In this work we use the geometrical point of view of the Ronchi test and the caustic-touching theorem to describe the structure of the ronchigrams for a parabolical mirror when the point light source is on and off the optical axis and the grating is placed at the caustic associated with the reflected light rays. We find that for a given position of the point light source the structure of the ronchigram is determined by the form of the caustic and the relative position between the grating and the caustic. We remark that the closed loop fringes commonly observed in the ronchigrams appear when the grating and the caustic are tangent to each other. Furthermore, we find that the caustic locally has singularities of the purse or hyperbolic umbilic type, and the ronchigram obtained when the grating is located at certain specific positions at the caustic locally is of the serpentine type. The main motivation of this work is that nowadays a quantitative analysis of the Ronchi test is applied only when the grating is outside the caustic, and we claim that by working at the caustic, the sensitivity of the Ronchi test will be improved. Therefore, a clear understanding of the properties of the ronchigrams when the grating is placed at the caustic will be needed to extend the Ronchi test to that region.

Describing the structure of ronchigrams when the grating is placed at the caustic region: the parabolical mirror

We present a ray-tracing-based method for simulation of interference fringe patterns (IFPs) for measuring gear tooth flanks with a two-path interferometer. This simulation method involves two steps. In the first step, the profile of an IFP is achieved by means of ray tracing within the object path of the interferometer. In the second step, the profile of an IFP is filled with interference fringes, according to a set of functions from an optical path length to a fringe gray level. To examine the correctness of this simulation method, simulations are performed for two spur involute gears, and the simulated IFPs are verified by experiments using the actual two-path interferometer built on an optical platform.

Simulation method for interference fringe patterns in measuring gear tooth flanks by laser interferometry

The TUS space fluorescence detector for study of UHECR and other phenomena of variable fluorescence light in the atmosphere

The aim of this work is threefold: first we obtain analytical expressions for the wavefront train and the caustic associated with the refraction of a plane wavefront by an axicon lens, second we describe the structure of the ronchigram when the ronchiruling is placed at the flat surface of the axicon and the screen is placed at different relative positions to the caustic region, and third we describe in detail the structure of the null ronchigrating for this system; that is, we obtain the grating such that when it is placed at the flat surface of the axicon its associated pattern, at a given plane perpendicular to the optical axis, is a set of parallel fringes. We find that the caustic has only one branch, which is a segment of a line along the optical axis; the ronchigram exhibits self-intersecting fringes when the screen is placed at the caustic region, and the null ronchigrating exhibits closed loop rulings if we want to obtain its associated pattern at the caustic region.

Wavefronts, caustic, ronchigram, and null ronchigrating of a plane wave refracted by an axicon lens

We present a simple algorithm that makes possible the simulation of ronchigrams for any optical system in which it is possible to make an exact ray tracing. We report the simulations for the following grids: the Ronchi classical, square, circular, radial, circular-radial, biparabolic, elliptic-hyperbolic, bipolar, and bielliptic ones.

Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates.

Low-frequency Fresnel mirrors for fluorescence detectors

An adaptive lens can be made from plastic and elastic material, its focal distance can be changed by appling radial forces at the lens border ring. To make these kind of lenses it is necessary to figure molds. However, these molds can not be figured by using rigid tools for rapid surfaces. Then we are developing a new technique based in a linear array of independent sub-tools. A linear tool consists of subtools, the pressures of each one can be regulated according to the measured surface errors. The pressures are given by weights put over each sub-tool. By using genetic algorithms the pressure values of each subtool have been calculated in order to obtain the optimal wear. They are shown numerical and experimental results for several axisymmetrical surfaces.

José de Jesús Díaz-Anzures

Papers

Algorithm for the simulation of ronchigrams of arbitrary optical systems and Ronchi grids in generalized coordinates.

Low-frequency Fresnel mirrors for fluorescence detectors

Calculating subtool pressures by using genetic algorithms