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

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.