Filter construction using Ronchi masks and Legendre polynomials to analyze the noise in aberrations by applying the irradiance transport equation.

We tested different optical elements placed in three different positions by applying the irradiance transport equation (ITE), obtaining the wavefront $[ W(x,y) ]$[W(x,y)] and aberration surface [$ \textit{AS}(r,\theta ) $AS(r,θ)]. The existing noise in the captures $ I $I as well as in the $ W $W and $ AS $AS were analyzed applying several filters: first a filter based on Legendre polynomials (LP), generating the most probable points increasing the data resolution; second, a filter based on a 50 deg 2D-LP was used as a multilineal fit (multiple linear regression); and third, an ideal bandpass filter in the Fourier space after inducing a periodicity using Ronchi simulated masks with periods in $ x,y,xy $x,y,xy was used to perform data scanning (similar to the four-step phase-shifting method). Signal-to-noise ratio values were obtained for each proposed filter along with the most probable image free from noise, determined from a linear combination of the original data and the applied filters.

Moiré-Ronchigram analysis applied in the characterization of aberration surfaces and optical surface parameters from 3D wavefronts.

In this work, we propose the construction of the Moiré-Ronchigram as a pattern obtained from simple Ronchigrams, superposed and with a slight degree of rotation, to obtain a 3D wavefront. The aberrations in the obtained wavefront are fitted to the aberration Zernike polynomial of degree 12 in order to obtain a polynomial expression of a high degree of efficiency, which is subsequently compared with the general equation of quadrics (considering the coefficients accordingly) to obtain essential parameters (as focus, eccentricity, or F number) that allow us to understand and manipulate the optical elements under test optimally. Finally, we compare our results analyzing optical surfaces to make a weak statistic of our proposed method.