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Correction of Presbyopia by Monocular Bi-Aspheric Ablation Profile
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Orthonormal aberration polynomials for anamorphic optical imaging systems with rectangular pupils.

Virendra N Mahajan1

  • 1The Aerospace Corporation, 2310 El Segundo Blvd., El Segundo, California 90245, USA. virendra.n.mahajan@aero.org

Applied Optics
|December 22, 2010
PubMed
Summary
This summary is machine-generated.

Researchers balanced optical aberrations in anamorphic systems by minimizing variance across rectangular pupils. Balanced aberrations are products of Legendre polynomials, offering a new orthogonal basis for optical design.

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Area of Science:

  • Optical Engineering
  • Image Science

Background:

  • Classical aberrations in anamorphic optical systems are power-series expansions.
  • These aberrations are separable in the Cartesian coordinates of the pupil.

Purpose of the Study:

  • To balance classical aberrations in anamorphic systems.
  • To minimize aberration variance across a rectangular pupil.
  • To introduce a new set of orthogonal polynomials for optical design.

Main Methods:

  • Power-series expansion of aberration functions.
  • Variance minimization techniques.
  • Legendre polynomial analysis.

Main Results:

  • Classical aberrations are separable in pupil Cartesian coordinates.
  • Balanced aberrations are products of two Legendre polynomials.
  • Compound Legendre polynomials are orthogonal across rectangular pupils.

Conclusions:

  • A novel method for balancing optical aberrations in anamorphic systems is presented.
  • The derived compound Legendre polynomials provide an orthogonal basis for analyzing aberrations in rectangular pupils.
  • This approach differs from methods used for rotationally symmetric systems.