Simple and practical approach for computing the ray Hessian matrix in geometrical optics

Area of Science:

• Optics
• Computational Optics
• Geometrical Optics

Background:

• Calculating the ray Hessian matrix is crucial for analyzing optical systems.
• Previous methods involved complex computations with angular variables.
• Reducing computational complexity is essential for efficient optical design.

Purpose of the Study:

• To propose a novel method for simplifying the computation of the ray Hessian matrix.
• To reduce computation time and complexity in geometrical optics.
• To demonstrate the applicability of the method in aberration analysis.

Main Methods:

• Replacing angular variables with cosine and sine functions in the system variable vector.
• Defining boundary surface variable vectors to exclude angular variables.
• Utilizing polynomial differentiation instead of trigonometric function calls.

Main Results:

• The proposed method reduces Hessian matrix computation time by approximately 10 times.
• The method significantly lowers computational complexity by eliminating trigonometric functions.
• The approach is applicable to various pose matrices and aberration calculations.

Conclusions:

• The developed method offers a computationally efficient alternative for ray Hessian matrix calculation.
• This simplification is beneficial for analyzing optical systems and their aberrations.
• The method's polynomial nature enhances its practical application in optical design.