Abstract

Achromatic interferometers are developed that perform optical processing operations and record both the phase and amplitude of the output by means of a coherent reference beam. The interferometers simultaneously carry out the data processing tasks and form fringes with white light extended sources.

© 1980 Optical Society of America

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References

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  1. B. J. Chang, R. Alferness, E. N. Leith, Appl. Opt. 14, 1592 (1975).
    [CrossRef] [PubMed]
  2. E. Leith, J. Roth, Appl. Opt. 16, 2565 (1977).
    [CrossRef] [PubMed]
  3. S. Benton, in Proceedings of the ICO Jerusalem 1976 Conference on Holography and Optical Processing, E. Marom, A. Friesem, E. Wiener-Avnear, Eds. (Pergamon, New York, 1977).
  4. L. Cross, in SPIE Proc. 120, “Three Dimensional Imaging,” held Aug 25–26, 1977.

1977 (1)

1975 (1)

Alferness, R.

Benton, S.

S. Benton, in Proceedings of the ICO Jerusalem 1976 Conference on Holography and Optical Processing, E. Marom, A. Friesem, E. Wiener-Avnear, Eds. (Pergamon, New York, 1977).

Chang, B. J.

Cross, L.

L. Cross, in SPIE Proc. 120, “Three Dimensional Imaging,” held Aug 25–26, 1977.

Leith, E.

Leith, E. N.

Roth, J.

Appl. Opt. (2)

Other (2)

S. Benton, in Proceedings of the ICO Jerusalem 1976 Conference on Holography and Optical Processing, E. Marom, A. Friesem, E. Wiener-Avnear, Eds. (Pergamon, New York, 1977).

L. Cross, in SPIE Proc. 120, “Three Dimensional Imaging,” held Aug 25–26, 1977.

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Figures (11)

Fig. 1
Fig. 1

Basic correlator–interferometer.

Fig. 2
Fig. 2

Exosystem; O.P. is the optical processor.

Fig. 3
Fig. 3

Spectra S and MTF H showing reference function spatial frequencies fa and fb.

Fig. 4
Fig. 4

Endosystem; O.P. is the optical processor.

Fig. 5
Fig. 5

Model for analysis. P1 is input plane, P2 is output plane, and O.P. is optical processor.

Fig. 6
Fig. 6

Generalized n-grating interferometer.

Fig. 7
Fig. 7

One-, two-, and three-grating interferometers.

Fig. 8
Fig. 8

Basic optical correlator.

Fig. 9
Fig. 9

Three-grating device.

Fig. 10
Fig. 10

Output from a slit signal.

Fig. 11
Fig. 11

Achromatic fringes (150 lines/mm) produced by the three-grating system.

Equations (13)

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u i = exp ( j 2 π f 0 x ) ,
u 0 = exp j 2 π ( f 0 + δ 1 f 1 + δ 2 f 2 + + δ n f n ) x × exp - j π λ [ f 0 + δ 1 f 1 ) 2 + ( f 0 + δ 1 f 1 + δ 2 f 2 ) 2 + + ( f 0 + δ 1 f 1 + + δ n f n ) 2 .
I 0 = 2 + 2 cos { 2 π [ ( δ 1 - δ 1 ) f 1 + + ( δ n - δ n ) f n ] x - π λ [ d 1 ( f 0 + δ 1 f 1 ) 2 + + d n ( f 0 + δ 1 f 1 + + δ n f n ) 2 - d 1 ( f 0 + δ 1 f 1 ) 2 - - d n ( f 0 + δ 1 f 1 + + δ n f n ) 2 ] } ,
½ A = n ( δ 1 - δ 1 ) f 1 d 1 + ( n - 1 ) ( δ 2 - δ 2 ) f 2 d 2 + + ( δ n - δ n ) f n , d n
A / 2 = f 1 d 1 - 3 f 2 d 2 + f 1 d 2 ,
B = - d 1 f 1 2 - d 2 f 1 2 + 2 d 2 f 1 f 2 ,
A / 2 = - f 3 d 3 + f 1 d 1 + f 1 d 2 - f 2 d 2 + f 1 d 3 - f 2 d 3 ,
B = d 3 f 3 2 - d 1 f 1 2 - ( d 1 + d 3 ) ( f 1 - f 2 ) 2 .
d 2 / d 1 = f 1 / ( 2 f 2 - f 1 ) ;
d 2 / d 1 = f 1 ( f 2 - f 3 ) / f 3 ( f 1 - f 2 ) ,
d 3 / d 1 = f 1 f 2 / f 3 ( f 2 - f 1 + f 3 ) ,
½ + ½ cos ( 2 π f 0 y + β x 2 ) .
I = ½ [ 1 + a cos ( 2 π f 0 y + ϕ ) ] ,

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