Demonstration of Curvature Polynomials for Determining the Zernike Coefficients from Wavefront Curvature Data

Abstract

We describe numerical simulations to demonstrate the use of curvature polynomials introduced by Mahajan and Acosta in their paper “Zernike coefficients from wavefront curvature data” for determining the Zernike coefficients from wavefront curvature data. The wavefront curvature data was determined by evaluating the irradiance distributions in two planes that were symmetric about the focal plane. The irradiance distributions were calculated using the Zemax OpticStudio software program.For the aberration function, the wavefront curvature data was generated from the irradiance distributions. This data consists of the Laplacian of the wavefront across the pupil and its outward normal slope at its circular boundary. The inner products of the curvature polynomials and Laplacian of the wavefront are used to calculate the m ≠ n (i.e., non-harmonic) Zernike aberration coefficients, and the inner product of the boundary slope and curvature polynomials are required to calculate the m = n (i.e., harmonic) Zernike aberration coefficients. We explain the process of obtaining the Laplacian and slope of the wavefront from the two irradiance distributions. Independent case studies of different simulations are performed and explained in detail. The results obtained and limitations of the software are also presented.