本征函数法求解光强传输方程的相位反演方法  

Phase Retrieval Using Eigenfunctions to Solve Transport-of-Intensity Equation

作　　者：黄盛炀[1] 习锋杰[1] 刘长海[1] 姜宗福[1] 

机构地区：[1]国防科学技术大学光电科学与工程学院,湖南长沙410073

出　　处：《光学学报》2011年第10期7-11,共5页Acta Optica Sinica

基　　金：国家自然科学基金(60908027)资助课题

摘　　要：提出了一种采用本征函数法求解光强传输方程的相位反演算法。相位可由拉普拉斯算子本征函数展开,各阶本征函数的系数可以由光强沿光轴的微分和本征函数两者的积分得到,由此实现相位恢复。给出了圆形区域和矩形区域拉普拉斯算子本征函数的解析形式,数值模拟了在这两种区域上采用该算法实现相位恢复的过程,结果表明该算法可以很好地实现相位恢复。An algorithm based on eigenfunctions was proposed for phase retrieval by solving transport-of-intensity equation.The phase could be expanded as a series of Laplacian′s eigenfunctions,and the coefficients of eigenfunction could be obtained by the integral of eigenfunction and intensity derivative along the optical axis,then the phase was reconstructed.The analytic expressions of Laplacian′s eigenfunctions on unit circle and rectangular domain were achieved.Phase retrieval by eigenfunctions on both domains was simulated,and an accurate reconstruction result could be obtained by the algorithm.

关 键 词：相位反演 光强传输方程 波前曲率传感器 拉普拉斯算子 本征函数 

分 类 号：O438[机械工程—光学工程]