Abstract

We report what to our knowledge is a new technique for encoding both amplitude and phase information onto a single binary-valued spatial light modulator. In our approach, we spatially modulate the diffraction efficiency of the filter. Light that is not diffracted into the first order is sent into the zero order, effectively allowing amplitude modulation of either the first-order or zero-order diffracted light. This technique has applications in both optical pattern recognition and image processing. Experimental results are included.

© 2003 Optical Society of America

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References

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  1. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
    [CrossRef]
  2. S. Wentzel, A. Jendral, R. Brauer, O. Bryngdahl, “Increase of the space-bandwidth produce of computer-generated near-field holograms by optical means,” Opt. Lett. 19, 1352–1354 (1994).
    [CrossRef] [PubMed]
  3. J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Bessel function output from an optical correlator using an inverse filter written onto a phase-only spatial light modulator,” Appl. Opt. 38, 6709–6713 (1999).
    [CrossRef]
  4. J. Campos, A. Marquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only filters,” Appl. Opt. 39, 5965–5970 (2000).
    [CrossRef]
  5. M. J. Yzuel, J. Campos, A. Marquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal devices,” Appl. Opt. 39, 6034–6039 (2000).
    [CrossRef]
  6. J. A. Davis, D. E. McNamara, D. M. Cottrell, J. Campos, M. Yzuel, I. Moreno, “Encoding complex diffractive optical elements onto a phase-only liquid crystal spatial light modulator,” Opt. Eng. 40, 327–329 (2001).
    [CrossRef]
  7. A. Marquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
    [CrossRef]
  8. J. A. Davis, D. A. Smith, D. E. McNamara, D. Cottrell, J. Campos, “Fractional derivatives—Analysis and experimental implementation,” Appl. Opt. 40, 5943–5948 (2001).
    [CrossRef]
  9. See, for example, Spatial Light Modulator Technology, U. Efron, ed. (Marcel Dekker, New York, 1995), Chap. 6 and 7.
  10. W. H. Lee, “Sampled Fourier transform hologram generated by computer,” Appl. Opt. 9, 639–643 (1970).
    [CrossRef] [PubMed]
  11. C. B. Burckhardt, “A simplification of Lee’s method of generating holograms by computer,” Appl. Opt. 9, 1949 (1970).
  12. C. K. Hsueh, A. A. Sawchuk, “Computer-generated double phase holograms,” Appl. Opt. 17, 3874–3884 (1978).
    [CrossRef] [PubMed]
  13. J. N. Mait, G. S. Himes, “Computer-generated holograms by means of a magneto-optic spatial light modulator,” Appl. Opt. 28, 4879–4887 (1989).
    [CrossRef] [PubMed]
  14. J. A. Davis, M. A. Waring, G. W. Bach, R. A. Lilly, D. M. Cottrell, “Compact optical correlator design,” Appl. Opt. 28, 10–11 (1989).
    [CrossRef] [PubMed]
  15. J. A. Davis, D. M. Cottrell, R. A. Lilly, S. W. Connely, “Multiplexed phase-encoded lenses written on programmable spatial light modulators,” Opt. Lett. 14, 420–422 (1989).
    [CrossRef] [PubMed]
  16. W. H. Lee, “High efficiency multiple beam gratings,” Appl. Opt. 18, 2152–2158 (1979).
    [CrossRef] [PubMed]
  17. C. Robledo-Sánchez, G. Camacho-Basilo, A. Jaramillo-Nunez, A. Cornejo-Rodriguez, “Binary grating with variable bar/space ratio following a geometrical progression,” Opt. Commun. 119, 465–470 (1995).
    [CrossRef]
  18. C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  19. J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
    [CrossRef]
  20. I. Moreno, J. A. Davis, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
    [CrossRef]
  21. J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
    [CrossRef] [PubMed]

2001 (3)

2000 (2)

1999 (2)

1998 (2)

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

1995 (1)

C. Robledo-Sánchez, G. Camacho-Basilo, A. Jaramillo-Nunez, A. Cornejo-Rodriguez, “Binary grating with variable bar/space ratio following a geometrical progression,” Opt. Commun. 119, 465–470 (1995).
[CrossRef]

1994 (2)

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

S. Wentzel, A. Jendral, R. Brauer, O. Bryngdahl, “Increase of the space-bandwidth produce of computer-generated near-field holograms by optical means,” Opt. Lett. 19, 1352–1354 (1994).
[CrossRef] [PubMed]

1989 (3)

1985 (1)

1979 (1)

1978 (1)

1970 (2)

Bach, G. W.

Brauer, R.

Bryngdahl, O.

Burckhardt, C. B.

Camacho-Basilo, G.

