title: Mapping of error cells in clinical measure to symmetric power space.
abstract: During the refraction procedure, the power of the nearest equivalent sphere lens, known as the scalar power, is conserved within upper and lower bounds in the sphere (and cylinder) lens powers. Bounds are brought closer together while keeping the circle of least confusion on the retina. The sphere and cylinder powers and changes in these powers are thus dependent. Changes are depicted in the cylinder-sphere plane by error cells with one pair of parallel sides of negative gradient and the other pair aligned with the graph axis of cylinder power. Scalar power constitutes a vector space, is a meaningful ophthalmic quantity and is represented by the semi-trace of the dioptric power matrix. The purpose of this article is to map to error cells for the following: coordinates of the dioptric power matrix, its principal powers and meridians and its entries from error cells surrounding powers in sphere, cylinder and axis. Error cells in clinical measure for conserved scalar power now contain more compensatory lens powers. Such cells and their respective mappings in terms of most scientific and alternate clinical quantities now image consistently not only to the cells from where they originate but also to each other.
authors: School of Computational and Applied Mathematics, University of the Witwatersrand, Private Bag 3, Wits 2050, South Africa. Herven.Abelman@wits.ac.za
authors: H
authors: H
authors: Abelman
authors: S
authors: S
authors: Abelman
mesh_terms: D000065:Accommodation, Ocular / Q000502:physiology*; D005139:Eyeglasses / Q000592:standards*; D006801:Humans; D008433:Mathematics; D008954:Models, Biological; D009799:Ocular Physiological Phenomena; D055095:Optics and Photonics / Q000295:instrumentation*; D009907:Optometry / Q000592:standards*; D012029:Refraction, Ocular / Q000502:physiology*; D012030:Refractive Errors