为了在弱光条件下由光场的强度分布求得其相位分布，利用分数阶傅里叶变换与光学系统之间的关系，基于Gerchberg-Saxton算法研究了Zernike相差的恢复问题，并进行了数值模拟。通过研究分数阶傅里叶变换与菲涅耳衍射之间的关系，改进了Lohmann光学系统；基于小波理论初步分析了菲涅耳近场与远场输出面对高频和低频成分恢复效果的影响。数值模拟结果表明该算法有良好的收敛性和恢复精度，均方根误差(RMSE)值均保持在0.15λ(λ为光波长)以下，且位于菲涅耳衍射近场的输出面对相位的高频部分恢复效果较好，位于远场的输出面对低频部分恢复效果较好。

In order to obtain the phase distribution from the intensity distribution of the light field in low-light conditions, we investigate the Zernike phase retrieval based on the Gerchberg-Saxton algorithm using the fractional Fourier transform and the corresponding optical system. By studying the relationship between fractional Fourier transform and Fresnel diffraction, the Lohmann optical system is improved. How the Fresnel near-field and far-field outputs influence the high and low frequency parts of phase recovery is analyzed based on wavelet theory. The numerical results show that the algorithm has good convergence and recovery accuracy with root-mean-square error (RMSE) less than 0.15λ(λ is the wavelength). When the outputting planes are placed in the Fresnel near-field, the high-frequency part of the recovery phase is better, while when they are placed in the far-field, the low-frequency part is better.