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J Cataract Refract Surg. 2001 Jan;27(1):31-49.

Astigmatism analysis by the Alpins method.

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To determine the effectiveness of correcting astigmatism by laser refractive surgery by a vectorial astigmatism outcome analysis that uses 3 fundamental vectors: target induced astigmatism vector (TIA), surgically induced astigmatism vector, and difference vector, as described by the Alpins method.


A data set of 100 eyes that had laser in situ keratomileusis to correct myopia and astigmatism (minimum preoperative refractive astigmatism 0.75 diopter) was analyzed. The data included preoperative and 3 month postoperative values for manifest refraction and standard keratometry. Using the ASSORT or VectrAK analysis program, individual and aggregate data analyses were performed using simple, polar, and vector analysis of astigmatism and an analysis of spherical change. Statistical analysis of the results was used for means and confidence limits, as well as to examine the differences between corneal and refractive astigmatism outcomes.


At an individual patient level, the angle of error was found to be significant, suggesting variable factors at work, such as healing or alignment. A systematic error of undercorrection of astigmatism is prevalent in the treatment of these 100 patients by a factor of between 15% and 30%, depending on whether refractive or corneal values are examined. Spherical correction showed systematic undercorrection of 11%, and parallel indices demonstrated it to be more effective than the astigmatic correction.


This method of astigmatism analysis enables the examination of results of astigmatism treatment measured by both refractive and corneal measurements using vector analysis. By examining individual vector relationships to the TIA (ie, the correction index, index of success, and flattening index), a comprehensive astigmatism analysis is completed. Each index provides information necessary for understanding any astigmatic change. Astigmatic outcome parameters are more favorable when measured by subjective refractive than objective corneal methods.

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