Calculation of aberration coefficients by ray tracing

Area of Science:

• Optics and Photonics
• Computational Physics
• Optical Engineering

Background:

• Accurate calculation of aberration coefficients is crucial for optical system design.
• Traditional methods like aberration integrals and differential algebra can be complex and computationally intensive.
• A need exists for more accessible and scalable methods to determine optical aberrations.

Purpose of the Study:

• To present a novel approach for calculating aberration coefficients using accurate ray tracing.
• To demonstrate the method's ease of use and scalability with increasing optical system complexity.
• To compute fifth-order geometrical and third-order chromatic aberrations for a weak electrostatic lens.

Main Methods:

• Computing intersections of numerous trajectories with a plane using ray tracing.
• Applying least-squares fitting of an analytical model to computed trajectory positions in the Gaussian image plane.
• Developing a tested procedure for selecting initial conditions for the ray tracing.

Main Results:

• Successfully calculated fifth-order geometrical and third-order chromatic aberration coefficients for a weak electrostatic lens.
• The ray tracing method proved to be relatively easy to implement and use.
• Computational complexity remained manageable even with a complex optical system.

Conclusions:

• The proposed ray tracing method offers a practical and efficient alternative for calculating aberration coefficients.
• This technique simplifies the analysis of optical aberrations compared to existing methods.
• The results obtained are comparable to those from established methods, validating the approach.