## Abstract

A novel method of fabricating phase-only optical filters that is based on the properties of a uniaxial crystal is proposed. With these optical filters, the phase differences are tunable among the different filter zones. Many focal patterns can be obtained if these optical filters are placed in front of a lens; furthermore, these optical filters can also be used to make up for the distortions in fabrications in which they were used only as untunable optical filters.

© 2004 Optical Society of America

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### Equations (6)

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(1)
$${n}_{e}\left(\mathrm{\theta}\right)={\left(\frac{{cos}^{2}\mathrm{\theta}}{n_{o}{}^{2}}+\frac{{sin}^{2}\mathrm{\theta}}{n_{e}{}^{2}}\right)}^{1/2},$$
(2)
$${n}_{a}sin\mathrm{\theta}={n}_{e}\left(\mathrm{\varphi}+\mathrm{\vartheta}\right)sin\mathrm{\vartheta},$$
(3)
$$\mathrm{\phi}={\mathit{kn}}_{e}\left(\mathrm{\varphi}+\mathrm{\vartheta}\right)\frac{l}{cos\mathrm{\vartheta}},$$
(4)
$$\mathrm{\delta}h=\frac{1}{cos\mathrm{\vartheta}}sin\left(\mathrm{\theta}-\mathrm{\vartheta}\right).$$
(5)
$$U\left(v,0\right)=2{\int}_{0}^{1}P\left(\mathrm{\rho}\right){J}_{0}\left(v\mathrm{\rho}\right)\mathrm{\rho}\mathrm{d}\mathrm{\rho},$$
(6)
$$U\left(0,u\right)={\int}_{0}^{1}P\left(\mathrm{\rho}\right)exp\left(\mathit{ju}{\mathrm{\rho}}^{2}/2\right)\mathrm{\rho}\mathrm{d}\mathrm{\rho},$$