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Published on: February 17, 2019
Wavefronts and caustic of a spherical wave reflected by an arbitrary smooth surface
Edwin Román-Hernández1, José Guadalupe Santiago-Santiago, Gilberto Silva-Ortigoza
1Facultad de Ciencias Físico Matemáticas de la Universidad Autónoma de Puebla, Apartado Postal 1152, 72001, Puebla, Puebla, México.
Summary
This study derives formulas for light ray wavefronts and caustics reflected from surfaces. For parabolic mirrors, off-axis sources create specific wavefront and caustic singularities.
Area of Science:
- Optics
- Mathematical Physics
Background:
- Understanding light propagation and caustic formation is crucial in geometrical optics.
- Existing methods for analyzing reflected wavefronts and caustics can be complex.
Purpose of the Study:
- To derive general expressions for wavefront trains and caustics of light rays reflected from arbitrary smooth surfaces.
- To analyze the specific case of a parabolic mirror with an off-axis point source.
Main Methods:
- Utilizing the k-function associated with the general integral of Stavroudis to the eikonal equation.
- Applying definitions of critical and caustic sets to map wavefront evolution.
- Employing exact ray tracing for verification.
Main Results:
- Obtained general expressions for reflected wavefronts and caustics.
- Confirmed that the derived caustic expression matches existing literature results.
- Identified hyperbolic umbilic, cusp ridge, and swallowtail singularities for off-axis parabolic mirror illumination.
Conclusions:
- The developed method provides a unified approach to analyzing reflected wavefronts and caustics.
- Singularity analysis reveals complex wavefront behavior near caustics for specific optical systems.
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