Abstract

The use of computer generated holograms for the testing of aspheric wavefronts is described. An analysis of the errors produced by emulsion movement, incorrect hologram size and position, and distortion in hologram plotter and photoreduction lens is given, and it is shown that all the errors are proportional to the slope of the aspheric wavefront. Experimental results verifying the error analysis are shown for testing rotationally nonsymmetric wavefronts having slopes as large as 125 waves per radius and departures as large as sixty-five waves.

© 1972 Optical Society of America

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References

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  1. A. Offner, Appl. Opt. 2, 153 (1963).
    [CrossRef]
  2. A. B. Meinel, Technical Report I, Introduction to Design of Astronomical Telescope (University of Arizona Press, Tucson1965), p. 66.
  3. R. Hilbert, M. Rimmer, J. Opt. Soc. Am. 59, 485 (1969).
  4. R. E. Fischer, J. Opt. Soc. Am. 61, 655 (1971).
    [CrossRef]
  5. W. J. Smith, Appl. Opt. 10, 2389 (1971).
  6. R. E. Parks, J. Opt. Soc. Am. 62, 726 (1972).
  7. J. Pastor, Appl. Opt. 8, 525 (1969).
  8. J. Pastor, J. S. Harris, G. E. Evans, J. Opt. Soc. Am. 58, 1556A (1968).
    [CrossRef]
  9. A. J. MacGovern, J. C. Wyant, Appl. Opt. 10, 619 (1971).
    [CrossRef] [PubMed]
  10. J. C. Wyant, A. J. MacGovern, International Symposium Application de l’Holographie, Besangon, France, July 1970.

1972 (1)

R. E. Parks, J. Opt. Soc. Am. 62, 726 (1972).

1971 (3)

R. E. Fischer, J. Opt. Soc. Am. 61, 655 (1971).
[CrossRef]

W. J. Smith, Appl. Opt. 10, 2389 (1971).

A. J. MacGovern, J. C. Wyant, Appl. Opt. 10, 619 (1971).
[CrossRef] [PubMed]

1969 (2)

R. Hilbert, M. Rimmer, J. Opt. Soc. Am. 59, 485 (1969).

J. Pastor, Appl. Opt. 8, 525 (1969).

1968 (1)

J. Pastor, J. S. Harris, G. E. Evans, J. Opt. Soc. Am. 58, 1556A (1968).
[CrossRef]

1963 (1)

Evans, G. E.

J. Pastor, J. S. Harris, G. E. Evans, J. Opt. Soc. Am. 58, 1556A (1968).
[CrossRef]

Fischer, R. E.

R. E. Fischer, J. Opt. Soc. Am. 61, 655 (1971).
[CrossRef]

Harris, J. S.

J. Pastor, J. S. Harris, G. E. Evans, J. Opt. Soc. Am. 58, 1556A (1968).
[CrossRef]

Hilbert, R.

R. Hilbert, M. Rimmer, J. Opt. Soc. Am. 59, 485 (1969).

MacGovern, A. J.

A. J. MacGovern, J. C. Wyant, Appl. Opt. 10, 619 (1971).
[CrossRef] [PubMed]

J. C. Wyant, A. J. MacGovern, International Symposium Application de l’Holographie, Besangon, France, July 1970.

Meinel, A. B.

A. B. Meinel, Technical Report I, Introduction to Design of Astronomical Telescope (University of Arizona Press, Tucson1965), p. 66.

Offner, A.

Parks, R. E.

R. E. Parks, J. Opt. Soc. Am. 62, 726 (1972).

Pastor, J.

J. Pastor, Appl. Opt. 8, 525 (1969).

J. Pastor, J. S. Harris, G. E. Evans, J. Opt. Soc. Am. 58, 1556A (1968).
[CrossRef]

Rimmer, M.

R. Hilbert, M. Rimmer, J. Opt. Soc. Am. 59, 485 (1969).

Smith, W. J.

W. J. Smith, Appl. Opt. 10, 2389 (1971).

Wyant, J. C.

A. J. MacGovern, J. C. Wyant, Appl. Opt. 10, 619 (1971).
[CrossRef] [PubMed]

J. C. Wyant, A. J. MacGovern, International Symposium Application de l’Holographie, Besangon, France, July 1970.

Appl. Opt. (4)

J. Opt. Soc. Am. (4)

J. Pastor, J. S. Harris, G. E. Evans, J. Opt. Soc. Am. 58, 1556A (1968).
[CrossRef]

R. E. Parks, J. Opt. Soc. Am. 62, 726 (1972).

R. Hilbert, M. Rimmer, J. Opt. Soc. Am. 59, 485 (1969).

R. E. Fischer, J. Opt. Soc. Am. 61, 655 (1971).
[CrossRef]

Other (2)

J. C. Wyant, A. J. MacGovern, International Symposium Application de l’Holographie, Besangon, France, July 1970.

A. B. Meinel, Technical Report I, Introduction to Design of Astronomical Telescope (University of Arizona Press, Tucson1965), p. 66.

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Figures (6)

Fig. 1
Fig. 1

Modified Twyman-Green interferometer.

Fig. 2
Fig. 2

Peak wavefront error vs. number of plotter resolution points.

Fig. 3
Fig. 3

Experimental setup to obtain nonsymmetric aspheric wavefront.

Fig. 4
Fig. 4

Typical computer plot.

Fig. 5
Fig. 5

CGH test of aspheric wavefront having a maximum slope of thirty-five waves per radius and nineteen waves departure. (a) Results of CGH test. (b) Interference of aberrated wavefront and plane wave.

Fig. 6
Fig. 6

CGH test of aspheric wavefront having a maximum slope of 126 waves per radius and sixty-four waves departure. (a) Results of CGH test. (b) Interference of aberrated wavefront and plane wave.

Tables (5)

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Table I Main Source of Error in CGH to Test Aspheric Wavefronts

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Table II Average rms and Peak Error in Wavefront Produced by Hologram

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Table III Results of Testing Spherical Wavefronts Produced by CGH

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Table IV Summary of Experimental Results

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Table V Estimate of Peak Errors

Equations (6)

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2 π ( S / P ) rad or S / P waves .
ϑ ( r M , θ ) = ϑ [ r + ( 1 M - 1 ) r , θ ] = ϑ ( r , σ ) + ϑ ( r . θ ) r ( 1 M - 1 ) r + .
ϑ ( r M , θ ) - ϑ ( r , θ ) = ϑ ( r , θ ) r ( 1 M - 1 ) r + .
M ( α ) = [ 1 + α ( r ) ] / [ 1 + α ( r max ) ] .
ϑ ( χ + Δ χ , y ) - ϑ ( χ , y ) [ ϑ ( χ , y ) / χ ] Δ χ .
ϑ ( r , θ + Δ θ ) - ϑ ( r , θ ) [ ϑ ( r , θ ) / θ ] Δ θ .

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