Showing papers by "Alberto Cordero-Dávila published in 1998"
TL;DR: The necessary equations are derived for the design of aplanatic microscope objectives consisting of two mirrors, one concave and the other convex, and the first-order parameters are calculated along with the conic constants of the mirrors, determined by means of an exact analysis.
Abstract: The necessary equations are derived for the design of aplanatic microscope objectives consisting of two mirrors, one concave and the other convex. The first-order parameters are calculated along with the conic constants of the mirrors, determined by means of an exact analysis to arrive at an aplanatic system.
7 citations
TL;DR: This work presents an algorithm to estimate the coefficients of the nonlinear system by applying the Newton-Raphson method and starting the iteration from the standard classic solution, obtaining not only the right coefficients but also the adequate election of the terms to be included in the model.
Abstract: Assuming that the measured coordinates of the fringes of an interferogram have random errors and that they are considered Gaussian, the system of normal equations that is obtained on application of the least-squares method is converted into a nonlinear set of equations. We present an algorithm to estimate the coefficients of the nonlinear system by applying the Newton–Raphson method and starting the iteration from the standard classic solution. This algorithm is applied to a pattern of straight and equally spaced fringes, obtaining not only the right coefficients but also the adequate election of the terms to be included in the model, to show the contrast with the results of the classic method.
2 citations