A transformation approach for aberration-mode coefficients of Walsh functions and Zernike polynomials

Abstract

Walsh functions have been modified and utilized as binary-aberration-mode basis which are especially suitable for representing discrete wavefronts. However, when wavefront sensing techniques based on binary-aberration-mode detection trying to reconstruct common wavefronts with continuous forms, the Modified Walsh functions are incompetent. The limited space resolution of Modified Walsh functions will leave substantial residual wavefronts. In order to sidestep the space-resolution problem of binary-aberration modes, it’s necessary to transform the Modified-Walsh-function expansion coefficients of wavefront to Zernike-polynomial coefficients and use Zernike polynomials to represent the wavefront to be reconstructed. For this reason, a transformation method for wavefront expansion coefficients of the two aberration modes is proposed. The principle of the transformation is the linear of wavefront expansion and the method of least squares. The numerical simulation demonstrates that the coefficient transformation with the transformation matrix is reliable and accurate.