This paper presents a model to design bi-aspherical catadioptric lenses with limited image diffraction. A first refractive Cartesian oval surface that does not introduce any spherical aberration is used. When total internal reflection occurs, this surface can also be simultaneously used as a mirror. The reflective characteristics of Cartesian ovals are also well described in this paper. The theoretical work described here can considerably reduce computing time in optical system design. This model is applied to examples of antennae design for visible light communications (VLC).
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Valencia-Estrada et al. (2017) studied this question.
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