Study of the factors that affect the correlation behavior during the evaluation of interferograms

Abstract

In recent years, the correlation coefficient has been used as a tool for comparison between experimental and synthetic interferograms in algorithms of evaluation, in the areas of optical fabrication and testing. This coefficient has been used with the aim of eliminating the observer criterion during the fabrication process, and in this sense, to make a quantitative test to compare experimental and synthetic interferograms using the correlation as a parameter of evaluation. However, this coefficient is dramatically affected when laboratory conditions are not adequate. Therefore, in this work, we present a detailed analysis of the correlation behavior when interferograms with different values of visibility, Gaussian noise, and background illumination are evaluated/correlated. To analyze the correlation behavior, we simulated different interferograms, where these parameters were varied and examined how they affect the interference patterns. We found that a bad illumination dramatically affects the value of correlation, causing it to decrease to 0.1046, with σ ¼ 0.1.

Reconstruyendo La Diferencia De Camino Óptico De Un Interferograma Real Degradado Por Ruido Mediante La Solución De Diferentes Problemas De Optimización

“…Teniendo en consideración que recientemente en un estudio numérico el coeficiente de correlación ha sido propuesto para comparar la similitud entre dos interferogramas acorde a la descripción proporcionada en la Ec. (3) [14], en este trabajo se presenta un experimento numérico comparativo que demuestra la eficacia de la optimización estocástica para reconstruir la función DCO de un interferograma real degradado por ruido (I d ), ya sea maximizando el coeficiente de correlación o minimizando la distancia euclidiana, evitando, en cualquiera de los dos procesos de optimización propuestos, la convergencia prematura a unóptimo local. Por lo tanto, para resolver el problema de maximización nosotros proponemos el uso de un algoritmo genético con la formulación de Kingslake descrita en la Ec.…”