Abstract

A cyclic interferometer can be used for both lateral and radial shearing. Being common-path this interferometer is quite stable. The use of a cyclic shear interferometer for phase shifting interferometry is discussed. The phase shifting is provided here by polarization techniques. Some useful cyclic phase shifting interferometer arrangements are discussed, and the working of a polarization phase shifting cyclic shear interferometer is demonstrated.

© 1985 Optical Society of America

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References

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  1. D. Malacara, Ed., Optical Shop Testing (Wiley, New York, 1978), Chaps. 4 and 5.
  2. J. H. Bruning, “Fringe Scanning Interferometers,” in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978).
  3. Y. Y. Cheng, J. C. Wyant, “Two-Wavelength Phase Shifting Interferometry,” Appl. Opt. 23, 4539 (1984).
    [CrossRef] [PubMed]
  4. P. Hariharan, B. F. Oreb, Z. Wanzhi, “Measurement of Aspheric Surfaces using a Microcomputer-Controlled Digital Radial-Shear Interferometer,” Opt. Acta 31, 981 (1984).
    [CrossRef]
  5. T. Yatagai, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt. 23, 3676 (1984).
    [CrossRef] [PubMed]
  6. G. E. Sommargren, “Up-Down Frequency Shifter for Optical Heterodyne Interferometry,” J. Opt. Soc. Am. 65, 960 (1975).
    [CrossRef]
  7. H. Z. Hu, “Polarization Heterodyne Interferometry Using a Simple Rotating Analyzer. 1: Theory and Error Analysis,” Appl. Opt. 22, 2052 (1983).
    [CrossRef] [PubMed]
  8. R. N. Shagam, J. C. Wyant, “Optical Frequency Shifter for Heterodyne Interferometers Using Multiple Rotating Polarization Retarders,” Appl. Opt. 17, 3034 (1978).
    [CrossRef] [PubMed]
  9. Oriel Catalogue, Vol. 3, Optics and Filters (Oriel Corp., Stratford, Conn., 1984).
  10. M. P. Kothiyal, C. Delisle, “Polarization Component Phase Shifters in Phase Shifting Interferometry: Error Analysis,” to appear in Opt. Acta.
  11. M. P. Kothiyal, C. Delisle, “Rotating Analyzer Heterodyne Interferometer: Error Analysis,” Appl. Opt. 24, 2288 (1985).
    [CrossRef] [PubMed]

1985 (1)

1984 (3)

Y. Y. Cheng, J. C. Wyant, “Two-Wavelength Phase Shifting Interferometry,” Appl. Opt. 23, 4539 (1984).
[CrossRef] [PubMed]

P. Hariharan, B. F. Oreb, Z. Wanzhi, “Measurement of Aspheric Surfaces using a Microcomputer-Controlled Digital Radial-Shear Interferometer,” Opt. Acta 31, 981 (1984).
[CrossRef]

T. Yatagai, “Fringe Scanning Ronchi Test for Aspherical Surfaces,” Appl. Opt. 23, 3676 (1984).
[CrossRef] [PubMed]

1983 (1)

1978 (1)

1975 (1)

Bruning, J. H.

J. H. Bruning, “Fringe Scanning Interferometers,” in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978).

Cheng, Y. Y.

Delisle, C.

M. P. Kothiyal, C. Delisle, “Rotating Analyzer Heterodyne Interferometer: Error Analysis,” Appl. Opt. 24, 2288 (1985).
[CrossRef] [PubMed]

M. P. Kothiyal, C. Delisle, “Polarization Component Phase Shifters in Phase Shifting Interferometry: Error Analysis,” to appear in Opt. Acta.

Hariharan, P.

P. Hariharan, B. F. Oreb, Z. Wanzhi, “Measurement of Aspheric Surfaces using a Microcomputer-Controlled Digital Radial-Shear Interferometer,” Opt. Acta 31, 981 (1984).
[CrossRef]

Hu, H. Z.

Kothiyal, M. P.

M. P. Kothiyal, C. Delisle, “Rotating Analyzer Heterodyne Interferometer: Error Analysis,” Appl. Opt. 24, 2288 (1985).
[CrossRef] [PubMed]

M. P. Kothiyal, C. Delisle, “Polarization Component Phase Shifters in Phase Shifting Interferometry: Error Analysis,” to appear in Opt. Acta.

Oreb, B. F.

P. Hariharan, B. F. Oreb, Z. Wanzhi, “Measurement of Aspheric Surfaces using a Microcomputer-Controlled Digital Radial-Shear Interferometer,” Opt. Acta 31, 981 (1984).
[CrossRef]

Shagam, R. N.

Sommargren, G. E.

Wanzhi, Z.

P. Hariharan, B. F. Oreb, Z. Wanzhi, “Measurement of Aspheric Surfaces using a Microcomputer-Controlled Digital Radial-Shear Interferometer,” Opt. Acta 31, 981 (1984).
[CrossRef]

Wyant, J. C.

Yatagai, T.

Appl. Opt. (5)

J. Opt. Soc. Am. (1)

Opt. Acta (1)

P. Hariharan, B. F. Oreb, Z. Wanzhi, “Measurement of Aspheric Surfaces using a Microcomputer-Controlled Digital Radial-Shear Interferometer,” Opt. Acta 31, 981 (1984).
[CrossRef]

Other (4)

D. Malacara, Ed., Optical Shop Testing (Wiley, New York, 1978), Chaps. 4 and 5.

J. H. Bruning, “Fringe Scanning Interferometers,” in Optical Shop Testing, D. Malacara, Ed. (Wiley, New York, 1978).

Oriel Catalogue, Vol. 3, Optics and Filters (Oriel Corp., Stratford, Conn., 1984).

M. P. Kothiyal, C. Delisle, “Polarization Component Phase Shifters in Phase Shifting Interferometry: Error Analysis,” to appear in Opt. Acta.

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Figures (6)

Fig. 1
Fig. 1

Cyclic shear interferometer for polarization phase shifting: PBS, polarizing beam splitter; S, shear system; M1 and M2, mirrors; P, polarizer.

Fig. 2
Fig. 2

Polarization phase shifter arrangements: H(rot), rotating half-wave plate; Q, quarter-wave plate at an azimuth of π/4; P, polarizer; P(rot), rotating polarizer.

Fig. 3
Fig. 3

Cyclic shear interferometer for collimated beam input using a polarization phase shifter: T, test surface; PS, phase shifter; BS, beam splitter; PBS, polarizing beam splitter; L1 and L2, shear system; M1 and M2, mirrors.

Fig. 4
Fig. 4

Cyclic radial shear interferometer for convergent light. Notation same as in Fig. 3.

Fig. 5
Fig. 5

Radial shear fringes for three settings of the phase shifter.

Fig. 6
Fig. 6

Lateral shear fringes for three settings of the phase shifter.

Equations (3)

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I = a 2 + b 2 + 2 a b sin ( ϕ + α ) ,
ϕ = n θ ,
tan α = I 1 I 3 I 2 I 4 ,

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