Abstract

Pseudorandom encoding with quantized real modulation values encodes only continuous real-valued functions. However, an arbitrary complex value can be represented if the desired value is first mapped to the closest real value realized by use of pseudorandom encoding. Examples of encoding real- and complex-valued functions illustrate performance improvements over conventional minimum distance mapping methods in reducing peak sidelobes and in improving the uniformity of spot arrays.

© 1999 Optical Society of America

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References

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    [CrossRef]
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    [CrossRef]
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1999

R. W. Cohn, “Analyzing the encoding range of amplitude-phase coupled spatial light modulators,” Opt. Eng. 38, 361–367 (1999).
[CrossRef]

R. W. Cohn, Markus Duelli, “Ternary pseudorandom encoding of Fourier transform holograms,” J. Opt. Soc. Am. A 16, 71–84 (1999).
[CrossRef]

1998

1996

1994

1993

1992

1989

1973

1966

Brown, B. R.

Chu, D. C.

Cohn, R. W.

R. W. Cohn, “Analyzing the encoding range of amplitude-phase coupled spatial light modulators,” Opt. Eng. 38, 361–367 (1999).
[CrossRef]

R. W. Cohn, Markus Duelli, “Ternary pseudorandom encoding of Fourier transform holograms,” J. Opt. Soc. Am. A 16, 71–84 (1999).
[CrossRef]

R. W. Cohn, “Pseudorandom encoding of fully complex functions onto amplitude coupled phase modulators,” J. Opt. Soc. Am. A 15, 868–883 (1998).
[CrossRef]

L. G. Hassebrook, M. E. Lhamon, R. C. Daley, R. W. Cohn, M. Liang, “Random phase encoding of composite fully complex filters,” Opt. Lett. 21, 272–274 (1996).
[CrossRef] [PubMed]

R. W. Cohn, M. Liang, “Pseudorandom phase-only encoding of real-time spatial light modulators,” Appl. Opt. 35, 2488–2498 (1996).
[CrossRef] [PubMed]

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

M. Duelli, M. Reece, R. W. Cohn are preparing a manuscript to be called “Modified minimum distance criterion for blended random and nonrandom encoding.”

R. W. Cohn, L. G. Hassebrook, “Representations of fully complex functions on real-time spatial light modulators,” in Optical Information Processing, F. T. S. Yu, S. Jutamulia, eds. (Cambridge University, Cambridge, UK, 1998), Chap. 15, pp. 396–432.

Daley, R. C.

Dallas, W. J.

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed. (Springer-Verlag, Berlin, 1980), Chap. 6, pp. 291–366.

Duelli, M.

M. Duelli, M. Reece, R. W. Cohn are preparing a manuscript to be called “Modified minimum distance criterion for blended random and nonrandom encoding.”

Duelli, Markus

Fienup, J. R.

Flannery, D. L.

Giles, M. K.

Goodman, J. W.

Hassebrook, L. G.

L. G. Hassebrook, M. E. Lhamon, R. C. Daley, R. W. Cohn, M. Liang, “Random phase encoding of composite fully complex filters,” Opt. Lett. 21, 272–274 (1996).
[CrossRef] [PubMed]

R. W. Cohn, L. G. Hassebrook, “Representations of fully complex functions on real-time spatial light modulators,” in Optical Information Processing, F. T. S. Yu, S. Jutamulia, eds. (Cambridge University, Cambridge, UK, 1998), Chap. 15, pp. 396–432.

Juday, R. D.

Kast, B. A.

Krackhardt, U.

Lee, W.-H.

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–231.
[CrossRef]

Lhamon, M. E.

Liang, M.

Lindell, S. D.

Lohmann, A. W.

Mait, J. N.

Neto, L. G.

Reece, M.

M. Duelli, M. Reece, R. W. Cohn are preparing a manuscript to be called “Modified minimum distance criterion for blended random and nonrandom encoding.”

Roberge, D.

Sheng, Y.

Streibl, N.

Appl. Opt.

J. Opt. Soc. Am. A

Opt. Eng.

R. W. Cohn, “Analyzing the encoding range of amplitude-phase coupled spatial light modulators,” Opt. Eng. 38, 361–367 (1999).
[CrossRef]

Opt. Lett.

Opt. Photon. News

J. N. Mait, “Diffractive beauty,” Opt. Photon. News 52, 21–25 (1998).
[CrossRef]

Other

W.-H. Lee, “Computer-generated holograms: techniques and applications,” in Progress in Optics, E. Wolf, ed. (Elsevier, Amsterdam, 1978), Vol. 16, pp. 119–231.
[CrossRef]

W. J. Dallas, “Computer-generated holograms,” in The Computer in Optical Research, B. R. Frieden, ed. (Springer-Verlag, Berlin, 1980), Chap. 6, pp. 291–366.

M. Duelli, M. Reece, R. W. Cohn are preparing a manuscript to be called “Modified minimum distance criterion for blended random and nonrandom encoding.”

VLSI Spatial Light Modulators, Operations Manual for 128 × 128 analog SLM, revision 1.6 (Boulder Nonlinear Systems Inc., Lafayette, Colo., 1998).

R. W. Cohn, L. G. Hassebrook, “Representations of fully complex functions on real-time spatial light modulators,” in Optical Information Processing, F. T. S. Yu, S. Jutamulia, eds. (Cambridge University, Cambridge, UK, 1998), Chap. 15, pp. 396–432.

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Figures (4)

Fig. 1
Fig. 1

Pixel-oriented encoding methods: (a) PRE, (b) MDE, (c) mMD-PRE. Method (c) also describes MD-PRE if the desired function is strictly real.

Fig. 2
Fig. 2

Performance of MDE and MD-PRE as a function of the magnitude scaling parameter for encoding the real-valued function.

Fig. 3
Fig. 3

Diffraction patterns for (a) MD-PRE for γ = 1.1 and (b) MDE for γ = 1.13 for the real-valued desired function and (c) mMD-PRE for γ = 1.05 and (d) MDE for γ = 1.9 for the complex-valued desired function. The intensity images are saturated so that the full white gray scale corresponds to 1/10 of the average intensity of the 49 spots. Also, the images are shown rotated by 45° from the xy coordinate system.

Fig. 4
Fig. 4

Performance of MDE and mMD-PRE as a function of the magnitude scaling parameter for encoding the complex-valued function.

Tables (2)

Tables Icon

Table 1 Performance for Encoding the Real-Valued Function

Tables Icon

Table 2 Performance for Encoding the Complex-Valued Function

Equations (4)

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

ai=sgnReaci if ½|Reaci|,ai=0 if |Reaci|<1½,
aci=γ expjβaci,
p=|Reaci|.
ai=sgnReaci if 0si<pi or 1<pi,ai=0 if pisi1,

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