Among the best known non-interferometric optical tests are the wire test, the Foucault test and Ronchi test with a low frequency grating. Since the wire test is the seed to understand the other ones, the aim of the present work is to do a thorough study of this test for a lens with symmetry of revolution and to do this study for any configuration of the object and detection planes where both planes could intersect: two, one or no branches of the caustic region (including the marginal and paraxial foci). To this end, we calculated the vectorial representation for the caustic region, and we found the analytical expression for the pattern; we report that the analytical pattern explicitly depends on the magnitude of a branch of the caustic. With the analytical pattern we computed a set of simulations of a dynamical adaptation of the optical wire test. From those simulations, we have done a thorough analysis of the topological structure of the pattern; so we explain how the multiple image formation process and the image collapse process take place for each configuration, in particular, when both the wire and the detection planes are placed inside the caustic region, which has not been studied before. For the first time, we remark that not only the intersections of the object and detection planes with the caustic are important in the change of pattern topology; but also the projection of the intersection between the caustic and the object plane mapped onto the detection plane; and the virtual projection of the intersection between the caustic and the detection plane mapped onto the object plane. We present that for the new configurations of the optical system, the wire image is curves of the Tschirnhausen’s cubic, the piriform and the deformed eight-curve types.