Surgically induced astigmatism: distinguishing between dioptric vectors and non-vectors.

To the Editor: I read with interest the October editorial, “JRS Standard for Reporting Astigmatism Outcomes of Refractive Surgery”1 by Reinstein et al.; however, some clarification is required. I advocated common standards for reporting surgically induced astigmatism in 1997.2 In 2008, a comprehensive analysis of assessment methods and statistical analysis of surgically induced astigmatism was published.3 None of these articles were quoted in the editorial. However, during this period, considerable progress toward a common understanding of astigmatism has evolved: a net astigmatism is given as (M @ ), where M is the astigmatic magnitude in diopters and  is the astigmatic direction in degrees. A net astigmatism can be used to characterize a single astigmatism, but is not a vector or any other entity subjectable to the usual rules for algebraic conversions.4 Therefore, net astigmatisms cannot be used for calculations and isolated analysis of astigmatic direction and magnitude will yield systematic errors for aggregate data.2,5 To perform calculations (of surgically induced astigmatism), net astigmatism must be converted to dioptric vectors. As mentioned in the editorial, most ophthalmologists advocate conversion to two double-angled components, namely a meridional power giving the over/undercorrection and a torsional power giving a rotation of the cylinder meridian. For the net astigmatism (M @ ) and the reference meridian , this vector has the following general format: