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Howard C. Howland; Optical oblique astigmatism of the human eye. Journal of Vision 2009;9(14):3. doi: 10.1167/9.14.3.
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© ARVO (1962-2015); The Authors (2016-present)
Purpose: To characterize the oblique astigmatism of the human eye. Methods: In a study of peripheral refractions of 47 young college students we collected data on the magnitude of cylinders and their axes at the fovea and at 4 points, 25° away from the fovea in superior, temporal, inferior, and nasal positions using a PowerRefractor [MultiChannel System, Reutlingen, Germany] . A number of the subjects were measured at yearly intervals yielding 87 binocular refractions. For the data of each subject, the foveal astigmatism was subtracted from the peripheral values to determine the optical oblique astigmatism, and the data were averaged vectorially. Due to the large scatter of the axes of small nasal cylinders a correction factor of the magnitude of these cylinders was made under the assumption that the variance of their axes was equivalent to that of the (larger) temporal cylinders. Because the oblique astigmatism increases with the square of the distance from the nominal axis, a parabola was fit to the peripheral, temporal and (corrected) nasal cylinder magnitudes and the distance of the fovea from the optic axis, a, and the cylinder constant of the parabola, k, were computed in the equation: cylinder magnitude = k (8-x)2, where x is the distance from the fovea measured in degrees and the cylinder is measured in diopters. A bootstrap program was used to compute the standard deviations of the average values of temporal and nasal cylinders as well as the values of k, x and their standard deviations. Results: The average values of the temporal and nasal oblique cylinders were: Temporal: 1.51° + 0.18° [D] SD, Nasal 1.08+ 0.45 [D] SD, with parabolic parameters: x = 2.61° + 2.54° SD , and k = 0.00204 + 0.00048 SD. The axes of oblique astigmatism did not differ significantly from those predicted by optical theory.
Discussion: Both the value of the parabolic constant and that of the angular distance between the fovea and optic axis (angle alpha = approx. angle kappa) are in reasonable agreement with results from model eyes and prior empirical measurements.
Conclusions: Refractive estimates of the oblique astigmatism of the human eye exhibit a temporal-nasal asymmetry that allows one to compute the angular distance between the fovea and optic axis. This angle, cylinder magnitudes and axes found from this method are in reasonable agreement with prior empirical and theoretical findings. between the fovea and optic axis. This angle, cylinder magnitudes and axes found from this method are in reasonable agreement with prior empirical and theoretical findings.
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