Showing papers by "Alberto Cordero-Dávila published in 2010"
13 Jun 2010
TL;DR: In the manufacturing process of an optical surface with rotational symmetry the ideal ronchigram is simulated and compared with the experimental ron chigram and the technician estimated the error on the surface by means of cubic splines.
Abstract: In Ronchi test Malacara formula is used to evaluate surface errors, which are represented by cubic splines. The spline coefficients are estimated by means of genetic algorithms.
9 citations
22 Apr 2010
TL;DR: In this paper, a method for phase retrieval by using Fourier analysis and techniques to solve differential equations is presented, where the phase function consists of a family of potential functions which are orthogonal to a vectorial field which is the phase gradient.
Abstract: In this paper, a method for phase retrieval by using Fourier analysis and techniques to solve differential equations is presented. From the technique proposed by Takeda et al., the function c(x,y) = (1/2)⋅b(x,y)⋅exp[io/(x,y)] is first calculated from a certain interference pattern given by a(x,y)+b(x,y)⋅coso/(x,y). By deriving c(x,y) and c*(x,y) with respect to x and y, it is then possible to find the corresponding phase gradient ∇o/(x,y), from which a Pfaff equation can be obtained. In this paper, we show that the solution of the Pfaff equation is the desired phase function plus a constant phase offset accordingly to the theory of differential equations. From this point of view, the phase function consists of a family of potential functions, which are orthogonal to a vectorial field which is the phase gradient. With this technique, the phase function o/(x,y) can be calculated from an interference pattern without the need of any phase unwrapping stage. A theoretical analysis and both numerical and experim...
4 citations