Demystifying the sequential ray tracing algorithm

The act of performing a sequential trigonometric ray trace through an optical system is as simple as applying Snell's Laws of refraction and reflection, along with some form of the grating equation, to the geometric description of the lenses and mirrors which can comprise that system. The orderly incorporation. of these physical laws into an algorithm, which at the same time incorporates all possible geometries which may occur in this optical system, will be the result of this paper. The ray/surface equations and other useful numerical techniques will be spelled out in detail so that this paper can be used as a starting point for their own ray tracing program when commercial optical design codes are either not available or inappropriate.