Abstract

We realized what we believe is a new phase-shifting scatterplate interferometer by exploiting the polarization characteristics of a birefringent scatterplate. The common-path design of the interferometer reduces its sensitivity to environmental effects, and phase shifting allows quick and accurate quantitative measurements of the test surface. A major feature of the birefringent scatterplate approach for phase shifting is that no high-quality optical components are required in the test setup. The theory of the interferometer is presented, the procedure for the fabrication of the birefringent scatterplate is described, and experimental results are shown.

© 2002 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
  15. W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 33.1–33.101.

1998

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

1996

1991

D.-C. Su, L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

1988

J. Huang, T. Honda, N. Ohyama, J. Tsuiiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235–238 (1988).
[CrossRef]

1984

1980

L. Rubin, “Scatterplate interferometry,” Opt. Eng. 19, 815–824 (1980).
[CrossRef]

1975

1974

1969

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

R. M. Scott, “Scatterplate interferometry,”Appl. Opt. 8, 531–537 (1969).

1966

P. Carré, “Installation et Utilisation du Comparateur Photoelectrique et Interferentiel du Bureau International des Poids de Mesures,” Metrologia 2, 13–16 (1966).
[CrossRef]

1953

J. M. Burch, “Scatter fringes of equal thickness,” Nature (London) 171, 889 (1953).
[CrossRef]

Abedin, K. M.

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

Bokor, J.

Brangaccio, D. J.

Bruning, J. H.

Burch, J. M.

J. M. Burch, “Scatter fringes of equal thickness,” Nature (London) 171, 889 (1953).
[CrossRef]

J. M. Burch, “Interferometry in scattered light,” in Optical Instruments and Techniques, J. H. Dickson, ed. (Oriel, London, 1970), pp. 220–229.

Carré, P.

P. Carré, “Installation et Utilisation du Comparateur Photoelectrique et Interferentiel du Bureau International des Poids de Mesures,” Metrologia 2, 13–16 (1966).
[CrossRef]

Crane, R.

R. Crane, “Interference phase measurement,” Appl. Opt. 8, 538–542 (1969).

Creath, K.

C. R. Mercer, K. Creath, N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 87–93 (1995).
[CrossRef]

Eiju, T.

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

Gallagher, J. E.

Goldberg, K. A.

Harris, T. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 33.1–33.101.

Herriott, D. R.

Honda, T.

J. Huang, T. Honda, N. Ohyama, J. Tsuiiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235–238 (1988).
[CrossRef]

Huang, J.

J. Huang, T. Honda, N. Ohyama, J. Tsuiiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235–238 (1988).
[CrossRef]

Kwon, O. K.

Matsuda, K.

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

Medecki, H.

Mercer, C. R.

C. R. Mercer, K. Creath, N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 87–93 (1995).
[CrossRef]

Ohyama, N.

J. Huang, T. Honda, N. Ohyama, J. Tsuiiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235–238 (1988).
[CrossRef]

Peiponen, K.

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

Rashidnia, N.

C. R. Mercer, K. Creath, N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 87–93 (1995).
[CrossRef]

Rässänen, J. T.

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

Rosenfeld, D. P.

Rubin, L.

L. Rubin, “Scatterplate interferometry,” Opt. Eng. 19, 815–824 (1980).
[CrossRef]

Scott, R. M.

R. M. Scott, “Scatterplate interferometry,”Appl. Opt. 8, 531–537 (1969).

Shyu, L.-H.

D.-C. Su, L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

Su, D.-C.

D.-C. Su, L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

Tejnil, E.

Tenjimbayashi, K.

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

Thomas, M. E.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 33.1–33.101.

Tropf, W. J.

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 33.1–33.101.

Tsuiiuchi, J.

J. Huang, T. Honda, N. Ohyama, J. Tsuiiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235–238 (1988).
[CrossRef]

White, A. D.

Wyant, J. C.

Appl. Opt.

