interferometric laser profilometer for rough surfaces,” Opt. Lett. 16, 357–359 (1991).
[CrossRef] [PubMed]

P. de Groot, “Range dependent optical feedback effects on the multimode spectrum of laser diodes,” J. Mod. Opt. 37, 1199–1214 (1990).
[CrossRef]

P. de Groot, S. Kishner, “Synthetic wavelength stabilization of a two-color laser diode interferometer,” Appl. Opt. (to be published).

de Groot, P. J.

P. J. de Groot, “Laser diode technologies for in-process metrology,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 195–203 (1900).

den Boef, A. J.

Eiju, T.

Fercher, A. F.

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

Gillard, C. W.

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

Grattan, K. T. V.

Hariharan, P.

Kishner, S.

P. de Groot, S. Kishner, “Synthetic wavelength stabilization of a two-color laser diode interferometer,” Appl. Opt. (to be published).

Meggitt, B. T.

Michelson, A. A.

A. A. Michelson, J. R. Benoit, Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Ning, Y.

Oreb, B. F.

Palmer, A. W.

Telford, C. R.

Vry, U.

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

Werner, W.

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

Wickramasinghe, H. K.

C. C. Williams, H. K. Wickramasinghe, “Absolute optical ranging with 200-nm resolution,” Opt. Lett. 14, 542–544 (1989).
[CrossRef] [PubMed]

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Williams, C. C.

C. C. Williams, H. K. Wickramasinghe, “Absolute optical ranging with 200-nm resolution,” Opt. Lett. 14, 542–544 (1989).
[CrossRef] [PubMed]

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

Wolf, E.

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

Wyant, J. C.

Appl. Opt. (5)

J. Appl. Phys. (1)

C. C. Williams, H. K. Wickramasinghe, “Optical ranging by wavelength-multiplexed interferometry,” J. Appl. Phys. 60, 1900–1903 (1986).
[CrossRef]

J. Mod. Opt. (1)

P. de Groot, “Range dependent optical feedback effects on the multimode spectrum of laser diodes,” J. Mod. Opt. 37, 1199–1214 (1990).
[CrossRef]

Opt. Eng. (1)

C. W. Gillard, N. E. Buholz, “Progress in absolute distance interferometry,” Opt. Eng. 22, 348–353 (1983).

Opt. Lasers Eng. (1)

A. F. Fercher, U. Vry, W. Werner, “Two-wavelength speckle interferometry on rough surfaces using a mode hopping diode laser,” Opt. Lasers Eng. 11, 271–279 (1989).
[CrossRef]

Opt. Lett. (2)

Trav. Mem. Bur. Int. Poids Mes. (1)

A. A. Michelson, J. R. Benoit, Trav. Mem. Bur. Int. Poids Mes. 11, 1 (1895).

Other (3)

M. Born, E. Wolf, Principles of Optics (Pergamon, New York, 1980).

P. de Groot, S. Kishner, “Synthetic wavelength stabilization of a two-color laser diode interferometer,” Appl. Opt. (to be published).

P. J. de Groot, “Laser diode technologies for in-process metrology,” in Advanced Optical Manufacturing and Testing, G. M. Sanger, P. B. Reid, L. Baker, eds., Proc. Soc. Photo-Opt. Instrum. Eng.1333, 195–203 (1900).

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Figures (4)

Fig. 1
Fig. 1

Combined optical spectrum of two multimode laser diodes. Synthetic wavelengths of 720 and 20 μm for use in absolute distance measurements were obtained by selecting two wavelengths from the 785-nm region and one wavelength from the 815-nm region.

Fig. 2
Fig. 2

Three-color interferometer for absolute distance measurement and surface profiling. The emissions from two multimode laser diodes are transmitted through optical fiber to the phase-modulation, two-beam interferometer optics. The reflected object and reference beams are transmitted back through the fiber to a diffraction grating. Detectors measure the intensity at three different wavelengths, and a computer calculates the fringe numbers and determines the object distance.

Fig. 3
Fig. 3

High-resolution displacement measurement performed by the three-wavelength interferometer shown in Fig. 2. The object was moved slowly toward the interferometer optics using a piezoelectric translator behind the object mirror. The measurement repeatability was 0.5 nm.

Fig. 4
Fig. 4

Profile of the central 1-cm × 1-cm region of a 7.5-cm diameter, f/2 unsilvered parabolic mirror. Each of the 100 independent distance measurements made for this profile was absolute. The three-color interferometer is particularly useful for profiling unusual topographical surfaces and optical components that cannot be tested by conventional full-aperture interferometry.

Equations (18)

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h ( L , λ ) = cos 2 ( 2 π L / λ ) ,
L = m λ / 2 ,
h ( m ) = cos 2 ( m π ) .
1 / Λ i j = 1 / λ i 1 / λ j , λ j > λ i .
M i j = m i m j .
L = M i j Λ i j / 2 .
M 12 = f ( M 12 ) = f ( m 1 ) f ( m 2 ) .
M 13 = f ( M 13 ) + I [ M 12 Λ 12 Λ 13 f ( M 13 ) ] ,
f ( M 13 ) = f ( m 1 ) f ( m 3 ) ,
m 1 = f ( m 1 ) + I [ M 13 Λ 13 λ 1 f ( m 1 ) ] .
| δ [ M 12 Λ 12 Λ 13 f ( M 13 ) ] | < 1 / 2 ,
| δ m 1 ( Λ 12 Λ 13 1 ) δ m 2 Λ 12 Λ 13 + δ m 3 + L Λ 13 ( δ Λ 12 Λ 12 δ Λ 13 Λ 13 ) | < 1 2 .
Δ m = | δ m 1 | max = | δ m 2 | max = | δ m 3 | max , × Δ Λ 12 / Λ 12 = | δ Λ 12 / Λ 12 | max , Δ Λ 13 / Λ 13 = | δ Λ 13 / Λ 13 | max .
Λ 12 < 1 Δ m [ Λ 13 4 L 2 ( Δ Λ 12 Λ 12 + Δ Λ 13 Λ 13 ) ] .
Λ 13 < 1 Δ m [ λ 4 L 2 ( Δ Λ 13 Λ 13 + Δ Λ λ ) ] + λ 2 ,
f ( m ) = 1 2 π tan 1 ( X Y sin β ) + 1 4 ( 1 Y | Y | ) ,
X = 2 [ J ( 4 ) J ( 2 ) ] ,
Y = 2 J ( 3 ) J ( 5 ) J ( 1 ) ,

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