根据波前编码系统的设计理论，在兼顾图像恢复能力的基础上，提出利用不同离焦距离的点扩散函数与焦面处的点扩散函数之间的希尔伯特空间角作为成像特性一致性的评价函数，结合遗传算法，对扩大景深的波前编码成像系统的相位板参数进行优化。分别在空间域和频率域上分析应用波前编码技术前后光学系统的成像特性，并利用最小二乘数字滤波器对中间模糊图像进行复原。仿真实验结果表明: 在三次相位板上应用此方法获得的最佳相位板参数使波前编码系统焦深扩展了10倍。

According to the design theory of wavefront coding, taking the imaging restorability into consideration, we used the angle in Hilbert space between in-focus PSF and several defocus PSFs as an evaluation for making the shape and intensity of point spread function (PSF) insensitive with defocus over a wide range of defocus parameter values. The angle in Hilbert space is capable of evaluating similarity of the PSFs of different defocus parameter values and was used to optimize the design of phase mask in real wavefront coding systems. A doublet-wavefront coding system was designed based on a finite focused doublet system. The simulation results show that the phase mask can extend the depth of focus by an order of magnitude more than that of Hopkins defocus criterion. Better and more stable imaging quality over a large depth of focus is acquired with the optimized pupil phase mask.