基于星点图像的小像差复原

提出了一种基于星点图像的小像差光学系统像差复原方法.应用标量衍射理论和Bessel级数,推导了以波像差的Zernike系数为参量的小像差光学系统点扩散函数的解析计算公式,利用该公式给出了基于星点图像的小像差复原问题的目标函数及梯度函数的表达式,并采用最优化方法进行求解.分别在理想情况和噪声情况下数值模拟了光学系统的像差复原,验证了本文提出的像差复原方法的有效性,并分析了星点目标尺寸对复原效果的影响.该方法以波像差的Zernike系数为优化变量,并利用推导得到的解析表达式计算目标函数及其梯度值,避免了常用像差复原算法中所需的傅里叶变换和有限差分等数值运算,提高了复原算法的运算速度.

Small-aberration retrieval based on spot images

A small-aberration retrieval method based on spot images was introduced and an analytic formula to computer the point spread function for a small aberration optical system was derived according to the scalar diffraction theory and Bessel series.With this formula,the objective function and its gradient were given for the small-aberration retrieval method.Then,the optimized method was used to solve this problem.The effectiveness of this method was demonstrated by using the numerical simulation under ideal and noisy conditions,respectively,and the influence of the size of spot object on the retrieval results was also analyzed.This method uses aberration’s Zernike coefficients as optimization variants and computes the objective function and its gradient with analytic expressions to avoid Fourier transform or numerical integral needed in common aberration retrieval methods.Therefore,it improves the speed of aberration retrieval greatly.