Irradiance transport equation applied to propagation of wavefront obtained by the Bi-Ronchi test using point cloud

Abstract

In this work, we show a Bi-Ronchi test (BRT) proposal using point cloud for sensing the whole surface and wavefront of spherical mirrors as a fast computational test with efficiency comparable with the Ronchi test. We also show an application of the Irradiance Transport equation based on the differential form of the circular Zernike polynomials, to obtain the Phase Transport equation, with capabilities to study the wavefront propagation. To this aim, we experimentally analyze the propagation of W with the BRT, to validate the experimental propagation performed with the Irradiance Transport Equation, giving place to a Phase Transport equation. For this purpose, we use square rulings to observe bi-Ronchigrams and their corresponding Transversal Aberrations as well as their W. We validated our results by comparing the BRT with the Ronchi Test for several measurements of a given wavefront W with Ronchi rulings in the same position. Three different bRR were placed in several locations before and beyond the mirror curvature Radius in order to characterize the experimental propagation of W and test the reflection relation of W before and beyond the mirror Curvature Radius. Finally, we use the Phase Transport equation to analyze the propagation of an efficient W in terms of the differential circular Zernike Polynomials in order to obtain a Riemann-integrable function to numerically find a solution for validating the experimental propagation, the symmetry of the wavefronts, the existence of a symmetry matrix, and the BRT.