Abstract

We show that computer generated holograms, implemented with amplitude-only liquid crystal spatial light modulators, allow the synthesis of fully complex fields with high accuracy. Our main discussion considers modified amplitude holograms whose transmittance is obtained by adding an appropriate bias function to the real cosine computer hologram of the encoded signal. We first propose a bias function, given by a soft envelope of the signal modulus, which is appropriate for perfect amplitude modulators. We also consider a second bias term, given by a constant function, which results appropriate for modulators whose amplitude transmittance is coupled with a linear phase modulation. The influence of the finite pixel size of the spatial light modulator is compensated by digital pre-filtering of the encoded complex signal. The performance of the discussed amplitude CGHs is illustrated by means of numerical simulations and the experimental synthesis of high order Bessel beams.

© 2005 Optical Society of America

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Appl. Opt.

in Optical Pattern Recognition XI

R. D. Juday, J. M. Rollins, S. E. Monroe, Jr., and M. V. Morelli, �??Full-phase full-complex characterization of a reflective SLM,�?? in Optical Pattern Recognition XI, David P. Casasent, Tien-Hsin Chao; eds., Proc. SPIE 4043, 80-89 (2000).

Introduction to Fourier Optics

J. W. Goodman, �??Analog Optical Information Processing,�?? in Introduction to Fourier Optics (McGraw-Hill, 1996) pp. 217-294.

J. W. Goodman, �??Holography,�?? in Introduction to Fourier Optics (McGraw-Hill, 1996) pp. 295-392.

IRE Trans. Inform. Theory IT

L. J. Cutrona, E. N. Leith, C. J. Palermo, and L. J. Porcello, �??Optical data processing and filtering systems,�?? IRE Trans. Inform. Theory IT-6, 386-400 (1960).

J. Opt. Soc. Am. A

J. Optics

I. Juvells, A. Carnicer, , S. Vallmitjana, and J. Campos, �??Implementation of real filters in a joint transform correlator using positive-only display,�?? J. Optics 25, 33 (1994).

JOSA A

Josep Nicolás, Juan Campos, María J. Yzuel, �??Phase and amplitude modulation of elliptic polarization states by nonabsorbing anisotropic elements: application to liquid-crystal devices,�?? JOSA A 19, 1013 (2002).

Lasers

A. E. Siegman, �??Wave Optics and Gaussian Beams�?? and �??Physical Properties of Gaussian Beams,�?? in Lasers (University Science Books, Mill Valley Ca., 1986) pp. 626-697.

Opt. Lett.

Optical Engineering

K. Lu, B. E. A. Saleh, "Theory and design of the liquid crystal TV as an optical spatial phase modulator," Optical Engineering 29, 240 (1990).
[CrossRef]

Proc. IEEE

J. Burch, �??A computer algorithm for the synthesis of spatial frequency filters,�?? Proc. IEEE 55, 599 (1967).

Prog. Opt.

W. H. Lee, �??Computer generated holograms,�?? Prog. Opt. 16, 121 (1978).

Other

L Allen, Stephen M Barnett, and Miles J Padgett, Optical Angular Momentum (Institute of Physics Publishing, 2003).

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