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Orthonormal aberration polynomials for anamorphic optical imaging systems with circular pupils
1The Aerospace Corporation, El Segundo, California 90245, USA. virendra.n.mahajan@aero.org
Applied Optics
|June 23, 2012
Summary
Anamorphic optical systems with circular pupils have non-separable aberration polynomials, unlike those with rectangular pupils. This means standard Zernike polynomials are unsuitable for describing aberrations in anamorphic systems with circular pupils.
Area of Science:
- Optical Engineering
- Aberration Theory
- Image Science
Background:
- Classical aberrations in anamorphic optical systems with rectangular pupils are separable in Cartesian coordinates.
- Orthonormal aberration polynomials for rectangular pupils are products of Legendre polynomials, separable in x and y.
- A symmetry exists where interchanging x and y yields corresponding polynomials.
Purpose of the Study:
- To investigate the nature of orthonormal aberration polynomials for anamorphic systems with circular pupils.
- To determine if these polynomials are separable in Cartesian coordinates.
- To assess the suitability of Zernike polynomials for anamorphic systems.
Main Methods:
- Gram-Schmidt orthogonalization of 2D Legendre polynomials applied to a circular pupil.
- Analysis of the separability of the resulting orthonormal polynomials.
- Comparison with aberration polynomials for rectangular pupils and Zernike polynomials.
Main Results:
- Orthonormal aberration polynomials for circular pupils are not separable in Cartesian coordinates.
- Interchanging x and y does not yield corresponding polynomials, indicating a loss of symmetry.
- Zernike circle polynomials are not suitable for anamorphic systems as they do not represent balanced aberrations.
Conclusions:
- The mathematical framework for describing aberrations differs significantly between anamorphic systems with rectangular and circular pupils.
- The non-separability of polynomials for circular pupils necessitates new approaches to aberration analysis.
- Zernike polynomials are inappropriate for anamorphic systems, highlighting the need for specialized aberration descriptions.
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