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In refractive surgery, the cubic spline fit for the transition zone breaks down for myopia and myopic meridians in mixed astigmatism as in many cases the cubic spline function runs into negative values. In this paper, the complementary error function is proposed instead of the cubic spline function as the transition zone function, due to the availability of analytical expression of its derivatives and the nonnegativity fact. It is shown that with the use of the complementary error function, transition zones for all refractive types work correctly.

Application of Complementary Error Function to the Transition Zone of Myopic Ablation Shapes in Refractive Surgery