Lie algebraic treatment of dioptric power and optical aberrations
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Updated: Oct 28, 2026

Correction of Presbyopia by Monocular Bi-Aspheric Ablation Profile
Published on: September 20, 2024
V Lakshminarayanan1, R Sridhar, R Jagannathan
1School of Optometry, University of Missouri at St. Louis 63121-4499, USA.
Abstract:
The dioptric power of an optical system can be expressed as a four-component dioptric power matrix. We generalize and reformulate the standard matrix approach by utilizing the methods of Lie algebra. This generalization helps one deal with nonlinear problems (such as aberrations) and further extends the standard matrix formulation. Explicit formulas giving the relationship between the incident and the emergent rays are presented. Examples include the general case of thick and thin lenses. The treatment of a graded-index medium is outlined.
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