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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 new method of fast phase recovery of annular pupil based on asterisk image is proposed. The analytical formula of annular pupil point expansion function is deduced and expressed as a linear combination of polynomials. The coefficient of the polynomial is the ring Zernike polynomial expansion coefficient of the pupil phase distribution. This formula is used to calculate the objective function and its gradient in the phase recovery of the annular pupil, which avoids the Fourier transform and finite difference computation required in the commonly used phase recovery method and greatly reduces the computational complexity during phase recovery. The effectiveness of the proposed method is verified by numerical simulation and phase restoration experiments. The experimental results show that this method can effectively improve the phase recovery speed of annular pupil.