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    Area of Science:

    • Optical Engineering
    • Applied Physics

    Background:

    • Designing catadioptric lenses with minimal aberrations is crucial for advanced optical systems.
    • Traditional lens design often involves complex computations and iterative processes.

    Purpose of the Study:

    • To present a theoretical model for designing bi-aspherical catadioptric lenses with limited image diffraction.
    • To leverage Cartesian ovals for both refractive and reflective properties to simplify optical design.

    Main Methods:

    • Development of a mathematical model based on the properties of Cartesian ovals.
    • Utilizing total internal reflection on a refractive Cartesian oval surface as a mirror.
    • Describing the reflective characteristics of Cartesian ovals.

    Main Results:

    • A novel model for bi-aspherical catadioptric lens design with reduced spherical aberration.
    • Demonstrated application of the model to antenna design for visible light communications (VLC).
    • Significant reduction in optical system design computing time is theoretically achievable.

    Conclusions:

    • The proposed model offers an efficient approach to designing high-performance catadioptric lenses.
    • Cartesian ovals provide a versatile optical surface for combined refractive and reflective functions.
    • This work facilitates faster and more effective design of optical components, particularly for emerging technologies like VLC.