Image formation through aspheric concave Fresnel-type mirrors

We study the formation of caustic surfaces produced by concave Fresnel-type mirrors, whose parent curve is defined by an aspherical curve rotationally symmetric about the optical axis. We assume that a point light source is placed at arbitrary distances along the optical axis considering three different cases, providing either real or virtual caustic surfaces. Alternatively, varying the parameters of design, it is possible to reduce the size and modify the shape of the caustic surfaces, which have wide potential applications in both fields of imaging and non-imaging optical systems based on Fresnel-type mirrors. Finally, the cuspid of the caustics formed around the central groove near the optical axis coincides with the position of paraxial images in such a way that we provide the mirror-image equation for Fresnel-type mirrors.