Abstract

The application of computer generated holograms to the interferometric testing of aspheric optical elements has been investigated, and it has been shown that they provide a convenient and practical method of producing an aspheric reference wavefront.

© 1971 Optical Society of America

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References

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  1. A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 739 (1967).
  2. W. H. Lee, Appl. Opt. 9, 639 (1970).
    [CrossRef] [PubMed]
  3. J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, New York, 1968).

1970 (1)

1967 (1)

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 739 (1967).

Goodman, J. W.

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

Lee, W. H.

Lohmann, A. W.

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 739 (1967).

Paris, D. P.

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 739 (1967).

Appl. Opt. (2)

A. W. Lohmann, D. P. Paris, Appl. Opt. 6, 739 (1967).

W. H. Lee, Appl. Opt. 9, 639 (1970).
[CrossRef] [PubMed]

Other (1)

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

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Figures (13)

Fig. 1
Fig. 1

Modified Twyman-Green interferometer.

Fig. 2
Fig. 2

Structure of Lee type resolution cell.

Fig. 3
Fig. 3

Spatial filtering of hologram reconstruction.

Fig. 4
Fig. 4

Arrangement that reduces errors due to sampling.

Fig. 5
Fig. 5

Procedure for generating synthetic holograms.

Fig. 6
Fig. 6

Half of Lohmann and Paris hologram of defocused parabolic wavefront.

Fig. 7
Fig. 7

Half of Lee type hologram of defocused parabolic wavefront.

Fig. 8
Fig. 8

Arrangement for testing quality of synthetic hologram.

Fig. 9
Fig. 9

Interferogram resulting from interfering plane wavefront with parabolic wavefront produced by Lohmann and Paris type hologram.

Fig. 10
Fig. 10

Interferogram resulting from interfering plane wavefront with parabolic wavefront produced by Lee type hologram.

Fig. 11
Fig. 11

Interferogram resulting from interfering parabolic wavefront produced by hologram with wavefront produced by parabolic mirror.

Fig. 12
Fig. 12

Interferograms obtained from holograms having 36° and 90° phase quantization.

Fig. 13
Fig. 13

Arrangement for testing aspherics with hologram acting as a null lens.

Equations (9)

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( 2 π / δ x ) · x - j 2 π = ϕ ( x , y ) ,
( 2 π / δ x ) · x - j 2 π = ϕ ( n δ x , m δ y ) ,
a ( p , q ) = - A ( x , y ) exp [ i ( p x + q y ) ] d x d y .
a ( p , q ) = ( n , m ) n δ x - b n m / 2 + S n m n δ x + b n m / 2 + S n m exp ( ipx ) d x × m δ y - c n m / 2 m δ y + c n m / 2 exp ( iqy ) d y ,
a ( p , q ) = ( n , m ) b n m c n m sin c ( p b m n 2 ) sin c ( q c n m 2 ) × exp [ i p ( n δ x + S n m ) ] exp [ i q ( m δ y ) ] ,
A ( x , y ) = - a ( p , q ) F ( p , q ) exp [ i ( p x + q y ) ] d p d q .
A ( x , y ) = ( K - 1 / 2 ) 2 π / δ x ( K + 1 / 2 ) 2 π / δ x - π / δ y π / δ y a ( p , q ) exp [ i ( p x + q y ) ] d p d q .
A ( x , y ) = constant exp ( i K 2 π δ x · x ) ( n , m ) N M b n m c n m × sinc [ π δ x ( n δ x + S n m + x ) ] exp ( i K S n m 2 π δ x ) × sinc π δ y ( m δ y + y ) .
S n m = ϕ ( n δ x + S n m , m δ y ) ( δ x / 2 π ) ,

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