从空域和频域两个方面利用新的数学工具对扩大景深的波前编码成像系统的一些重要特性进行了阐释和分析。空域中,主要利用维格纳分布函数的正则投影来分析系统的点扩展函数对离焦像差的变化不敏感特性；频域中,则利用考纽螺线的图解方法来分析系统的光学传递函数对离焦像差的变化不敏感特性。简单讨论了波前编码成像技术所涉及的数字图像处理方法,并且用数值仿真实验验证了波前编码成像系统的这些优越特性。

New mathematical tools are used to explore and analyze the well-known properties of imaging system for extending the depth of field from spatial and frequency domain, respectively. In the spatial domain, canonical projection of the Wigner distribution function of the associated pupil function to show the insensitivity of the system's point spread function to the defocus-related aberrations is mainly used, and in the frequency domain, it is shown that the optical transfer function of such a system is also insensitive to misfocus through a geometrical description of the so-called Cornu spiral. The involved digital image processing is also briefly discussed and a digital simulated experiment is done to affirm these excellent properties of the wave-front coding imaging system.