Abstract

In this work we present experimental evidence of an anamorphic and spatial frequency dependent phase modulation in commercially available twisted nematic liquid crystal spatial light modulators. We have found that the phase modulation depth depends on the magnitude of the local spatial frequency component along the horizontal direction. Along the vertical direction the phase modulation depth does not depend on the spatial frequency. This phenomenon is related with the electronics driving the device and in no way related to liquid crystal physics. It causes a reduction of the optical efficiency of a diffractive optical element displayed onto this type of modulator. We present an algorithm to correct this effect and more efficiently display a diffractive optical element. We apply it to the particular case of a Fresnel lens. Experimental results that confirm the improvements in the efficiency of the displayed diffractive lens are presented.

© 2005 Optical Society of America

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References

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Appl. Opt.

J. Opt. Soc. Am.

J. Opt. Soc. Am. A

Jap. J. Appl. Phys.

I. Moreno, J. Campos, C. Gorecki and M. J. Yzuel, �??Effects of amplitude and phase mismatching errors in the generation of a kinoform for pattern recognition,�?? Jap. J. Appl. Phys. 34, 6423-6434 (1995).
[CrossRef]

Opt. Commun.

V. Laude, �??Twisted-nematic liquid crystal pixelated active lens,�?? Opt. Commun. 153, 134-152 (1998).
[CrossRef]

Y. Takaki and H. Ohzu, �??Liquid-crystal active lens: a reconfigurable lens employing a phase modulator,�?? Opt. Commun. 126, 123-134 (1996).

Opt. Eng.

A. Márquez, C. Iemmi, I. Moreno, J. A. Davis, J. Campos and M. J. Yzuel, �??Quantitative prediction of the modulation behavior of twisted nematic liquid crystal displays,�?? Opt. Eng. 40, 2558-2564 (2001).
[CrossRef]

Z. Zhang, G. Lu and F. T. S Yu, �??A simple method for measuring phase modulation in LCTVs,�?? Opt. Eng. 33, 3018-3022 (1994).
[CrossRef]

Opt. Express

Opt. Lett.

Other

P. Yeh, Optics of liquid crystal displays (John Wiley & Sons, New York, 1999).

J. W. Goodman, Introduction to Fourier Optics (McGraw-Hill, 1996), 16-19.

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Figures (7)

Fig. 1.
Fig. 1.

Normalized intensity transmission for the phase-only modulation configuration of the twisted nematic LCD.

Fig. 2.
Fig. 2.

Intensity of zero (•) and first (○) diffracted orders generated by a binary grating displayed on the LCD with gray levels 0 and g 2, as a function of g 2. (a) 64 rows/period (vertical frequency). (b) 2 rows/period (vertical frequency). (c) 64 columns/period (horizontal frequency). (d) 2 columns/period (horizontal frequency).

Fig. 3.
Fig. 3.

Phase modulation as a function of the addressed gray level and for binary gratings with period of 64, 32, 16, 8, 4 and 2 pixels. (a) Vertical frequency (rows/period). (b) Horizontal frequency (columns/period).

Fig. 4.
Fig. 4.

Maximum phase modulation as a function of the vertical period, measured in pixels.

Fig. 5.
Fig. 5.

Look up tables that assign a gray value to a phase value for different horizontal frequencies.

Fig. 6.
Fig. 6.

Modulation diffraction efficiency for cylindrical lenses as a function of the mismatch parameter c of a modulator with limited phase depth. The line shows the theoretical efficiency (Eq. (2)). H: horizontal lenses. V: vertical lenses. VC: corrected vertical lenses.

Fig. 7.
Fig. 7.

Modulation diffraction efficiency of spherical lenses as a function of the mismatch parameter c. White dots correspond to lenses without correction and black dots to equivalent lenses with correction of the anamorphic phase modulation.

Equations (5)

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p ( φ ) = { φ if φ < ε ε if ε < φ < ε 2 + π , 0 if φ > ε 2 + π
η m = { ε 2 π + 1 π sin ( ε 2 ) } 2 = { 1 c + 1 π sin ( π ( 1 c ) ) } 2 .
φ ( x , y ) = π r 2 λ f .
ν x = 1 2 π φ ( x , y ) x
ν x = x λ f

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