Total Internal Reflection (TIR) is a phenomenon where a light ray is caused to reflect completely (100% reflection) when the light ray is traveling inside a higher-index medium and strikes a surface boundary into a lower-index medium.  When the light strikes this surface boundary at a certain angle (or greater angles), the light is completely reflected back into the higher-index medium.

Some optical systems (such as light pipes and reflective prisms like the Pechan) depend on this total internal reflection, to keep light contained inside a higher-index medium (such as glass or plastic), preventing any light from escaping into the lower-index medium (such as air).  Other optical systems (such as fingerprint scanners) take advantage of the fact that TIR can be spoiled, by bringing another higher-index object into near-contact with the medium that contains the light.  When this happens, and some of the light that should be totally internally reflected actually escapes across the small airgap into the second higher-index object, the situation is called Frustrated Total Internal Reflection (FTIR).

The amount of light that can be drawn out with FTIR is dependent on many things: wavelength, airgap thickness, refractive index of each medium, and angle of incidence.  The physics behind FTIR can be complicated, but ZEMAX models it very accurately using simple instructions.

Please note that while this article concentrates on the use of non-sequential ray-tracing, FTIR can be modeled in sequential ray-tracing using the same techniques as described in this article.