Modification of readings along oblique principal meridians to fit regular corneal surfaces

Abstract

Anterior astigmatic corneal surface elements may have their continuity disturbed by environmental factors. Powers detected along principal meridians define matrices whose natures distinguish the continuity of surface elements. This work aims to adapt the matrix nature of data to fit closely, uniquely and holistically with the matrix nature in a sample of data for smooth astigmatic corneas that have powers along rectangular meridians. Matrices from continuous surfaces approximate matrices with outliers from irregular surfaces explicitly. Only approximations that minimize the Frobenius norm of the residual matrices are selected. Data from smooth astigmatic corneal surfaces, in an augmented sample, may now produce more reliable analyses.

Keywords:

• astigmatism
• asymmetric
• closest matrix approximation
• Frobenius norm
• oblique
• orthogonal
• outlier
• paraxial

Acknowledgements

The hospitality of the University of the Witwatersrand, Johannesburg is acknowledged. S.A. gratefully acknowledges support from the University of the Witwatersrand, Johannesburg and the National Research Foundation, Pretoria, South Africa.

Disclosure statement

No potential conflict of interest was reported by the authors.