## Abstract

A general focal length function is proposed to design microlenses with long extended focal depth and high lateral resolution. The focal performance of the designed microlenses, including the actual focal depth, the focal spot size, and the diffraction efficiency, is calculated by rigorous electromagnetic theory and the boundary-element method for several *f*-numbers. In contrast to conventional microlenses, the numerical results indicate that the designed microlenses can exhibit long extended focal depth and good focal performance. It is expected that the long focal length function will be widely used to design microlenses with long focal depth characteristics.

© 2007 Optical Society of America

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### Equations (5)

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(1)
$$\varphi \left(r\right)=\frac{2\pi}{\lambda}\frac{{n}_{2}}{{n}_{1}-{n}_{2}}[\sqrt{{f}^{2}\left(r\right)+{r}^{2}}-f\left(r\right)],$$
(2)
$$f\left(r\right)={f}_{0}+a{r}^{b},$$
(3)
$$a=\delta f\u2215{R}^{b}.$$
(4)
$$f\left(r\right)={f}_{0}+\delta f{(r\u2215R)}^{b}.$$
(5)
$$\mathbf{E}\left({\mathbf{r}}_{2}\right)=-{\int}_{\Gamma}[{\mathbf{E}}_{\Gamma}\left({\mathbf{r}}_{\Gamma}^{\prime}\right)\frac{\partial {G}_{2}({\mathbf{r}}_{2},{\mathbf{r}}_{\Gamma}^{\prime})}{\partial \widehat{n}}-{G}_{2}({\mathbf{r}}_{2},{\mathbf{r}}_{\Gamma}^{\prime})\frac{\partial {\mathbf{E}}_{\Gamma}\left({\mathbf{r}}_{\Gamma}^{\prime}\right)}{\partial \widehat{n}}]\mathrm{d}{l}^{\prime},$$