The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials

Iskander, Robert, Nam, Jayoung, & Thibos, Larry N. (2009) The statistics of refractive error maps : managing wavefront aberration analysis without Zernike polynomials. Ophthalmic And Physiological Optics, 29, pp. 292-299.

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The refractive error of a human eye varies across the pupil and therefore may be treated as a random variable. The probability distribution of this random variable provides a means for assessing the main refractive properties of the eye without the necessity of traditional functional representation of wavefront aberrations. To demonstrate this approach, the statistical properties of refractive error maps are investigated. Closed-form expressions are derived for the probability density function (PDF) and its statistical moments for the general case of rotationally-symmetric aberrations. A closed-form expression for a PDF for a general non-rotationally symmetric wavefront aberration is difficult to derive. However, for specific cases, such as astigmatism, a closed-form expression of the PDF can be obtained. Further, interpretation of the distribution of the refractive error map as well as its moments is provided for a range of wavefront aberrations measured in real eyes. These are evaluated using a kernel density and sample moments estimators. It is concluded that the refractive error domain allows non-functional analysis of wavefront aberrations based on simple statistics in the form of its sample moments. Clinicians may find this approach to wavefront analysis easier to interpret due to the clinical familiarity and intuitive appeal of refractive error maps.

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4 citations in Scopus
4 citations in Web of Science®
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ID Code: 31097
Item Type: Journal Article
Refereed: Yes
Keywords: Non-parametric statistics, refraction, wavefront aberrations, wavefront vergence
DOI: 10.1111/j.1475-1313.2008.00631.x
ISSN: 0275-5408
Divisions: Current > QUT Faculties and Divisions > Faculty of Health
Current > Institutes > Institute of Health and Biomedical Innovation
Current > Schools > School of Optometry & Vision Science
Deposited On: 02 Mar 2010 23:19
Last Modified: 09 May 2017 02:52

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