## Abstract

A recent publication [Opt. Express **16**, 20540–20561 (2008)] presented a way for extending the depth of field (DOF) of imaging systems using a binary phase mask made of annular rings delivering a $\pi $-phase shift. Usually, such masks are designed with respect to some central wavelength; they will thus deliver a different phase shift for other wavelengths. This issue is reexamined in this paper, where it is shown that polychromatic masks that deliver the same phase shift over a wide range of wavelengths provide improved imaging over an extended DOF. The simulation results demonstrate the improved performance of imaging systems using such masks.

© 2013 Optical Society of America

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### Equations (9)

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(1)
$$\psi =\frac{\pi {R}^{2}}{\lambda}(\frac{1}{{z}_{\text{img}}}+\frac{1}{{z}_{\text{obj}}}-\frac{1}{f}),$$
(2)
$$\underset{\mathbf{r}}{\mathrm{max}}\underset{\psi \in \mathrm{DOF}}{\mathrm{min}}[\nu :\mathrm{MTF}(\nu ,\mathbf{r},\psi )={C}_{d}],$$
(3)
$${\phi}_{\text{mask}}=\frac{2\pi}{\lambda}h(n(\lambda )-1),$$
(4)
$$\underset{\mathbf{r}}{\mathrm{max}}\underset{\psi \in \mathrm{DOF},\lambda \in \{{\lambda}_{i}\}}{\mathrm{min}}[\nu :\mathrm{MTF}(\lambda ,\nu ,\mathbf{r},\psi )={C}_{d}],$$
(5)
$${\phi}_{\mathrm{MPM}}=\frac{2\pi}{\lambda}h(n(\lambda )-1).$$
(6)
$${\phi}_{\mathrm{PCM}}={\phi}_{1}+{\phi}_{2}=\frac{2\pi}{\lambda}{h}_{1}({n}_{1}(\lambda )-1)+\frac{2\pi}{\lambda}{h}_{2}({n}_{2}(\lambda )-1).$$
(7)
$$\underset{{h}_{1},{h}_{2}}{\mathrm{min}}\left[{\int}_{{\lambda}_{1}}^{{\lambda}_{2}}{({\phi}_{\mathrm{PCM}}(\lambda ,{n}_{1},{h}_{1},{n}_{2},{h}_{2})-{\phi}_{\text{desired}})}^{2}\mathrm{d}\lambda \right],$$
(8)
$${\phi}_{\mathrm{PCM}}=\frac{2\pi}{\lambda}{h}_{1}[({n}_{1}(\lambda )+\alpha (1-{n}_{2}(\lambda )))-1],$$
(9)
$${\phi}_{\mathrm{PCM}}=\frac{2\pi}{\lambda}{h}_{1}[{n}^{*}(\lambda )-1],$$