Several ray trace algorithms are developed by changing the independent variable for describing the ray and eikonal equations to the quasiray path, the ray path, the optical path length, and the quasioptical path length. By using the Runge-Kutta-Gill method, it is shown that for a given step size the accuracy of these algorithms is equal to or higher than that by Sharma's algorithm in both computations of ray position and optical path length, and that these algorithms have a performance comparable with Sharma's algorithm when evaluated by the equivalent step size.
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Toyokazu Sakamoto (1987) studied this question.
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