Abstract

A method for reducing errors in aspherical mirror testing using a computer-generated hologram (CGH) is described. By using a modified filtering method the carrier frequency in the CGH can be reduced by two-thirds, and the resulting error due to distortion is only one-half of that of a conventional CGH. By adopting a Fizeau-type optical setup, only the surface quality of the reference affects the measured results.

© 1985 Optical Society of America

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References

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  1. Y. Ichioka, A. W. Lohmann, “Interferometric Testing of Large Optical Components with Circular Computer Holograms,” Appl. Opt. 11, 2597 (1972).
    [CrossRef] [PubMed]
  2. A. J. MacGovern, J. C. Wyant, “Computer Generated Holograms for Testing Optical Elements,” Appl. Opt. 10, 619 (1971).
    [CrossRef] [PubMed]
  3. J. C. Wyant, P. K. O'Neill, “Computer Generated Hologram; Null Lens Test of Aspheric Wavefronts,” Appl. Opt. 13, 2762 (1974).
    [CrossRef] [PubMed]
  4. H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).
  5. J. S. Loomis, “Application of Computer-Generated Holograms in Optical Testing,” Ph.D. Dissertation, U. Arizona (1980).
  6. T. Yatagai, H. Siato, “Interferometric Testing with Computer-Generated Holograms: Aberration Balancing Method and Error Analysis,” Appl. Opt. 17, 558 (1978).
    [CrossRef] [PubMed]
  7. A. F. Fercher, “Computer-Generated Holograms for Testing Optical Element: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
    [CrossRef]
  8. J. C. Wyant, V. P. Bennett, “Using Computer Generated Holograms to Test Aspheric Wavefronts,” Appl. Opt. 11, 2833 (1972).
    [CrossRef] [PubMed]
  9. J. C. Wyant, P. K. O'Neill, A. J. MacGovern, “Interferometric Method of Measuring Plotter Distortion,” Appl. Opt. 13, 1549 (1974).
    [CrossRef] [PubMed]
  10. A. Ono, J. C. Wyant, “Plotting Errors Measurement in CGH Using an Improved Interferometric Method,” Appl. Opt. 23, 3905 (1984).
    [CrossRef] [PubMed]
  11. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1984

1980

H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

1978

1976

A. F. Fercher, “Computer-Generated Holograms for Testing Optical Element: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
[CrossRef]

1974

1972

1971

Bennett, V. P.

Fercher, A. F.

A. F. Fercher, “Computer-Generated Holograms for Testing Optical Element: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
[CrossRef]

Goodman, J. W.

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

Ichioka, Y.

Lohmann, A. W.

Loomis, J. S.

J. S. Loomis, “Application of Computer-Generated Holograms in Optical Testing,” Ph.D. Dissertation, U. Arizona (1980).

MacGovern, A. J.

O'Neill, P. K.

Ono, A.

Siato, H.

Tiziani, H. J.

H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

Wyant, J. C.

Yatagai, T.

Appl. Opt.

Opt. Acta

A. F. Fercher, “Computer-Generated Holograms for Testing Optical Element: Error Analysis and Error Compensation,” Opt. Acta 23, 347 (1976).
[CrossRef]

Proc. Soc. Photo-Opt. Instrum. Eng.

H. J. Tiziani, “Prospects of Testing Aspheric Surfaces with Computer-Generated Holograms,” Proc. Soc. Photo-Opt. Instrum. Eng. 235, 72 (1980).

Other

J. S. Loomis, “Application of Computer-Generated Holograms in Optical Testing,” Ph.D. Dissertation, U. Arizona (1980).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

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Figures (8)

Fig. 1
Fig. 1

Typical optical setup using an off-axis CGH for testing an aspherical mirror.

Fig. 2
Fig. 2

Spatial frequency distribution of the diffracted beams from the reference wave produced by a CGH.

Fig. 3
Fig. 3

Spatial frequency distribution of the diffracted beams from the object beam.

Fig. 4
Fig. 4

Optical setup.

Fig. 5
Fig. 5

CGH pattern used for aspherical mirror testing.

Fig. 6
Fig. 6

Interferogram obtained measuring CGH distortion using the interferometric method.

Fig. 7
Fig. 7

Resultant interferogram for testing a parabolic mirror using the optical setup shown in Fig. 4.

Fig. 8
Fig. 8

Amplitude distribution for a gray tone rectangular grating.

Equations (13)

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Δ W = ( 2 Δ W b ) 2 + Δ W r 2 + Δ W d 2 .
I o = C R 0 ( T r ) 2 D 1 I r = C R r D 0 ,
T r = 1 R r .
R r = 1 + D 0 D 1 ( D 0 D 1 ) 2 + 4 R 0 ( D 0 D 1 ) 2 R 0 .
R r = 0.038.
f = 23.44 / r ,
Δ W = f m f g Δ P 2 N λ ,
r = l d 2 l m r m ,
Δ W r Δ r f λ .
Δ W 23.44 2 Δ r l m λ l d r m .
g ( x ) = b δ ( x ) + a sinc x 2 n = δ ( x n π ) .
I ( 0 ) = ( a + b ) 2 = a 2 + b 2 + 2 ab , I ( 1 ) = a 2 ( sinc π 2 ) 2 = 0.405 a 2 ; 1 st order .
a = 0.8 0.2 2 = 0.223 , b = 0.2 = 0.447 .

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