Astigmatism analysis with the Alpins method
Updated on version: 1.0.1


This function computes the mean (standard deviation) and the median (interquartile range) from an array of astigmatism values containing the Magnitude and Direction


Astigmatism analysis with the Alpins method


This function computes the mean (standard deviation) and the median (interquartile range) from an array of astigmatism values containing the Magnitude and Direction. The mean computed without considering the axis, only describes information about the magnitude of astigmatism but not about the type of astigmatism (with-the-rule, WTR; against-the-rule, ATR; oblique). For considering not only the magnitude but also the orientation a previous decomposition in the orthogonal X and Y components over a double angle plot figure is required. Then, inferential statistics can be applied considering these orthogonal components.

Astigmatism analysis is based on vector arithmetic. The current standard method in Ophthalmology practice is the Alpins method1 whereas in Optometry practice is more common to use the Thibos method.2 In the practice, both methods result in similar outputs.


  1. Alpins NA. A new method of analyzing vectors for changes in astigmatism. J. Cataract Refract. Surg. 1993; 19: 524–33. 2.
  2. Thibos LN, Wheeler W, Horner D. Power vectors: an application of Fourier analysis to the description and statistical analysis of refractive error. Optom Vis Sci. 1997; 74: 367–75.

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