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Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change

Unacceptable principal powers in well-centred lenses may require a toric over-refraction which differs in nature from the one where correct powers have misplaced meridians. This paper calculates residual (over) refractions and their natures. The magnitude of the power of the over-refraction serves a...

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Detalles Bibliográficos
Autores principales: Abelman, Herven, Abelman, Shirley
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Hindawi Publishing Corporation 2014
Materias:
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4244934/
https://www.ncbi.nlm.nih.gov/pubmed/25478004
http://dx.doi.org/10.1155/2014/492383
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author Abelman, Herven
Abelman, Shirley
author_facet Abelman, Herven
Abelman, Shirley
author_sort Abelman, Herven
collection PubMed
description Unacceptable principal powers in well-centred lenses may require a toric over-refraction which differs in nature from the one where correct powers have misplaced meridians. This paper calculates residual (over) refractions and their natures. The magnitude of the power of the over-refraction serves as a general, reliable, real scalar criterion for acceptance or tolerance of lenses whose surface relative curvatures change or whose meridians are rotated and cause powers to differ. Principal powers and meridians of lenses are analogous to eigenvalues and eigenvectors of symmetric matrices, which facilitates the calculation of powers and their residuals. Geometric paths in symmetric power space link intended refractive correction and these carefully chosen, undue refractive corrections. Principal meridians alone vary along an arc of a circle centred at the origin and corresponding powers vary autonomously along select diameters of that circle in symmetric power space. Depending on the path of the power change, residual lenses different from their prescription in principal powers and meridians are pure cross-cylindrical or spherocylindrical in nature. The location of residual power in symmetric dioptric power space and its optical cross-representation characterize the lens that must be added to the compensation to attain the power in the prescription.
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spelling pubmed-42449342014-12-04 Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change Abelman, Herven Abelman, Shirley Comput Math Methods Med Research Article Unacceptable principal powers in well-centred lenses may require a toric over-refraction which differs in nature from the one where correct powers have misplaced meridians. This paper calculates residual (over) refractions and their natures. The magnitude of the power of the over-refraction serves as a general, reliable, real scalar criterion for acceptance or tolerance of lenses whose surface relative curvatures change or whose meridians are rotated and cause powers to differ. Principal powers and meridians of lenses are analogous to eigenvalues and eigenvectors of symmetric matrices, which facilitates the calculation of powers and their residuals. Geometric paths in symmetric power space link intended refractive correction and these carefully chosen, undue refractive corrections. Principal meridians alone vary along an arc of a circle centred at the origin and corresponding powers vary autonomously along select diameters of that circle in symmetric power space. Depending on the path of the power change, residual lenses different from their prescription in principal powers and meridians are pure cross-cylindrical or spherocylindrical in nature. The location of residual power in symmetric dioptric power space and its optical cross-representation characterize the lens that must be added to the compensation to attain the power in the prescription. Hindawi Publishing Corporation 2014 2014-11-12 /pmc/articles/PMC4244934/ /pubmed/25478004 http://dx.doi.org/10.1155/2014/492383 Text en Copyright © 2014 H. Abelman and S. Abelman. https://creativecommons.org/licenses/by/3.0/ This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
spellingShingle Research Article
Abelman, Herven
Abelman, Shirley
Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change
title Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change
title_full Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change
title_fullStr Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change
title_full_unstemmed Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change
title_short Tolerance and Nature of Residual Refraction in Symmetric Power Space as Principal Lens Powers and Meridians Change
title_sort tolerance and nature of residual refraction in symmetric power space as principal lens powers and meridians change
topic Research Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC4244934/
https://www.ncbi.nlm.nih.gov/pubmed/25478004
http://dx.doi.org/10.1155/2014/492383
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