Generalized Aldis theorem for calculating aberration contributions in freeform systems

Area of Science:

• Optical Engineering
• Computational Optics
• Freeform Optics Design

Background:

• Compact folded imaging systems frequently utilize freeform surfaces to mitigate off-axis aberrations like astigmatism.
• Analyzing aberration contributions in non-rotationally symmetric systems is mathematically challenging, hindering precise optical design.
• Quantifying the impact of individual surfaces within complex freeform systems remains a significant hurdle in optical engineering.

Purpose of the Study:

• To develop a novel matrix method for analyzing aberrations in freeform optical systems.
• To enable the quantification of aberration contributions from each individual surface.
• To provide a universal tool for aberration calculations in complex optical designs.

Main Methods:

• A matrix method based on the propagation of differential ray pairs was developed.
• The method mathematically determines the aberration contribution of each surface for arbitrary rays.
• A head-mounted display lens was used for experimental verification and testing.

Main Results:

• The developed matrix method successfully quantifies individual surface aberration contributions.
• Mathematical proof confirms the sum of calculated aberrations matches exact ray-tracing results at the image plane.
• The method demonstrated versatility and accuracy when applied to a head-mounted display lens.

Conclusions:

• The novel matrix method offers a universal and accurate approach to aberration analysis in freeform optical systems.
• This technique simplifies the complex task of quantifying surface-specific aberrations, aiding optical designers.
• The findings facilitate the design and optimization of advanced imaging systems, including head-mounted displays.