Abstract

Amplitude-transmitting filters for apodizing and hyperresolving applications can be easily implemented by use of a two-dimensional programmable liquid-crystal spatial light modulator operating in a transmission-only mode. Experimental results are in excellent agreement with theoretical predictions. This approach can permit the analysis of various filter designs and can allow the filters to be changed rapidly to modify the response of an optical system.

© 1999 Optical Society of America

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References

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  1. J. P. Mills and B. J. Thompson, J. Opt. Soc. Am. 3, 694 (1986).
    [CrossRef]
  2. C. S. Chung and H. H. Hopkins, J. Mod. Opt. 35, 1485 (1988).
    [CrossRef]
  3. J. Campos and M. J. Yzuel, J. Mod. Opt. 36, 733 (1989).
    [CrossRef]
  4. M. J. Yzuel, J. C. Escalera, and J. Campos, Appl. Opt. 29, 1631 (1990).
    [CrossRef] [PubMed]
  5. R. Hild, J. C. Escalera, M. J. Yzuel, and R. Muschall, Pure Appl. Opt. 14, 795 (1995).
    [CrossRef]
  6. C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am. A 5, 643 (1988).
    [CrossRef]
  7. E. W. S. Hee, Opt. Laser Technol. 4, 75 (1975).
    [CrossRef]
  8. C. Soutar and K. Lu, Opt. Eng. 33, 2704 (1994).
    [CrossRef]
  9. J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for liquid crystal spatial light modulators,” Opt. Eng. (to be published).
  10. J. A. Davis, P. Tsai, K. G. D’Nelly, and I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. (to be published).
  11. K. Lu and B. E. A. Saleh, Opt. Eng. 29, 240 (1990).
    [CrossRef]

1995 (1)

R. Hild, J. C. Escalera, M. J. Yzuel, and R. Muschall, Pure Appl. Opt. 14, 795 (1995).
[CrossRef]

1994 (1)

C. Soutar and K. Lu, Opt. Eng. 33, 2704 (1994).
[CrossRef]

1990 (2)

1989 (1)

J. Campos and M. J. Yzuel, J. Mod. Opt. 36, 733 (1989).
[CrossRef]

1988 (2)

C. S. Chung and H. H. Hopkins, J. Mod. Opt. 35, 1485 (1988).
[CrossRef]

C. J. R. Sheppard and Z. S. Hegedus, J. Opt. Soc. Am. A 5, 643 (1988).
[CrossRef]

1986 (1)

J. P. Mills and B. J. Thompson, J. Opt. Soc. Am. 3, 694 (1986).
[CrossRef]

1975 (1)

E. W. S. Hee, Opt. Laser Technol. 4, 75 (1975).
[CrossRef]

Allison, D. B.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for liquid crystal spatial light modulators,” Opt. Eng. (to be published).

Campos, J.

Chung, C. S.

C. S. Chung and H. H. Hopkins, J. Mod. Opt. 35, 1485 (1988).
[CrossRef]

D’Nelly, K. G.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for liquid crystal spatial light modulators,” Opt. Eng. (to be published).

J. A. Davis, P. Tsai, K. G. D’Nelly, and I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. (to be published).

Davis, J. A.

J. A. Davis, P. Tsai, K. G. D’Nelly, and I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. (to be published).

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for liquid crystal spatial light modulators,” Opt. Eng. (to be published).

Escalera, J. C.

R. Hild, J. C. Escalera, M. J. Yzuel, and R. Muschall, Pure Appl. Opt. 14, 795 (1995).
[CrossRef]

M. J. Yzuel, J. C. Escalera, and J. Campos, Appl. Opt. 29, 1631 (1990).
[CrossRef] [PubMed]

Hee, E. W. S.

E. W. S. Hee, Opt. Laser Technol. 4, 75 (1975).
[CrossRef]

Hegedus, Z. S.

Hild, R.

R. Hild, J. C. Escalera, M. J. Yzuel, and R. Muschall, Pure Appl. Opt. 14, 795 (1995).
[CrossRef]

Hopkins, H. H.

C. S. Chung and H. H. Hopkins, J. Mod. Opt. 35, 1485 (1988).
[CrossRef]

Lu, K.

C. Soutar and K. Lu, Opt. Eng. 33, 2704 (1994).
[CrossRef]

K. Lu and B. E. A. Saleh, Opt. Eng. 29, 240 (1990).
[CrossRef]

Mills, J. P.

