Determination of caustic surfaces using point spread function and ray Jacobian and Hessian matrices

Area of Science:

• Optics and Photonics
• Computational Physics
• Optical Engineering

Background:

• Current methods for determining caustic surfaces rely on flux density singularity or wavefront curvature.
• These methods often depend on ray tracing and finite difference approximations for Jacobian and Hessian matrices.
• Analytical expressions for these matrices have been historically complex or unattainable.

Purpose of the Study:

• To propose a robust numerical method for determining caustic surfaces.
• To leverage established analytical Jacobian and Hessian matrices of a ray.
• To offer a computationally straightforward approach for optical systems.

Main Methods:

• A novel numerical method based on a point spread function.
• Utilizes pre-established analytical Jacobian and Hessian matrices of a ray.
• Avoids the need for complex analytical equations or approximations.

Main Results:

• The proposed method accurately determines caustic surfaces in optical systems.
• It is computationally straightforward and convenient.
• Demonstrates substantial differences from existing flux density and wavefront curvature methods.

Conclusions:

• The new method provides an efficient and accessible way to determine caustic surfaces.
• It simplifies the analysis of both simple and complex optical systems.
• Represents a significant advancement over traditional techniques.