  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.
