## Abstract

Spatial light modulators are often used to implement phase modulation. Since they are pixelated, the phase function is usually approximated by a regularly sampled piecewise constant function, and the periodicity of the pixel sampling generates annoying diffraction peaks. We theoretically investigate two pixelation techniques: the isophase method and a new nonperiodic method derived from the Voronoi tessellation technique. We show that, for a suitable choice of parameters, the diffraction peaks disappear and are replaced by a smoothly varying halo. We illustrate the potential of these two techniques for implementing a lens function and wavefront correction.

© 2011 Optical Society of America

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### Equations (9)

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(1)
$${\phi}_{d}(x,y)=\frac{\pi}{\lambda f}({x}^{2}+{y}^{2})\mathrm{.}$$
(2)
$${\sigma}_{\mathrm{\Phi}}^{2}={\iint}_{D}({\phi}_{\text{ideal}}(x,y)-{\phi}_{p}{)}^{2}\mathrm{d}x\mathrm{d}y\mathrm{.}$$
(3)
$$\frac{\partial}{\partial {\phi}_{p}}{\iint}_{D}({\phi}_{\text{ideal}}(x,y)-{\phi}_{p}{)}^{2}\mathrm{d}x\mathrm{d}y=0.$$
(4)
$${\phi}_{p}=\frac{1}{s}{\iint}_{D}{\phi}_{\text{ideal}}(x,y)\mathrm{d}x\mathrm{d}y\mathrm{.}$$
(5)
$$E(\xi ,\eta )=\frac{I(\xi ,\eta )}{{I}_{\text{airy}}},$$
(6)
$$S=\mathrm{max}(E(\xi ,\eta ))\mathrm{.}$$
(7)
$$a=\frac{\alpha}{d}\mathrm{.}$$
(8)
$${\phi}_{\text{ast}}(X,Y)=2{A}_{\text{ast}}XY\mathrm{.}$$
(9)
$${\phi}_{\text{coma}}(X,Y)={A}_{\text{coma}}(-2Y+3{Y}^{3}+3{X}^{2}Y)\mathrm{.}$$