Abstract

We previously proposed a method of mapping full-complex spatial modulations into phase-only modulations. The Fourier transform of the encoded modulations approximates that of the original complex modulations. The amplitude of each pixel is encoded by the property that the amplitude of a random-phasor sum is reduced corresponding to its standard deviation. Pseudorandom encoding is designed for phase-only spatial light modulators that produce 360° phase shifts. Because such devices are rare, experiments are performed with a 326° modulator composed of two In Focus model TVT6000 liquid-crystal displays. Qualitative agreement with theory is achieved despite several nonideal properties of the modulator.

© 1996 Optical Society of America

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References

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  1. R. W. Cohn, M. Liang, “Approximating fully complex spatial modulation with pseudo-random phase-only modulation,” Appl. Opt. 33, 4406–4415 (1994).
    [CrossRef] [PubMed]
  2. J. L. Horner, P. D. Gianino, “Phase-only matched filtering,” Appl. Opt. 23, 812–816 (1984).
    [CrossRef] [PubMed]
  3. N. Konforti, E. Marom, S.-T. Wu, “Phase-only modulation with twisted nematic liquid-crystal spatial light modulators,” Opt. Lett. 13, 251–253 (1988).
    [CrossRef] [PubMed]
  4. J. Amako, T. Sonehara, “Kinoform using an electrically controlled birefringent liquid-crystal spatial light modulator,” Appl. Opt. 30, 4622–4628 (1991).
    [CrossRef] [PubMed]
  5. K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 241–246 (1990).
  6. J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Eng. 18, 1567–1569 (1993).
  7. C. Soutar, S. E. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, D. R. Pape, ed., Proc. SPIE2240, 280–291 (1994).
  8. C. Soutar, K. Lu, “Determination of the physical properties of arbitrary twisted-nematic liquid crystal cell,” Opt. Eng. 33, 2704–2712 (1994).
    [CrossRef]
  9. R. M. Boysel, J. M. Florence, W. R. Wu, “Deformable mirror light modulators for image processing,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 183–194 (1989).
  10. J. A. Loudin, “LCTV custom drive circuit,” in Optical Pattern Recognition V, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2237, 80–84 (1994).
  11. F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
    [CrossRef]
  12. R. W. Cohn, J. L. Horner, “Effects of systematic phase errors on phase-only correlation,” Appl. Opt. 33, 5432–5439 (1994).
    [CrossRef] [PubMed]
  13. C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
    [CrossRef]
  14. Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
    [CrossRef]

1994 (5)

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

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

R. W. Cohn, M. Liang, “Approximating fully complex spatial modulation with pseudo-random phase-only modulation,” Appl. Opt. 33, 4406–4415 (1994).
[CrossRef] [PubMed]

R. W. Cohn, J. L. Horner, “Effects of systematic phase errors on phase-only correlation,” Appl. Opt. 33, 5432–5439 (1994).
[CrossRef] [PubMed]

1993 (1)

J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Eng. 18, 1567–1569 (1993).

1991 (1)

1990 (1)

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 241–246 (1990).

1988 (1)

1984 (1)

1978 (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

Amako, J.

Boysel, R. M.

R. M. Boysel, J. M. Florence, W. R. Wu, “Deformable mirror light modulators for image processing,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 183–194 (1989).

Chipman, R. A.

J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Eng. 18, 1567–1569 (1993).

Cohn, R. W.

Florence, J. M.

R. M. Boysel, J. M. Florence, W. R. Wu, “Deformable mirror light modulators for image processing,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 183–194 (1989).

Gianino, P. D.

Harris, F. J.

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

Horner, J. L.

Knopp, J.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Konforti, N.

Liang, M.

Loudin, J. A.

J. A. Loudin, “LCTV custom drive circuit,” in Optical Pattern Recognition V, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2237, 80–84 (1994).

Lu, G.

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Lu, K.

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

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 241–246 (1990).

Marom, E.

Monroe, S. E.

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

C. Soutar, S. E. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, D. R. Pape, ed., Proc. SPIE2240, 280–291 (1994).

Pezzaniti, J. L.

J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Eng. 18, 1567–1569 (1993).

Saleh, B. E. A.

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 241–246 (1990).

Sonehara, T.

Soutar, C.

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

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

C. Soutar, S. E. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, D. R. Pape, ed., Proc. SPIE2240, 280–291 (1994).

Wu, S.-T.

Wu, W. R.

R. M. Boysel, J. M. Florence, W. R. Wu, “Deformable mirror light modulators for image processing,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 183–194 (1989).

Yu, F. T. S.

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Zhang, Z.

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Appl. Opt. (4)

Opt. Eng. (5)

K. Lu, B. E. A. Saleh, “Theory and design of the liquid crystal TV as an optical spatial phase modulator,” Opt. Eng. 29, 241–246 (1990).

