A top‐down philosophy for accurate numerical ray tracing

Several examples of the ease of application and accuracy of ray tracing resulting from the top‐down approach are given to demonstrate the results obtainable with today’s small computers. One example of a more traditional approach is given to demonstrate how easy it is to lose computational accuracy to mixing instead of isolating the steps in the solution. The current level of commonly available computing power means that it is important for the ordinary researcher to be aware of powerful integration subroutines. Their extraordinary accuracy makes the payoff worth the effort expended in understanding their use.