Finite element solution to the Poissonian irradiance transport equation applying structured patterns in SLM for wavefront sensing

We present a new technique, to our knowledge, to obtain the wavefront. We propose to modify the irradiance transport equation (ITE) by using fringe patterns of spatial light modulators (SLMs) and super-Gaussian Ronchi rulings (SG-RRs) to create the Poissonian irradiance transport equation (PITE) to solve the wavefront using the finite element method (FEM). We use a liquid crystal spatial light modulator (LCSLM) to build periodic patterns, which permits simplification of the irradiance transport equation (ITE) into a look-a-like Poisson’s equation under experimental conditions. First, we model different flat/parallel patterns based on super-Gaussian (SG) profiles with different frequencies optimizing the results when substituting the conventional Ronchi rulings in arrays for wavefront sensing. We then analyze the noise reduction in the experimental irradiance captures with the use of SG periodic profiles in LCSLM to induce periodicity in different irradiance distributions. We also analyze the difference between irradiance captures (according to the ITE) to obtain the PITE, which we subsequently solve as a Poisson’s equation applying the finite element method (FEM), with triangular symmetry between the mesh nodes. We do this for two meshes, having a different number of nodes, and obtaining for each the wavefront surface [ W ( ρ , θ )]. We characterize the aberrations in W ( ρ , θ ) by means of a multilinear fit of the Zernike polynomials ( Z i , j ) with degree M =50 to optimize the comparison between the main aberration coefficients in evaluation curves and to minimize the dispersion with comparable results obtained from software tools devoted to the analysis of interferograms. These software tools are APEX, FringeXP, and OpenFringe. Finally, we discuss our results.