Paraxial ocular measurements and entries in spectral and modal matrices: analogy and application.

Herven Abelman,Shirley Abelman

doi:10.1155/2014/950290

Abstract

Lensometers and keratometers yield powers along perpendicular meridians even if the principal meridians of the lens and the cornea are oblique. From each such instrument, multiple raw data represented on optical crosses require conversion to determine elementary statistics. Calculations for research decisions need to be authentic. Principles common to meridians generalize formulaic methods for oblique meridians. Like a lens or a cornea, matrix latent quantities are represented on a matrix cross. Our problem is to determine the matrix whose cross represents quantities on the optical cross. All measurements on an optical cross that include corneal and lens powers and oblique meridians can be considered. Once determined, a portfolio of matrix calculations applies and is justified for ophthalmic calculation. Matrices can be unique and, like a cornea before it is measured, contain latent observations. Asymmetric power component matrices quantify a deviation of a corneal surface from smoothness and toricity. Entries may identify those measurements causing irregular astigmatism that may stem from surgical or other external intervention. Irregular astigmatism is detected primarily from significant measurements in the paraxial range. Measurements are assimilated with matrix factors in a holistic way in order to support choices with calculations and statistics.

Highlights

Paraxial ocular measurements take on a format with standardized, clearly formulated rules for processing when represented by eigenvalues and eigenvectors of some array
On the small zone of the cornea sampled with a keratometer near an entrance pupil, we model the primary contribution to irregular astigmatism
A relaxation of these constraints reduces the rank of matrices and compromises uniqueness of the solution of linear equations (1)

Summary

Introduction

Paraxial ocular measurements take on a format with standardized, clearly formulated rules for processing when represented by eigenvalues and eigenvectors of some array. Distinct principal powers and meridians, real or complex conjugate, are used to obtain a unique real array holistically. The reverse process determines eigenvalues and eigenvectors of a given dioptric power array that represent principal powers and meridians. From the equations that ensure unique arrays we show that coincident real principal powers can yield multiple arrays. On the small zone of the cornea sampled with a keratometer near an entrance pupil, we model the primary contribution to irregular astigmatism. We use matrix properties to show unequivocally how an angle not 90∘ and not 0∘ between meridians and the length of the interval of Sturm in dioptres are paraxial contributors to this effect

Methods

Discussion

Conclusion