Power vector analysis of the optical outcome of refractive surgery

Purpose: To demonstrate the power vector method of representing and analyzi ng spherocylindrical refractive errors. Setting: School of Optometry, Indiana University, Bloomington, Indiana, USA . Methods: Manifest and keratometric refractive errors were expressed as powe r 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 prescript ion: a spherical lens of power M, a Jackson crossed cylinder of power J(0) with axes at 90 degrees and 180 degrees, and a Jackson crossed cylinder of power J(45) 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 sph erocylindrical lens or refractive error. Changes in refractive error due to surgery were computed by the ordinary rules of vector subtraction. Results: Frequency distributions of blur strength (B) clearly demonstrate t he effectiveness of refractive surgery in reducing the overall blurring eff ect of uncorrected refractive error. Power vector analysis also revealed a reduction in the astigmatic component of these refractive errors, Paired co mparisons revealed that the change in manifest astigmatism due to surgery w as well correlated with the change in keratometric astigmatism. Conclusions: Power vectors aid the visualization of complex changes in refr active error by tracing a trajectory in a uniform dioptric space. The Carte sian components of a power vector are mutually independent, which simplifie s 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.