An automatic fringe detection algorithm applied to moire deflectometry is presented. This algorithm is based on a set of points linked together and with a behavior similar to a rubber band, in which these points are attracted to fit the moire fringes. The collective behavior of these points gives rise to a final state which is their regularly spaced alignment along the fringe pattern. The algorithm is dynamic in the sense that it tracks the fringe even when it suffers continuous deformations. Once the rubber band is adapted, the rubber band's points coordinates are obtained and their distance to the starting straight line is found, as required by moire deflectometry.
We propose a technique for ray tracing, based in the propagation of a Gaussian shape invariant under the Fresnel diffraction integral. The technique uses two driving independent terms to direct the ray and is based on the fact that at any arbitrary distance, the center of the propagated Gaussian beam corresponds to the geometrical projection of the center of the incident beam. We present computer simulations as examples of the use of the technique consisting in the calculation of rays through lenses and optical media where the index of refraction varies as a function of position.
We present an efficient method to perform x-ray optics simulation with high or partially coherent x-ray sources using Gaussian superposition technique. In a previous paper, we have demonstrated that full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, x-rays, acoustic waves, etc. We describe the technique and include some computer simulations as illustrative examples for x-ray optical component. We show also that this method can be used to study partial or total coherence illumination problem.
Full characterization of optical systems, diffractive and geometric, is possible by using the Fresnel Gaussian Shape Invariant (FGSI) previously reported in the literature. The complex amplitude distribution in the object plane is represented by a linear superposition of complex Gaussians wavelets and then propagated through the optical system by means of the referred Gaussian invariant. This allows ray tracing through the optical system and at the same time allows calculating with high precision the complex wave-amplitude distribution at any plane of observation. This method is similar to conventional ray tracing additionally preserving the undulatory behavior of the field distribution. That is, we are propagating a linear combination of Gaussian shaped wavelets; keeping always track of both, the ray trajectory, and the wave phase of the whole complex optical field. This technique can be applied in a wide spectral range where the Fresnel diffraction integral applies including visible, X-rays, acoustic waves, etc. We describe the technique and we include one-dimensional illustrative examples.
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