title: Phase retrieval on annular and annular sector pupils by using the eigenfunction method to solve the transport of intensity equation.
abstract: Phase retrieval on an annular pupil and an annular sector pupil by using the eigenfunction method to solve the transport of intensity equation is proposed. The analytic expressions of Laplacian eigenfunctions with the Neumann boundary condition on an annular pupil and an annular sector pupil are given. The phase can be expanded as a set of eigenfunctions on the corresponding pupil, and the coefficients of the eigenfunctions can be obtained by the integral of the eigenfunction and the intensity derivative along the optical axis. Phase retrieval by the eigenfunction method on an annular pupil and an annular sector pupil is simulated, and accurate retrieved results are obtained.
authors.affiliation: College of Optoelectronic Science and Engineering, National University of Defense Technology, Changsha, Hunan, China. syhuang2008@yahoo.com.cn
authors.forename: Shengyang
authors.initials: S
authors.lastname: Huang
authors.forename: Fengjie
authors.initials: F
authors.lastname: Xi
authors.forename: Changhai
authors.initials: C
authors.lastname: Liu
authors.forename: Zongfu
authors.initials: Z
authors.lastname: Jiang