Modal wavefront reconstruction by Schwarz-Christoffel mapping and Zernike circle polynomials for noncircular pupils

Analyzing noncircular wavefront aberration require reconstructing orthonormal Zernike polynomials over noncircular pupils using Gram-Schmidt orthogonalization and nonrecursive matrix approach. However, these methods are computationally complex and time-consuming. We proposed a modal wavefront reconstruction method for noncircular pupils by Schwarz-Christoffel mapping and Zernike circle polynomials. Schwarz-Christoffel mapping is used to conformally transform the noncircular wavefront into a disk-shaped domain, enabling the mapped circular wavefronts to be fitted by Zernike circle polynomials. Experimental results demonstrate excellent agreement with measurements obtained from a commercial Fizeau interferometer. Furthermore, compared to the traditional orthonormal polynomials fitting method, the reconstruction accuracy of our method is higher than 90 %, and the time consuming is reduced by 2–5 times. This study presents a reliable modal wavefront reconstruction technique for noncircular pupils.