C. Robledo-Sánchez, G. Camacho-Basilo, A. Jaramillo-Nunez, A. Cornejo-Rodriguez, “Binary grating with variable bar/space ratio following a geometrical progression,” Opt. Commun. 119, 465–470 (1995).
[CrossRef]

Campos, J.

Connely, S. W.

Cornejo-Rodriguez, A.

C. Robledo-Sánchez, G. Camacho-Basilo, A. Jaramillo-Nunez, A. Cornejo-Rodriguez, “Binary grating with variable bar/space ratio following a geometrical progression,” Opt. Commun. 119, 465–470 (1995).
[CrossRef]

Cottrell, D.

Cottrell, D. M.

Davis, J. A.

J. A. Davis, D. E. McNamara, D. M. Cottrell, J. Campos, M. Yzuel, I. Moreno, “Encoding complex diffractive optical elements onto a phase-only liquid crystal spatial light modulator,” Opt. Eng. 40, 327–329 (2001).
[CrossRef]

A. Marquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

J. A. Davis, D. A. Smith, D. E. McNamara, D. Cottrell, J. Campos, “Fractional derivatives—Analysis and experimental implementation,” Appl. Opt. 40, 5943–5948 (2001).
[CrossRef]

M. J. Yzuel, J. Campos, A. Marquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal devices,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

J. Campos, A. Marquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only filters,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Bessel function output from an optical correlator using an inverse filter written onto a phase-only spatial light modulator,” Appl. Opt. 38, 6709–6713 (1999).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

I. Moreno, J. A. Davis, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

J. A. Davis, D. M. Cottrell, R. A. Lilly, S. W. Connely, “Multiplexed phase-encoded lenses written on programmable spatial light modulators,” Opt. Lett. 14, 420–422 (1989).
[CrossRef] [PubMed]

J. A. Davis, M. A. Waring, G. W. Bach, R. A. Lilly, D. M. Cottrell, “Compact optical correlator design,” Appl. Opt. 28, 10–11 (1989).
[CrossRef] [PubMed]

Escalera, J. C.

Himes, G. S.

Horner, J. L.

Hsueh, C. K.

Iemmi, C.

Jaramillo-Nunez, A.

C. Robledo-Sánchez, G. Camacho-Basilo, A. Jaramillo-Nunez, A. Cornejo-Rodriguez, “Binary grating with variable bar/space ratio following a geometrical progression,” Opt. Commun. 119, 465–470 (1995).
[CrossRef]

Jendral, A.

Ledesma, S.

Lee, W. H.

Leger, J. R.

Lilly, R. A.

Lu, K.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Mait, J. N.

Marquez, A.

McNamara, D. E.

J. A. Davis, D. A. Smith, D. E. McNamara, D. Cottrell, J. Campos, “Fractional derivatives—Analysis and experimental implementation,” Appl. Opt. 40, 5943–5948 (2001).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell, J. Campos, M. Yzuel, I. Moreno, “Encoding complex diffractive optical elements onto a phase-only liquid crystal spatial light modulator,” Opt. Eng. 40, 327–329 (2001).
[CrossRef]

Moreno, I.

Robledo-Sánchez, C.

C. Robledo-Sánchez, G. Camacho-Basilo, A. Jaramillo-Nunez, A. Cornejo-Rodriguez, “Binary grating with variable bar/space ratio following a geometrical progression,” Opt. Commun. 119, 465–470 (1995).
[CrossRef]

Sawchuk, A. A.

Smith, D. A.

Soutar, C.

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

Tsai, P.

Waring, M. A.

Wentzel, S.

Yzuel, M.

J. A. Davis, D. E. McNamara, D. M. Cottrell, J. Campos, M. Yzuel, I. Moreno, “Encoding complex diffractive optical elements onto a phase-only liquid crystal spatial light modulator,” Opt. Eng. 40, 327–329 (2001).
[CrossRef]

Yzuel, M. J.

Appl. Opt. (14)

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Bessel function output from an optical correlator using an inverse filter written onto a phase-only spatial light modulator,” Appl. Opt. 38, 6709–6713 (1999).
[CrossRef]

J. Campos, A. Marquez, M. J. Yzuel, J. A. Davis, D. M. Cottrell, I. Moreno, “Fully complex synthetic discriminant functions written onto phase-only filters,” Appl. Opt. 39, 5965–5970 (2000).
[CrossRef]

M. J. Yzuel, J. Campos, A. Marquez, J. C. Escalera, J. A. Davis, C. Iemmi, S. Ledesma, “Inherent apodization of lenses encoded on liquid-crystal devices,” Appl. Opt. 39, 6034–6039 (2000).
[CrossRef]

J. A. Davis, D. M. Cottrell, J. Campos, M. J. Yzuel, I. Moreno, “Encoding amplitude information onto phase-only filters,” Appl. Opt. 38, 5004–5013 (1999).
[CrossRef]

