Geometric treatment of the radiation captured by the Large Millimeter Telescope (LMT/GTM) and ronchigrams at the caustic region for a static source

Abstract

The aim of the present work is to determine the reflected light rays, wavefronts, caustic and the ronchigram associated with the reflection phenomenon of a plane wave on a parabolic mirror, in particular on the parabolic antenna of the Large Millimeter Telescope (LMT/GTM). The results presented here are general in the sense that the incident plane wavefront has an arbitrary direction Î(α, β), determined by the angles α and β. We present numerical results for two different cases: (α = π/200, β = 0) and (α = π/10, β = 0). From these results we find that in general the caustic is a surface with a stable singularity of a hyperbolic umbilic type. For these cases we compute the distribution of the reflected light rays at some representative planes, determined by the form and dimensions of the caustic, then assuming that the ronchigrating is placed at those representative planes we compute the associated ronchigram. These results are important because they could describe the behavior of the light emitted by a static pointlike source located far away in the Universe.