## Abstract

A traditional Shack–Hartmann wavefront sensor (SHWS) uses a physical microlens array to sample the incoming wavefront into a number of segments and to measure the phase profile over the cross section of a given light beam. We customized a digital SHWS by encoding a spatial light modulator (SLM) with a diffractive optical lens (DOL) pattern to function as a diffractive optical microlens array. This SHWS can offer great flexibility for various applications. Through fast-Fourier-transform (FFT) analysis and experimental investigation, we studied three sampling methods to generate the digitized DOL pattern, and we compared the results. By analyzing the diffraction efficiency of the DOL and the microstructure of the SLM, we proposed three important strategies for the proper implementation of DOLs and DOL arrays with a SLM. Experiments demonstrated that these design rules were necessary and sufficient for generating an efficient DOL and DOL array with a SLM.

© 2006 Optical Society of America

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### Equations (15)

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(1)
$$\varphi (r)=2\pi ({a}_{2}{r}^{2}+{a}_{4}{r}^{4}+\cdots \text{\hspace{0.17em}}),$$
(2)
$$1/f=-2{a}_{2}{\lambda}_{0}m,$$
(3)
$$N1=\frac{\sqrt{1/{a}_{2}}}{b}=\frac{\sqrt{2f\lambda}}{b},$$
(4)
$$f\ge 64{b}^{2}/2\lambda \mathrm{.}$$
(5)
$${d}_{\mathrm{min}}=2\sqrt{2f\lambda}\mathrm{.}$$
(6)
$$N=\frac{\sqrt{n}-\sqrt{n-1}}{b}\text{\hspace{0.17em}}\sqrt{2f\lambda}=1,$$
(7)
$$n=\frac{f\lambda}{2{b}^{2}}+\frac{1}{2}+\frac{{b}^{2}}{8f\lambda}\mathrm{.}$$
(8)
$${d}_{\mathrm{max}}=\frac{2f\lambda}{b}+b\mathrm{.}$$
(9)
$$2\sqrt{2f\lambda}\le d\le \frac{2f\lambda}{b}+b\mathrm{.}$$
(10)
$$p\text{\hspace{0.17em}}\mathrm{sin}\text{\hspace{0.17em}}\theta =m\lambda \mathrm{.}$$
(11)
$$\mathrm{sin}\text{\hspace{0.17em}}\theta =m\lambda /p,=\frac{632.8\times {10}^{-9}}{32\times {10}^{-6}}=0.019775$$
(12)
$$\theta =1.1331\xb0\mathrm{.}$$
(13)
$$\mathrm{tan}\text{\hspace{0.17em}}\theta =\frac{0.7\left[f\right]\times 32\times {10}^{-6}}{f\times {10}^{-3}}=0.0224$$
(14)
$$\theta =1.2832\xb0\mathrm{.}$$