Paraxial ocular measurements and entries in spectral and modal matrices: Analogy and application

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. © 2014 Herven Abelman and Shirley Abelman.