J. Mod. Opt.

D.-C. Su, L.-H. Shyu, “Phase-shifting scatter plate interferometer using a polarization technique,” J. Mod. Opt. 38, 951–959 (1991).
[CrossRef]

Metrologia

P. Carré, “Installation et Utilisation du Comparateur Photoelectrique et Interferentiel du Bureau International des Poids de Mesures,” Metrologia 2, 13–16 (1966).
[CrossRef]

Nature (London)

J. M. Burch, “Scatter fringes of equal thickness,” Nature (London) 171, 889 (1953).
[CrossRef]

Opt. Commun.

J. Huang, T. Honda, N. Ohyama, J. Tsuiiuchi, “Fringe scanning scatter plate interferometer using a polarized light,” Opt. Commun. 68, 235–238 (1988).
[CrossRef]

Opt. Eng.

L. Rubin, “Scatterplate interferometry,” Opt. Eng. 19, 815–824 (1980).
[CrossRef]

Opt. Lett.

Rev. Sci. Instrum.

J. T. Rässänen, K. Peiponen, K. M. Abedin, K. Tenjimbayashi, T. Eiju, K. Matsuda, “Integrated scatter plate and projection lens for scatter plate interferometer,” Rev. Sci. Instrum. 69, 1587–1590 (1998).
[CrossRef]

Other

W. J. Tropf, M. E. Thomas, T. J. Harris, “Properties of crystals and glasses,” in Handbook of Optics, M. Bass, ed. (McGraw-Hill, New York, 1995), Vol. 2, pp. 33.1–33.101.

C. R. Mercer, K. Creath, N. Rashidnia, “A phase-stepped point diffraction interferometer using liquid crystals,” in Interferometry VII: Techniques and Analysis, M. Kujawinska, R. J. Pryputniewicz, M. Takeda, eds., Proc. SPIE2544, 87–93 (1995).
[CrossRef]

J. M. Burch, “Interferometry in scattered light,” in Optical Instruments and Techniques, J. H. Dickson, ed. (Oriel, London, 1970), pp. 220–229.

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Figures (13)

Fig. 1
Fig. 1

Scatterplate interferometer for the testing of concave mirrors.

Fig. 2
Fig. 2

Inversion symmetry designed into a binary scatterplate.

Fig. 3
Fig. 3

Point-to-point analysis of inversion symmetry: (a) perfect alignment, (b) lateral misalignment of scatterplate, (c) longitudinal misalignment of scatterplate.

Fig. 4
Fig. 4

Typical scatterplate interferograms.

Fig. 5
Fig. 5

Birefringent scatterplate.

Fig. 6
Fig. 6

Phase-shifting scatterplate interferometer. LQR, liquid-crystal retarder.

Fig. 7
Fig. 7

Phase-shifted fringe patterns.

Fig. 8
Fig. 8

Scatterplate manufacturing process.

Fig. 9
Fig. 9

Etch depth versus etch time for calcite in diluted HCl.

Fig. 10
Fig. 10

Surface plot of birefringent scatterplate manufactured with a photomask.

Fig. 11
Fig. 11

Holographic exposure of a scatterplate.

Fig. 12
Fig. 12

f/number analysis for holographic exposure: (a) recording geometry, (b) interferometer geometry.

Fig. 13
Fig. 13

(a) Surface measurement taken with a phase-shifting scatterplate interferometer.(b) Surface measurement taken with a Wyko 6000 phase-shifting Fizeau interferometer.

Equations (11)

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

noλ2=1+0.8559λ2λ2-0.05882+0.8391λ2λ2-0.1412+0.0009λ2λ2-0.1972+0.6845λ2λ2-7.0052,
neλ2=1+1.0856λ2λ2-0.078972+0.0988λ2λ2-0.1422+0.317λ2λ2-11.4682,
n1.662=1.621298+1192615λ1042+7.658881×1012λ1044.
r=zλD,
f/number=z2D,
f/number=f2ρ.
Eenvelope=FFrectxarectya2=|a2 sincaξsincaη|2=a4 sinc2aξsinc2aη,
ξ=xλf,
η=yλf.
x=λfa,
f/numbermin=a2λ.

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