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Am J Ophthalmol. 1999 Mar;127(3):260-9.

Effect of astigmatic keratotomy on spherical equivalent: results of the Astigmatism Reduction Clinical Trial.

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Jules Stein Eye Institute and the Department of Ophthalmology, University of California, Los Angeles, USA.



To determine the effect of astigmatic keratotomy on spherical equivalent, as measured by the coupling ratio and a new quantity, coupling constant.


In a prospective multicenter study, subjects underwent arcuate keratotomy at a 7-mm optical zone by means of the Lindstrom nomogram for correction of astigmatism. One hundred fifty-seven eyes of 95 patients who had a follow-up examination 1 month postoperatively were studied. Mean preoperative refractive cylinder +/- SEM was 2.82 +/- 1.17 diopters. Coupling ratio was defined as the ratio of the flattening of the incised meridian to the steepening of the opposite meridian. Coupling constant was defined as the ratio of the change in spherical equivalent to the magnitude of the vector change in astigmatism. Coupling ratio, coupling constant, and change in spherical equivalent were calculated on the basis of change in refraction and keratometry.


On the basis of change in refraction, coupling ratio was 0.95 +/- 0.10 (mean +/- SEM) and coupling constant was -0.01 +/- 0.03, consistent with a minor shift in the spherical equivalent of -0.03 +/- 0.07 diopter. On the basis of change in keratometry, coupling ratio was 0.84 +/- 0.05 and coupling constant was -0.04 +/- 0.02, consistent with minor postoperative keratometric steepening of -0.10 +/- 0.04 diopter. Coupling ratio based on change in refraction was not statistically different from the coupling ratio predicted by the Gauss' law for inelastic domes (P = .370). Incision length and number, amount of achieved cylinder correction, age, and sex had no statistically significant effect on coupling ratio, coupling constant, and change in spherical equivalent.


Cornea behaved as an inelastic surface in response to arcuate keratotomy performed with the Astigmatism Reduction Clinical Trial study nomogram. On average, astigmatic keratotomy had a minimal effect on spherical equivalent refraction. There was variability, however, in coupling ratio, coupling constant, and change in spherical equivalent from eye to eye after astigmatic keratotomy. Caution is therefore advised when simultaneous correction of cylinder and spherical equivalent is planned.

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