J. P. Mills and B. J. Thompson, J. Opt. Soc. Am. 3, 694 (1986).
[CrossRef]

Moreno, I.

J. A. Davis, P. Tsai, K. G. D’Nelly, and I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. (to be published).

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for liquid crystal spatial light modulators,” Opt. Eng. (to be published).

Muschall, R.

R. Hild, J. C. Escalera, M. J. Yzuel, and R. Muschall, Pure Appl. Opt. 14, 795 (1995).
[CrossRef]

Saleh, B. E. A.

K. Lu and B. E. A. Saleh, Opt. Eng. 29, 240 (1990).
[CrossRef]

Sheppard, C. J. R.

Soutar, C.

C. Soutar and K. Lu, Opt. Eng. 33, 2704 (1994).
[CrossRef]

Thompson, B. J.

J. P. Mills and B. J. Thompson, J. Opt. Soc. Am. 3, 694 (1986).
[CrossRef]

Tsai, P.

J. A. Davis, P. Tsai, K. G. D’Nelly, and I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. (to be published).

Wilson, M. L.

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for liquid crystal spatial light modulators,” Opt. Eng. (to be published).

Yzuel, M. J.

R. Hild, J. C. Escalera, M. J. Yzuel, and R. Muschall, Pure Appl. Opt. 14, 795 (1995).
[CrossRef]

M. J. Yzuel, J. C. Escalera, and J. Campos, Appl. Opt. 29, 1631 (1990).
[CrossRef] [PubMed]

J. Campos and M. J. Yzuel, J. Mod. Opt. 36, 733 (1989).
[CrossRef]

Appl. Opt. (1)

J. Mod. Opt. (2)

C. S. Chung and H. H. Hopkins, J. Mod. Opt. 35, 1485 (1988).
[CrossRef]

J. Campos and M. J. Yzuel, J. Mod. Opt. 36, 733 (1989).
[CrossRef]

J. Opt. Soc. Am. (1)

J. P. Mills and B. J. Thompson, J. Opt. Soc. Am. 3, 694 (1986).
[CrossRef]

J. Opt. Soc. Am. A (1)

Opt. Eng. (2)

C. Soutar and K. Lu, Opt. Eng. 33, 2704 (1994).
[CrossRef]

K. Lu and B. E. A. Saleh, Opt. Eng. 29, 240 (1990).
[CrossRef]

Opt. Laser Technol. (1)

E. W. S. Hee, Opt. Laser Technol. 4, 75 (1975).
[CrossRef]

Pure Appl. Opt. (1)

R. Hild, J. C. Escalera, M. J. Yzuel, and R. Muschall, Pure Appl. Opt. 14, 795 (1995).
[CrossRef]

Other (2)

J. A. Davis, D. B. Allison, K. G. D’Nelly, M. L. Wilson, and I. Moreno, “Ambiguities in measuring the physical parameters for liquid crystal spatial light modulators,” Opt. Eng. (to be published).

J. A. Davis, P. Tsai, K. G. D’Nelly, and I. Moreno, “Simple technique for determining the extraordinary axis direction for twisted nematic liquid crystal spatial light modulators,” Opt. Eng. (to be published).

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Figures (4)

Fig. 1
Fig. 1

Amplitude pupil filter functions corresponding to a, uniform transmission; b, an axial apodizing filter, where tr=6.75r2-13.5r4+6.75r6; c, an axial hyperresolving filter, where tr=1-4r2+4r4.

Fig. 2
Fig. 2

Theoretically calculated intensity as a function of axial distance for the filters of Fig.  1. Symbols show axial positions where experimental measurements were made: a, uniform transmission; b, an axial apodizing filter, where tr=6.75r2-13.5r4+6.75r6; c, an axial hyperresolving filter, where tr=1-4r2+4r4.

Fig. 3
Fig. 3

Experimental measurements of the intensity of the focused spot at the axial positions denoted in Fig.  2: (a) with the uniformly transmitting filter of Fig.  1, line a, the intensity changes according to the expected sinc-squared behavior. (b) with the axial apodizing filter of Fig.  1, curve b, the intensity decreases more slowly as a function of axial distance, showing that the DOF has been increased.

Fig. 4
Fig. 4

Experimental measurements of the intensity of the focused spot at the axial positions denoted in Fig.  2 with the axial hyperresolving filter of Fig.  1, curve c. The intensity oscillates with axial position, as predicted by theory: (a) 3-D plots at various axial positions; (b) two-dimensional intensity plots at various axial positions.

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