Power vector analysis of the optical outcome of refractive surgery

TLDR

Power vectors represent spherocylindrical refractive errors as three independent Cartesian components (M, J0, J45), enabling visualization of changes in a uniform 3‑dimensional dioptric space. The study demonstrates the power vector method for representing and analyzing manifest and keratometric refractive errors as points in a 3‑dimensional dioptric space. The authors compute changes in refractive error by vector subtraction, use the Pythagorean length B to quantify overall blur, and link power vectors to wavefront aberrations via Zernike polynomials. Refractive surgery reduces overall blur strength and astigmatic components, with changes in manifest astigmatism closely correlated with changes in keratometric astigmatism.

Abstract

To demonstrate the power vector method of representing and analyzing spherocylindrical refractive errors.School of Optometry, Indiana University, Bloomington, Indiana, USA.Manifest and keratometric refractive errors were expressed as power vectors suitable for plotting as points in a 3-dimensional dioptric space. The 3 Cartesian coordinates (x, y, z) of each power vector correspond to the powers of 3 lenses that, in combination, fulfill a refractive prescription: a spherical lens of power M, a Jackson crossed cylinder of power J0 with axes at 90 degrees and 180 degrees, and a Jackson crossed cylinder of power J45 with axes at 45 degrees and 135 degrees. The Pythagorean length of the power vector, B, is a measure of overall blurring strength of a spherocylindrical lens or refractive error. Changes in refractive error due to surgery were computed by the ordinary rules of vector subtraction.Frequency distributions of blur strength (B) clearly demonstrate the effectiveness of refractive surgery in reducing the overall blurring effect of uncorrected refractive error.Power vector analysis also revealed a reduction in the astigmatic component of these refractive errors. Paired comparisons revealed that the change in manifest astigmatism due to surgery was well correlated with the change in keratometric astigmatism. Power vectors aid the visualization of complex changes in refractive error by tracing a trajectory in a uniform dioptric space. The Cartesian components of a power vector are mutually independent, which simplifies mathematical and statistical analysis of refractive errors. Power vectors also provide a natural link to a more comprehensive optical description of ocular refractive imperfections in terms of wavefront aberration functions and their description by Zernike polynomials.