Computing the circle of least confusion for designing aspheric Fresnel-type reflectors

We assume a bundle of rays propagating parallel to the optical axis incident on aspheric converging Fresnel-type reflectors (ACFR), to study the formation of caustic surfaces produced by reflection. Subsequently, we evaluate the circle of least confusion (CLC) produced by ACFR. Alternatively, varying the design parameters, it is possible to reduce the size and modify the shape of the caustic surfaces, which have wide potential applications for both imaging and non-imaging optical systems. We ideally provide a formula to evaluate the optical concentration ratio produced by ACFR. If we demand that the absorber is placed at CLC, we can optimize the design for ACFR by increasing its optical concentration ratio. Finally, an ACFR prototype is designed to minimize its CLC and consider the properties of caustic surfaces.