Open AccessGeneralized shift-rotation absolute measurement method for high-numerical-aperture spherical surfaces with global optimized wavefront reconstruction algorithm
Author(s) -
Zhongming Yang,
Jinyu Du,
Chao Tian,
Jiantai Dou,
Qun Yuan,
Zhishan Gao
Publication year - 2017
Publication title -
optics express
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.394
H-Index - 271
ISSN - 1094-4087
DOI - 10.1364/oe.25.026133
Subject(s) - rotation (mathematics) , zernike polynomials , translation (biology) , optics , wavefront , physics , position (finance) , approximation error , root mean square , algorithm , mathematics , geometry , biochemistry , chemistry , finance , quantum mechanics , messenger rna , economics , gene
In this paper, a generalized shift-rotation absolute measurement method is proposed to measure the absolute surface shape of high-numerical-aperture spherical surfaces. Based on the wavefront difference method, the high order misalignment aberrations can be removed from the measurements. Our generalized shift-rotation absolute measurement process only needs one rotational measurement position and one translational measurement position. A wavefront reconstruction method based on the self-adaptive differential evolution algorithm is proposed to calculate the Zernike polynomials coefficient a i of the absolute surface shape W test (x,y), the rotation angle Δθ, the translation δ x along the x axis, and the translation δ y along the y axis. The translation error and rotation error in other absolute measurement methods are avoided using our generalized shift-rotation absolute measurement method. Experimental absolute results of the test surface and reference surface are given and the difference of reference surface shapes between two testings in experiments is 0.12 nm root mean square.