Simple method for improving the sampling in profile measurements by use of the Ronchi test

Nonparaxial geometrical Ronchi test for spherical mirrors: an inverse ray-tracing approach

A geometrical model based on an inverse ray-tracing approach to describe the Ronchi test for a concave spherical mirror is presented. In contrast to the conventional ray-tracing method, which refers to information unavailable in ronchigrams, the proposed model provides an explicit relation between the available information in the ronchigram and the parameters of the setup (radius of the sphere, position of the source, position and orientation of the observation, and grating planes). This allows for extracting the parameters of interest by a simple fitting procedure, as demonstrated by an application. The derived model exhibits new unexplored potential applications of the Ronchi test, establishing it as a very useful, simple, and universal tool for optical evaluation.

Local and global surface errors evaluation using Ronchi test, without both approximation and integration

We have reproduced quantitatively the technique commonly used in optical shop to evaluate surface error from comparison between experimental and simulated Ronchigrams. We used this procedure to evaluate, from Ronchigrams of any number of fringes, the curvature radius and/or conic constant of conic surfaces. The error function is calculated without using integration (numerical or polynomial) so the corresponding problems were avoided. Furthermore, when the error function is described with cubic splines, then the local errors are very well reproduced, which is not the case with the polynomial description. We have described the error functions with conical surfaces or with cubic splines, and for the best reproduction of experimental Ronchigram we used genetic algorithms.

Comparison of cubic B-spline and Zernike-fitting techniques in complex wavefront reconstruction

We analyze an alternative to classical Zernike fitting based on the cubic B-spline model, and compare the strengths and weaknesses of each representation over a set of different wavefronts that cover a wide range of shape complexity. The results obtained show that a Zernike low-degree polynomial expansion or a cubic B-spline with a low number of breakpoints are the best choices for fitting simple wavefronts, whereas the cubic B-spline approach performs much better when more complex wavefronts are involved. The effect of noise level in the fit quality for the different wavefronts is also studied.