Abstract

We propose a new method for evaluating and correcting aberrations in a Vander Lugt correlator. The technique is achieved with liquid-crystal displays of the correlator and allows the task to be performed in situ. We present the theory on which the method is based and the experimental results that we obtained by applying it in a convergent correlator.

© 2003 Optical Society of America

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References

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  1. H. K. Liu, J. A. Davis, and R. A. Lilly, Opt. Lett. 10, 635 (1985).
    [CrossRef] [PubMed]
  2. C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, J. Mod. Opt. 39, 761 (1992).
    [CrossRef]
  3. J. Nicolás, J. Campos, C. Iemmi, I. Moreno, and M. J. Yzuel, Appl. Opt. 41, 1505 (2002).
    [CrossRef]
  4. R. R. Kallman and D. H. Goldstein, Opt. Eng. 33, 1806 (1994).
    [CrossRef]
  5. K. Styczynski, J. Campos, M. J. Yzuel, and K. Chalasinska Macukow, Opt. Commun. 118, 193 (1995).
    [CrossRef]
  6. A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, Opt. Eng. 40, 2558 (2001).
    [CrossRef]
  7. A. Vander Lugt, Appl. Opt. 6, 1221 (1967).
    [CrossRef]
  8. L. Cai, Y. Jin, S. Zhou, P. Yeh, N. Marzwell, and H. Liu, Opt. Eng. 35, 415 (1996).
    [CrossRef]
  9. M. Montes Usategui, S. E. Monroe, and R. D. Juday, Opt. Eng. 36, 1782 (1997).
    [CrossRef]
  10. J. Pérez Tudela, M. Montes Usategui, I. Juvells, and S. Vallmitjana, Opt. Commun. 184, 345 (2000).
    [CrossRef]
  11. O. López Coronado, I. Moreno, J. Campos, M. J. Yzuel, J. Mod. Opt. 45, 2461 (1998).
    [CrossRef]
  12. H. J. Caulfield, M. P. Schamschula, and L. Zhang, Opt. Lett. 20, 1803 (1995).
    [CrossRef]
  13. F. Zernike, Z. Tech. Phys. 16, 454 (1935).
  14. K. Creath, in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 350–393.
  15. D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Creath, K.

K. Creath, in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 350–393.

Malacara, D.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

Other (15)

H. K. Liu, J. A. Davis, and R. A. Lilly, Opt. Lett. 10, 635 (1985).
[CrossRef] [PubMed]

C. Soutar, Z. Q. Wang, C. M. Cartwright, and W. A. Gillespie, J. Mod. Opt. 39, 761 (1992).
[CrossRef]

J. Nicolás, J. Campos, C. Iemmi, I. Moreno, and M. J. Yzuel, Appl. Opt. 41, 1505 (2002).
[CrossRef]

R. R. Kallman and D. H. Goldstein, Opt. Eng. 33, 1806 (1994).
[CrossRef]

K. Styczynski, J. Campos, M. J. Yzuel, and K. Chalasinska Macukow, Opt. Commun. 118, 193 (1995).
[CrossRef]

A. Marquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos, and M. J. Yzuel, Opt. Eng. 40, 2558 (2001).
[CrossRef]

A. Vander Lugt, Appl. Opt. 6, 1221 (1967).
[CrossRef]

L. Cai, Y. Jin, S. Zhou, P. Yeh, N. Marzwell, and H. Liu, Opt. Eng. 35, 415 (1996).
[CrossRef]

M. Montes Usategui, S. E. Monroe, and R. D. Juday, Opt. Eng. 36, 1782 (1997).
[CrossRef]

J. Pérez Tudela, M. Montes Usategui, I. Juvells, and S. Vallmitjana, Opt. Commun. 184, 345 (2000).
[CrossRef]

O. López Coronado, I. Moreno, J. Campos, M. J. Yzuel, J. Mod. Opt. 45, 2461 (1998).
[CrossRef]

H. J. Caulfield, M. P. Schamschula, and L. Zhang, Opt. Lett. 20, 1803 (1995).
[CrossRef]

F. Zernike, Z. Tech. Phys. 16, 454 (1935).

K. Creath, in Progress in Optics, E. Wolf, ed., (Elsevier, Amsterdam, 1988), Vol. XXVI, pp. 350–393.

D. Malacara, Optical Shop Testing (Wiley, New York, 1978).

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Figures (4)

Fig. 1
Fig. 1

Schematic of a convergent optical correlator; Ls, convergent lenses; WPs, wave plates; Ps, polarizers. The scene and the filter are displayed on spatial light modulators LCD1 and LCD2, respectively. Π represents the final plane.

Fig. 2
Fig. 2

(a) Image of the final plane when no phase shift is introduced into the filter. In this case light does not impinge in the zone placed outside the circular diaphragm. (b) Image corresponding to expression C. One can evaluate the first term, C0, by taking an average of pixel values over that external zone (white arrow).

Fig. 3
Fig. 3

(a) Theoretical phase distribution, (b) experimental phase extraction, (c) result of the phase extraction obtained when the theoretical phase and the experimental phase were subtracted and displayed in LCD1, (d) line profile of (c).

Fig. 4
Fig. 4

(a) Measure of the phase distribution introduced by a piece of glass, (b) measure of the phase distribution after correction.

Equations (5)

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Hu=1+δuexpi2πnN-1,
Anx=fxexpiΨx*hx=fxexpiΨx+expi2πnN-1K,
C=n=0N-1AnAn*cos2πnN, S=n=0N-1AnAn*sin2πnN,
C=-NK2+NKfxcosΨx+μ, S=NKfxsinΨx+μ.
Ψx=tan-1S/C-C0-μ,

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