Caustics and wavefronts produced by multiple refraction-reflections through plane-parallel plates.

We study the formation of caustics and wavefronts produced by multiple refraction-reflections through a plane-parallel transparent plate, assuming a point source placed at an arbitrary position along the optical axis. The caustic surfaces are obtained by using the envelope's method. Subsequently, the wavefronts are directly related to the involutes, which are associated with the envelopes for all the rays. Hence by using the Malus-Dupin theorem, we obtain their respective wavefronts produced by multiple refraction-reflections through a plane-parallel transparent plate. On the other hand, we implement Huygens' principle to obtain the wavefronts leaving the plate after undergoing multiple reflections inside the plate, which we have called zero-distance phase wavefronts. Finally, we establish the correspondence between the wavefronts obtained by Huygens' principle and the involutes associated with caustic surfaces; they are brought in coincidence assuming parallel curves from each other.

Ronchi-Hartmann type null screens for testing a plano-freeform surface with a detection plane inside a caustic surface.

We have implemented an exact ray trace through a plano-freeform surface for an incident plane wavefront. We obtain two caustic surfaces and provide the critical points related to the ray tracing process. Additionally, we study the propagation of the refracted wavefronts through the plane-curved surface. Finally, by using the Ronchi-Hartmann type null screen and placing the detection plane within the caustic region, we have evaluated the shape of a plano-freeform optical surface under test, obtaining an RMS difference in sagitta value of 6.3 µm.

Sagittal and tangential foci produced by tilted plane wavefronts refracted through simple lenses.

We study the formation of caustic and wavefront surfaces produced by a tilted plane wavefront propagating through spherical positive lenses. The shape of the caustic surface is a function of the indices of refraction, the geometrical parameters of the lens involved in the process of refraction, and the obliquity angle with respect to the optical axis, as we expect. We provide exact and approximate analytic equations for tangential and sagittal focal surfaces and also for Petzval field curvature considering arbitrary lenses.