Exact computation of image disruption under reflection on a smooth surface and Ronchigrams

TL;DR

This paper presents an exact geometrical optics method to analyze how reflections on smooth surfaces alter image topology, explaining Ronchigram fringe disruptions observed in mirror testing, with specific focus on spherical mirrors and simple objects.

Contribution

It introduces an exact computational approach to study image disruptions caused by reflections on smooth surfaces, linking caustic geometry to Ronchigram fringe patterns.

Findings

Fringe disruptions are due to shadow disruptions at caustics.

Exact computation matches observed Ronchigram patterns.

Spherical mirrors with simple objects illustrate the method.

Abstract

We use geometrical optics and the caustic-touching theorem to study, in an exact way, the change in the topology of the image of an object obtained by reflections on an arbitrary smooth surface. Since the procedure that we use to compute the image is exactly the same as that used to simulate the ideal patterns, referred to as Ronchigrams, in the Ronchi test used to test mirrors, we remark that the closed loop fringes commonly observed in the Ronchigrams when the grating, referred to as a Ronchi ruling, is located at the caustic place are due to a disruption of fringes, or, more correctly, as disruption of shadows corresponding to the ruling bands. To illustrate our results, we assume that the reflecting surface is a spherical mirror and we consider two kinds of objects: circles and line segments.