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.

在这项工作中，我们展示了一个 Bi-Ronchi 测试 (BRT) 建议，它使用点云来感测球面镜的整个表面和波前，作为一种快速计算测试，其效率与 Ronchi 测试相当。我们还展示了基于圆形泽尼克多项式的微分形式的辐照度传输方程的应用，以获得相位传输方程，并具有研究波前传播的能力。为此，我们通过BRT实验分析了W的传播，以验证使用辐照度传输方程执行的实验传播，让位给相位传输方程。为此，我们使用平方规则来观察双 Ronchigrams 及其相应的横向像差以及它们的W. 我们通过比较 BRT 与 Ronchi 测试对给定波前W 的多次测量以及相同位置的 Ronchi 规则来验证我们的结果。为了表征W的实验传播并测试W在镜面曲率半径前后的反射关系，将三个不同的 brRR 放置在镜面曲率半径前后的几个位置。最后，我们使用相位传输方程来分析有效W的传播 在微分圆泽尼克多项式方面，以获得黎曼可积函数，以数值方式找到验证实验传播、波前对称性、对称矩阵的存在和 BRT 的解决方案。