Caustic produced by refractive conic surfaces

María C. López-Bautista; Maximino Avendaño-Alejo; Osvaldo Ponce-Hernández; Luis Castañeda

doi:10.1117/12.2633399

3 October 2022 Caustic produced by refractive conic surfaces

María C. López-Bautista, Maximino Avendaño-Alejo, Osvaldo Ponce-Hernández, Luis Castañeda

Proceedings Volume 12217, Current Developments in Lens Design and Optical Engineering XXIII; 122170D (2022) https://doi.org/10.1117/12.2633399
Event: SPIE Optical Engineering + Applications, 2022, San Diego, California, United States

Abstract

We study the formation of caustic produced by refraction through conic surfaces, considering a point source placed along the optical axis at arbitrary distances from the vertex of refracting surface. We demand that the optical surface is represented by a mathematical function, which is smooth, continuous, and derivable. We implement an exact ray trace to obtain a monoparametric equation that describes a family of refracted rays, which are propagated as a function of the angle of emission from the point source for each ray. Subsequently, by using the envelope’s method, we provide an analytical equation for the caustic surface as a function of all the parameters involved in the process of refraction. We analyze the paraxial approximation assuming a very small angle about the axis of the system. Additionally, we provide a formula, which describes the conditions for total internal reflection. Finally, we present the formation of caustic surfaces by considering a liquid polymer in a rotating vessel forming a paraboloid surface, also we present the caustic surface produced by the package of a Light Emitting Diode, to produce an uniform illumination pattern.

Conference Presentation

Citation Download Citation

María C. López-Bautista, Maximino Avendaño-Alejo, Osvaldo Ponce-Hernández, and Luis Castañeda "Caustic produced by refractive conic surfaces", Proc. SPIE 12217, Current Developments in Lens Design and Optical Engineering XXIII, 122170D (3 October 2022); https://doi.org/10.1117/12.2633399

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