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Orthogonal aberration functions for high-aperture optical systems.
1Division of Bioengineering, Department of Diagnostic Radiology, National University of Singapore, Singapore 117576. colin@nus.edu.sg
Summary
New aberration functions for optical systems are developed. These functions provide a complete, orthogonal, and normalized set for analyzing aberrations, including those from mirrors and Fresnel reflection losses.
Area of Science:
- Optical engineering
- Mathematical physics
Background:
- Aberrations limit optical system performance.
- Existing methods for aberration analysis can be complex.
Purpose of the Study:
- To develop a novel set of aberration functions.
- To provide a complete, orthogonal, and normalized basis set for aberration analysis.
Main Methods:
- Development of aberration functions over a weighted spherical pupil.
- Consideration of general weighting, including special cases for Abbe sine and Herschel conditions.
- Inclusion of paraboloidal mirrors and empirical accounting for Fresnel reflection losses.
Main Results:
- A complete, orthogonal, and normalized set of aberration functions is derived.
- The functions are expressed in an analytic form.
- Expressions for 24 low-order aberrations are provided.
Conclusions:
- The developed aberration functions offer a versatile tool for optical system analysis.
- The framework accommodates various optical configurations and loss factors.
- Provides a foundation for detailed aberration characterization.