提出了一种基于星点像的环形光瞳快速相位复原方法。推导了环形光瞳点扩展函数的解析计算公式，将其表示为多项式的线性组合，多项式的系数即为光瞳相位分布的环形Zernike多项式展开系数。将该公式用于计算环形光瞳相位复原中的目标函数及其梯度，避免了常用相位复原方法中所需的傅里叶变换和有限差分运算，大幅降低了相位复原过程中的运算量。利用数值模拟和相位复原实验对所提方法的有效性进行了验证，实验结果表明，该方法能够有效提高环形光瞳相位复原的速度。

A fast phase retrieval method for annular pupil using spot image is proposed. The analytic formula to compute point spread function for annular pupil is derived. With this formula, the point spread function is represented as linear composition of polynomials, the coefficients of which are just the annular Zernike expansion coefficients of the pupil phase. The objective function and its gradient in phase retrieval for annular pupil are computed with this formula. It can avoid the Fourier transform and finite differences, which are necessary in common phase retrieval method, and decrease the computational burden in phase retrieval. The effectiveness of the proposed fast phase retrieval for annular pupil is demonstrated using numerical simulation and phase retrieval experiment. Experimental results indicate that the proposed method can improve the speed of phase retrieval for annular pupil effectively.