A. Marquez, C. Iemmi, J. C. Escalera, J. Campos, S. Ledesma, J. A. Davis, M. J. Yzuel, “Amplitude apodizers encoded onto Fresnel lenses implemented on a phase-only spatial light modulator,” Appl. Opt. 40, 2316–2322 (2001).
[CrossRef]

J. A. Davis, D. A. Smith, D. E. McNamara, D. Cottrell, J. Campos, “Fractional derivatives—Analysis and experimental implementation,” Appl. Opt. 40, 5943–5948 (2001).
[CrossRef]

W. H. Lee, “Sampled Fourier transform hologram generated by computer,” Appl. Opt. 9, 639–643 (1970).
[CrossRef] [PubMed]

C. B. Burckhardt, “A simplification of Lee’s method of generating holograms by computer,” Appl. Opt. 9, 1949 (1970).

C. K. Hsueh, A. A. Sawchuk, “Computer-generated double phase holograms,” Appl. Opt. 17, 3874–3884 (1978).
[CrossRef] [PubMed]

J. N. Mait, G. S. Himes, “Computer-generated holograms by means of a magneto-optic spatial light modulator,” Appl. Opt. 28, 4879–4887 (1989).
[CrossRef] [PubMed]

J. A. Davis, M. A. Waring, G. W. Bach, R. A. Lilly, D. M. Cottrell, “Compact optical correlator design,” Appl. Opt. 28, 10–11 (1989).
[CrossRef] [PubMed]

W. H. Lee, “High efficiency multiple beam gratings,” Appl. Opt. 18, 2152–2158 (1979).
[CrossRef] [PubMed]

J. A. Davis, I. Moreno, P. Tsai, “Polarization eigenstates for twisted-nematic liquid-crystal displays,” Appl. Opt. 37, 937–945 (1998).
[CrossRef]

J. L. Horner, J. R. Leger, “Pattern recognition with binary phase-only filters,” Appl. Opt. 24, 609–611 (1985).
[CrossRef] [PubMed]

Opt. Commun. (1)

C. Robledo-Sánchez, G. Camacho-Basilo, A. Jaramillo-Nunez, A. Cornejo-Rodriguez, “Binary grating with variable bar/space ratio following a geometrical progression,” Opt. Commun. 119, 465–470 (1995).
[CrossRef]

Opt. Eng. (3)

C. Soutar, K. Lu, “Determination of the physical properties of an arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
[CrossRef]

I. Moreno, J. A. Davis, “Transmission and phase measurement for polarization eigenvectors in twisted-nematic liquid crystal light modulators,” Opt. Eng. 37, 3048–3052 (1998).
[CrossRef]

J. A. Davis, D. E. McNamara, D. M. Cottrell, J. Campos, M. Yzuel, I. Moreno, “Encoding complex diffractive optical elements onto a phase-only liquid crystal spatial light modulator,” Opt. Eng. 40, 327–329 (2001).
[CrossRef]

Opt. Lett. (2)

Other (1)

See, for example, Spatial Light Modulator Technology, U. Efron, ed. (Marcel Dekker, New York, 1995), Chap. 6 and 7.

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Figures (6)

Fig. 1
Fig. 1

Profile for a binary phase grating.

Fig. 2
Fig. 2

Technique for producing a binary phase grating: (a) phase grating profile with threshold levels, (b) binary grating produced by use of threshold level #1, where w/ d = 1/4, (c) binary grating produced by use of threshold level #2, where w/ d = 1/2.

Fig. 3
Fig. 3

Technique for producing an amplitude coded binary phase grating: (a) phase grating profile, (b) desired amplitude function |G(x)|, (c) sum of (a) and (b) with appropriate threshold, (d) resulting binary-phase grating with amplitude encoded as a varying w/ d ratio.

Fig. 4
Fig. 4

Experimental plots showing ±1 and zero order diffracted orders for: (a) grating with w/ d = 1/4, (b) grating with a low-pass filter where |G(x)| =cos4x/ L), (c) grating with a high-pass filter where |G(x)| = 1 -cos4x/ L).

Fig. 5
Fig. 5

Experimental results for: (a) binary hologram for letter “V,” (b) edge enhanced output from the binary hologram, (c) amplitude encoded binary hologram for letter “V,” (d) output with edge-enhancement removed.

Fig. 6
Fig. 6

Experimental output results for amplitude encoded binary holograms for the letter “V” with sizes of (a) 32 pixels, (b) 48 pixels, (c) 60 pixels, (d) 74 pixels.

Equations (4)

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

η+1=2πsinπ wd.
G=|Gx|expiϕx+2πAx.
η+1x=2πsinπ|Gx|2.
η+1x=2|Gx|π.

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