Abstract

Multiple invariant optical correlators are considered. By multiple invariance, we mean invariance to more than one distortion parameter per axis of the processor. Space variant optical processors using coordinate transformations and a new phase detection scheme are used to realize such correlators. A theoretical analysis and experimental verification are included.

© 1978 Optical Society of America

Full Article  |  PDF Article

References

  • View by:
  • |
  • |
  • |

  1. D. Casasent, “Pattern and Character Recognition,” in Handbook of Holography, H. J. Caulfield, Ed. (Academic, New York, 1978).
  2. D. Casasent, W. Sterling, IEEE Trans. Comput. C-24, 348 (1975).
    [CrossRef]
  3. J. W. Goodman, Proc. IEEE 65, 29 (1977).
    [CrossRef]
  4. D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
    [CrossRef]
  5. J. Soc. Photo. Opt. Instrum. Eng. 83, (1976).
  6. D. Casasent, D. Psaltis, Appl. Opt. 16, 2288 (1977).
    [CrossRef] [PubMed]
  7. E. B. Burkhardt, Appl. Opt. 6, 1359 (1967).
    [CrossRef]
  8. A. Rihaczek, Principles of High Resolution Radar (McGraw-Hill, New York, 1969).
  9. A. VanderLugt, Appl. Opt. 5, 1760 (1966).
    [CrossRef]
  10. D. Casasent, D. Psaltis, Appl. Opt. 15, 1795 (1976).
    [CrossRef] [PubMed]
  11. D. Psaltis, D. Casasent, Appl. Opt.April (1978).
  12. D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
    [CrossRef]

1978 (1)

D. Psaltis, D. Casasent, Appl. Opt.April (1978).

1977 (3)

J. W. Goodman, Proc. IEEE 65, 29 (1977).
[CrossRef]

D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
[CrossRef]

D. Casasent, D. Psaltis, Appl. Opt. 16, 2288 (1977).
[CrossRef] [PubMed]

1976 (3)

D. Casasent, D. Psaltis, Appl. Opt. 15, 1795 (1976).
[CrossRef] [PubMed]

J. Soc. Photo. Opt. Instrum. Eng. 83, (1976).

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

1975 (1)

D. Casasent, W. Sterling, IEEE Trans. Comput. C-24, 348 (1975).
[CrossRef]

1967 (1)

1966 (1)

Burkhardt, E. B.

Casasent, D.

D. Psaltis, D. Casasent, Appl. Opt.April (1978).

D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
[CrossRef]

D. Casasent, D. Psaltis, Appl. Opt. 16, 2288 (1977).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, Appl. Opt. 15, 1795 (1976).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

D. Casasent, W. Sterling, IEEE Trans. Comput. C-24, 348 (1975).
[CrossRef]

D. Casasent, “Pattern and Character Recognition,” in Handbook of Holography, H. J. Caulfield, Ed. (Academic, New York, 1978).

Goodman, J. W.

J. W. Goodman, Proc. IEEE 65, 29 (1977).
[CrossRef]

Psaltis, D.

D. Psaltis, D. Casasent, Appl. Opt.April (1978).

D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
[CrossRef]

D. Casasent, D. Psaltis, Appl. Opt. 16, 2288 (1977).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, Appl. Opt. 15, 1795 (1976).
[CrossRef] [PubMed]

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

Rihaczek, A.

A. Rihaczek, Principles of High Resolution Radar (McGraw-Hill, New York, 1969).

Sterling, W.

D. Casasent, W. Sterling, IEEE Trans. Comput. C-24, 348 (1975).
[CrossRef]

VanderLugt, A.

Appl. Opt. (5)

IEEE Trans. Comput. (1)

D. Casasent, W. Sterling, IEEE Trans. Comput. C-24, 348 (1975).
[CrossRef]

J. Soc. Photo. Opt. Instrum. Eng. (1)

J. Soc. Photo. Opt. Instrum. Eng. 83, (1976).

Opt. Commun. (1)

D. Casasent, D. Psaltis, Opt. Commun. 17, 59 (1976).
[CrossRef]

Proc. IEEE (2)

J. W. Goodman, Proc. IEEE 65, 29 (1977).
[CrossRef]

D. Casasent, D. Psaltis, Proc. IEEE 65, 77 (1977).
[CrossRef]

Other (2)

A. Rihaczek, Principles of High Resolution Radar (McGraw-Hill, New York, 1969).

D. Casasent, “Pattern and Character Recognition,” in Handbook of Holography, H. J. Caulfield, Ed. (Academic, New York, 1978).

Cited By

OSA participates in CrossRef's Cited-By Linking service. Citing articles from OSA journals and other participating publishers are listed here.

Alert me when this article is cited.


Figures (4)

Fig. 1
Fig. 1

Schematic block diagram of a multiple-invariant, space-variant optical correlator using the magnitude of the Fourier transform.

Fig. 2
Fig. 2

Schematic block diagram of a multiple-invariant, space-variant optical correlator with no phase loss of information.

Fig. 3
Fig. 3

Experimental demonstration of shift or phase extraction in a multiple-invariant, space-variant optical correlator: (a) magnitude of the Fourier transform of the interference pattern; (b) thresholded and pulse width normalized version of (a); (c) derivative of the first diffracted order of the pattern in (b) showing the input phase data; (d) same as (c) but for the pattern in (a) showing the need to remove the amplitude modulation.

Fig. 4
Fig. 4

Plot of actual vs experimentally determined values of the shift of the input function.

Equations (18)

Equations on this page are rendered with MathJax. Learn more.

f ( x ) = f ( x ) = f [ g ( x , a ) ] ,
ξ = h 1 ( x ) = d ξ 0 d a x g ( x , a ) x g ( x , a ) a d x .
f ( x ) = f ( x ) = f [ g ( x , a 1 , a 2 ) ] ,
( g ) / ( a i ) ( g ) / ( a j ) ,
g ( x , a 1 a 2 ) = g [ h ( ξ ξ 0 ) , a 2 ] ,
f ( ξ ξ 0 , a 2 ) = f { g [ h ( ξ ξ 0 ) , a 2 ] } .
[ f ( ξ ξ 0 , a 2 ) ] = exp ( j ω ξ 0 ) F ( ω ) ,
d T ( ω ) d ω = [ sin ( q ) ] [ d ϕ ( ω ) d ω + x 0 ] ,
x = g ( x , a 1 , a 2 ) .
g [ h 1 ( ξ 1 ) , a 1 , a 2 ] = g 1 ( ξ 1 ξ 01 , a 2 ) ,
f 1 ( ξ 1 ξ 01 , a 2 ) = f [ g 1 ( ξ 1 ξ 01 , a 2 ) ]
f { g 1 [ h 1 1 ( x ) , a 2 ] } = f [ g ( x , a 2 ) ] ,
f [ g ( x , a 1 , a 2 ) ] = f [ g ( x a 1 , a 2 ) ] ,
g ( x , a 1 , a 2 ) = x a 1 + a 2 ,
g [ exp ( exp ξ 1 ) , a 1 , a 2 ] = exp [ exp ( ξ 1 + ln a 1 ) ] + a 2 = g 1 ( ξ 1 ξ 01 , a 2 ) ,
g [ exp ( exp ξ 1 ) , 1 , a 2 ] = exp ( exp ξ 1 ) + a 2 = g 1 ( ξ 1 , a 2 ) .
g ( x , 1 , a 2 ) = x + a 2 .
f [ a 1 ( x a 2 ) a 3 ] .

Metrics