Computationally efficient gradient matrix of optical path length in axisymmetric optical systems

Area of Science:

• Optical engineering
• Computational optics
• Mathematical modeling

Background:

• Traditional methods for evaluating optical path length (OPL) changes rely on computationally intensive ray-tracing and finite-difference approximations.
• Assessing the impact of system variable changes on OPL typically requires multiple ray-tracing operations, limiting efficiency.

Purpose of the Study:

• To develop a novel mathematical method for determining the OPL gradient matrix relative to all system variables in a single pass.
• To enhance computational efficiency in optical system analysis by avoiding repeated ray-tracing.

Main Methods:

• A new mathematical approach is formulated to compute the OPL gradient matrix directly.
• The method allows for the evaluation of variable change effects in a single computational pass.

Main Results:

• The developed method significantly reduces the need for multiple ray-tracing operations.
• Demonstrated a computational time reduction of approximately 90% for a Petzval lens system compared to the finite-difference method.

Conclusions:

• The novel mathematical method offers a computationally efficient alternative for determining OPL gradients in optical systems.
• This approach streamlines the analysis of system variable effects, leading to faster design and optimization processes.