## Abstract

The degenerated performance of extend depth of field (EDoF) in wavefront coding system which using cubic phase mask is simulated. A periodical rotationally symmetric surface error structure is presented and combined with comparison the similarity of point spread function (PSF). The peak to valley (PV) error of the cubic surface is needed smaller than 15% compare with the sag of the cubic surface for low period error existed.

©2009 Optical Society of America

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### Equations (6)

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(1)
$$\mathrm{error}\left(x,y\right)=\sum _{n=0}^{\infty}\left[\frac{p{v}_{\mathrm{nx}}}{2}\xb7\mathrm{sin}\left(\mathrm{n\pi x}+{\phi}_{\mathrm{nx}}\right)+\frac{p{v}_{\mathrm{my}}}{2}\xb7\mathrm{sin}\left(\mathrm{m\pi y}+{\phi}_{{m}_{y}}\right)\right],$$
(2)
$$z\left(x,y\right)=\alpha \left({x}^{3}+{y}^{3}\right),$$
(3)
$$h\left(x,y\right)=\mathrm{circ}\left(x,y\right)\xb7\mathrm{Exp}\left\{-i\left[\alpha \left({x}^{3}+{y}^{3}\right)+\frac{2\pi}{\lambda}{Z}_{2}\sqrt{{x}^{2}+{y}^{2}}+\frac{2\pi}{\lambda}\mathrm{Error}\left(x,y\right)\right]\right\},$$
(4)
$$\mathrm{PSF}\left(x,y\right)=\Im \left\{h\right\}\xb7\Im {\left\{h\right\}}^{*},$$
(5)
$$r=\frac{\sum _{m}\sum _{n}\left({A}_{\mathrm{mn}}-\stackrel{\u0304}{A}\right)\left({B}_{\mathrm{mn}}-\stackrel{\u0304}{B}\right)}{\sqrt{\left[\sum _{m}\sum _{n}{\left({A}_{\mathrm{mn}}-A\right)}^{2}\right]\left[\sum _{m}\sum _{n}{\left({B}_{\mathrm{mn}}-B\right)}^{2}\right]}},$$
(6)
$$\mathrm{ratio}=\frac{{z\prime}_{2}-0.25}{0.25}.$$