J. L. Pezzaniti, R. A. Chipman, “Phase-only modulation of twisted nematic liquid-crystal TV by use of the eigenpolarization states,” Opt. Eng. 18, 1567–1569 (1993).

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

C. Soutar, S. E. Monroe, J. Knopp, “Measurement of the complex transmittance of the Epson liquid crystal television,” Opt. Eng. 33, 1061–1068 (1994).
[CrossRef]

Z. Zhang, G. Lu, F. T. S. Yu, “Simple method for measuring phase modulation in liquid crystal televisions,” Opt. Eng. 33, 3018–3022 (1994).
[CrossRef]

Opt. Lett. (1)

Proc. IEEE (1)

F. J. Harris, “On the use of windows for harmonic analysis with the discrete Fourier transform,” Proc. IEEE 66, 51–83 (1978).
[CrossRef]

Other (3)

R. M. Boysel, J. M. Florence, W. R. Wu, “Deformable mirror light modulators for image processing,” in Optical Information Processing Systems and Architectures, B. Javidi, ed., Proc. SPIE1151, 183–194 (1989).

J. A. Loudin, “LCTV custom drive circuit,” in Optical Pattern Recognition V, D. P. Casasent, T. H. Chao, eds., Proc. SPIE2237, 80–84 (1994).

C. Soutar, S. E. Monroe, “Selection of operating curves of twisted-nematic liquid crystal televisions,” in Advances in Optical Information Processing VI, D. R. Pape, ed., Proc. SPIE2240, 280–291 (1994).

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Figures (8)

Fig. 1
Fig. 1

Fraunhofer diffraction geometry illustrating superposition of a large number of wave fronts from independently phased, equal-intensity point sources.

Fig. 2
Fig. 2

Apparatus used for the experiments: VM, video microscope (or optical powermeter where noted in text); PC, personal computer that contains a frame grabber; VP, video projector; LC1 and LC2, LCTV’s from the video projector; S, viewing screen; M, video monitor; O, digital oscilloscope; P, polarizer; A1 and A2, apertures; Q1 and Q2, quarter-wave plates.

Fig. 3
Fig. 3

Point-spread function of the SLM aperture as measured and predicted. The cross section is taken across the center of the spot perpendicular to the horizontal lines of the SLM.

Fig. 4
Fig. 4

On-axis diffraction intensity for random binary grayscale patterns and with superpixels of various sizes. Each curve is normalized to the peak intensity with the gray scale equal to zero.

Fig. 5
Fig. 5

Intensity of the deflected point-spread function as a function of the carrier period. Intensities are normalized to the intensity of the undeflected (on-axis) point-spread function. The unit for the carrier period is the number of horizontal SLM lines per period.

Fig. 6
Fig. 6

Gray-scale images of the measured diffraction-pattern intensity: (a) the measured point-spread function (cross section shown in Fig. 3). The measured diffraction patterns that are designed to approximate a rect function in f y are of widths (b) w = 2, (c) w = 3, and (d) w = 4. The images are oriented so that f y is horizontal to the page.

Fig. 7
Fig. 7

Theoretical and measured diffraction patterns. Measured intensity curves are normalized with respect to the peak intensity of the measured point-spread function in Fig. 3. Cross sections are taken from the centers of the diffraction patterns shown in (a) Fig. 6(b) and (b) Fig. 6(c). Theoretical intensity plots are scaled by 1.96× in (a) and by 1.53× in (b) with respect to the peak intensity of the theoretical point-spread function from Fig. 3. Both measured curves are plotted with a +4-μm offset from the center of the measured point-spread function.

Fig. 8
Fig. 8

Theoretical (dashed curves) and measured (solid curves) diffraction patterns: (a) cross section of the center of the diffraction pattern shown in Fig. 6(d); (b) the average of 120 cross sections with a different random seed for each experiment; (c) the error bars (plus and minus one standard deviation) of the average intensity in (b). Curves are normalized the same as in Fig. 7 except that the measured curves are plotted with a +5-μm offset, and the theoretical curves are scaled in intensity by a factor of 1.64×.

Equations (9)

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ψ ¯ i = ψ i ,
ψ i = ψ ¯ i + δψ i ,
a ¯ i = exp ( j δψ i ) = sinc ( v i 2 π ) ,
t ( x ) = i = 1 N exp ( j ψ i ) r ( x x i ) ,
t ¯ ( x ) = i = 1 N a ¯ i exp ( j ψ ¯ i ) r ( x x i ) .
I ¯ ( f x ) = | T ¯ ( f x ) | 2 + N ( 1 η ) R 2 ( f x ) ,
η 1 N i = 1 N a ¯ i 2
I ( 0 ) = N 2 R 2 ( 0 ) 1 + cos ψ 2 ,
I ( f x , f y ) sinc 2 ( f x ) [ d ( f y ) * rect ( f y / w ) ] 2 ,

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