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Analytical design method for small-sag freeform surfaces in optical systems with rectangular fields of view.
Optics Express
|July 30, 2025
Summary
This study introduces an analytical method using rectangular Zernike polynomials to optimize freeform optical systems, reducing parameter magnitudes and improving tolerance sensitivity for better imaging quality and lower manufacturing costs.
Area of Science:
- Optical Engineering
- Computational Optics
Background:
- Freeform optical systems can suffer from overcompensation during optimization.
- Accurate modeling of freeform surfaces is crucial for system performance.
Purpose of the Study:
- To develop an analytical method for calculating freeform surface parameters.
- To mitigate overcompensation issues in multi-freeform optical systems.
Main Methods:
- Derivation of rectangular Zernike orthogonal polynomials.
- Application to freeform surface aberration expressions.
- Minimum-norm least squares solution for parameter calculation.
Main Results:
- The proposed method yields freeform parameters with smaller magnitudes.
- Lower tolerance sensitivity is achieved compared to traditional methods.
- Maintained imaging quality with reduced manufacturing and alignment costs.
Conclusions:
- The analytical method effectively optimizes multi-freeform optical systems.
- It offers a cost-effective alternative to standard optimization techniques.
- Enables more efficient design and manufacturing of complex optical systems.
