The Alpins method compared to other approaches

Many people have asked how the Alpins method of astigmatism analysis compares to approaches described by Holladay and others. An excellent summary of the various approaches is contained in the book, "Surgical Treatment of Astigmatism," by James P. Gills, MD, et al (1994, Slack Inc., Thorofare, N.J., pp 18 and 19). The chapter, "Astigmatic keratotomy in the refractive patient: The ARC-T study," by R. Bruce Grene, MD, and Richard L. Lindstrom, MD, includes the following passages:

"The angular solution of Holladay's formula, though fundamentally sound, does not provide for the possibility of functions returning the incorrect angle."

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"Alpins' method generates the same values for surgically induced astigmatic magnitude as do Naylor's and Holladay's formulae. Additionally, Alpins' method takes into account the cyclic nature of trigonometric functions, and with a modicum of change (adding a very small amount, 0.0000000001, to the X and Y components of the Targeted Induced Astigmatism) to account for a division-by-zero error when using targeted astigmatism of zero, Alpins' method generates the correct angular component."

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