Arquímedes Morales

Automatic fringe detection algorithm used for moire deflectometry

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 bands points coordinates are obtained and their distance to the starting straight line is found, as required by moire deflectometry.

Geometrical parameters in the Hartmann test of aspherical mirrors.

The Hartmann test has been used with great success to determine figuring errors in large aspherical concave surfaces for telescope mirrors. Here, a mathematical model is presented that allows us to compute the optimum geometrical parameters for this test. It is assumed that the light source is placed near the center of curvature.

Fresnel-Gaussian shape invariant for optical ray tracing

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.

A technique for calculating the amplitude distribution of propagated fields by Gaussian sampling

We present a technique to solve numerically the Fresnel diffraction integral by representing a given complex function as a finite superposition of complex Gaussians. Once an accurate representation of these functions is attained, it is possible to find analytically its diffraction pattern. There are two useful consequences of this representation: first, the analytical results may be used for further theoretical studies and second, it may be used as a versatile and accurate numerical diffraction technique. The use of the technique is illustrated by calculating the intensity distribution in a vicinity of the focal region of an aberrated converging spherical wave emerging from a circular aperture.

Refractive index and geometrical thickness measurement of a transparent pellicle in air by Gaussian beam defocusing

We demonstrate that it is possible to measure the local geometrical thickness and the refractive index of a transparent pellicle in air by combining the diffractive properties of a Gaussian beam with the analytical equations of the light that propagates through a thin layer. We show that our measurement technique is immune to inherent piston-like vibrations present in the pellicle. As our measurements are based on characterizing properly the Gaussian beam in a plane of detection, a homodyne technique for this purpose is devised and described. The feasibility of our proposal is confirmed by measuring local geometrical thicknesses and the refractive index of a commercially available stretch film.

Diffractive and geometric optical systems characterization with the Fresnel Gaussian shape invariant.

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.

Magnification effect and color blur behavior in holography

This paper describes the spatial behavior of the hologram image as a function of the geometric setup used in the recording and reconstruction steps. Given the equation of the holographic image and using paraxial theory and the synthetic division method, values of the longitudinal and lateral magnification are obtained. The location and magnification of the holographic image are found when the distance between the holographic plate and the object is changed. For white light reconstruction and 3-D scenes the effect of color blur can be expressed in terms of the parameters associated with the optical system that forms the image on the hologram and the recording geometry.

X-ray optics simulation using Gaussian superposition technique

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.

AXIAL TOLERANCE IN THE POSITION OF ABERRATION COMPENSATORS PLACED IN A CONVERGING BEAM

To perform a null test of aspherical surfaces we used a computer-generated hologram or a lens or a mirror compensator to compensate the aspherical aberration. When compensating in a convergent light beam the axial position of this hologram or compensator is critical. A holographic compensator to be used in the convergent beam of light was designed and constructed. We have established some relations to determine the tolerance in the axial positioning of these compensators.

Computer holographic lens

Calculation of the optical path difference between the input and the focal planes of a lens is used to compute the phase introduced by the lens. This represents a new way to create computer-generated optical elements. The phase change that takes place during the light propagation between the computer-generated hologram and the image plane is taken into consideration. Two examples that show different ways to plot the synthetic lens are presented.