title: Meridional profiles of variance-covariance of symmetric dioptric power: classes of variation that are uniform across the meridians of the eye.
abstract: Conventional dioptric power, including refractive status and keratometric measurements, can vary in a large variety of ways. The three-dimensional character of this type of power implies that six numbers are required for the complete representation of its variance: three variances and three covariances. Curves (called profiles) that show how these numbers compare in different meridians (or transverse directions) of the eye provide a useful graphical picture of the variation and its nature. This paper explores an important subclass of types of variation in which the variation is the same for all meridians. In this subclass the variation of power is said to be uniform across all meridians of the eye. It turns out that the uniformity may be either complete or partial. In the former case all aspects of the variation are the same. In the latter case certain aspects of the variation are the same across all meridians whereas others are not; in particular the variance of the torsional component of power is the same for every meridian whereas the variance of the curvital component changes from meridian to meridian. There is a range of types of completely uniform variation from spherical variation at one extreme to Jacksonian variation at the other. All types of uniform variation (partial or complete) are characterized by two indices called the jacksonian index and the completeness index. The types can be represented geometrically as points on the triangle of uniformity. Samples of measurements of dioptric power are selected to illustrate various types of uniform variation. Methods are presented for detecting and classifying uniform variation from profiles of variation and also from the variance-covariance matrix. Examples are given of uniform variation of refractive status and of keratometry of an eye. The variation is analyzed and classified. The concepts and methods are proving to be of fundamental importance in the study of the nature and underlying causes of fluctuations of refractive status and keratometric measurements.
authors.affiliation: Department of Optometry, Rand Afrikaans University, Johannesburg, South Africa. wfh@na.rau.ac.za
authors.forename: W F
authors.initials: WF
authors.lastname: Harris
mesh_terms: D000704:Analysis of Variance; D003315:Cornea / Q000033:anatomy & histology*; D005123:Eye / Q000033:anatomy & histology; D006801:Humans; D008433:Mathematics; D009799:Ocular Physiological Phenomena; D055095:Optics and Photonics; D009907:Optometry / Q000379:methods; D012029:Refraction, Ocular