Clearly tracing birefingent rays is more complex than ordinary ray-tracing: we must consider two refractive indices and the orientation of the ray and wave vectors relative to a crystal axis vector. So, birefringent ray tracing is performed only when called for. It starts when a ray hits a Birefringent In surface, and ends when the ray hits a Birefringent Out surface. Only Coordinate Break surfaces are allowed between a Birefringent IN and Birefringent Out surface.

In normal ray-tracing the ray vector S and the wave vector k point in the same direction: the direction of energy flow. Therefore in normal ray-tracing the k vector components define the ray's direction cosines.

In birefringent ray-tracing, k and S are not identical but are coplanar with the crystal axis vector a. The components of S now define the ray's direction cosines.

Here is an example of a ray entering a block of calcite. The dotted line represents the crystal axis:

The ray enters the calcite and appears to be split (more on this later) into two rays. The ordinary ray refracts normally, and as the surface is flat, it is not bent. The extraordinary ray undergoes double refraction, once at the surface and again at the crystal axis, and so is deviated, even though the surface is flat and the ray is at normal incidence.

This is how this is entered in ZEMAX:

The ray is traced surface-by-surface normally until it hits the Birefringent In surface. This has the same surface shape as the Standard surface (i.e., a conic asphere) Note the glass used is CALCITE: this is used as the ordinary index. ZEMAX will look in the same catalog for a glass named CALCITE-E. This contains the extraordinary index of the material. By using two glasses, every piece of data about the glass (transmission, dispersion, thermal properties etc) can be incorporated for both indices.

The crystal axis orientation relative to the surface normal is defined by the parameter data of the Birefringent-In surface:

The direction cosines of the crystal axis are entered directly, in the local coordinates of the Birefringent-In surface. The "Draw Axis" parameter specifies the length of the dotted line shown in layout plots to represent the axis, in lens units. This may be set to zero to avoid drawing the axis, if required.

Now the layout plot above is misleading: it appears to show a ray being split into ordinary and extraordinary components. In sequential ray-tracing, rays can never split: one ray in must give only one ray out. The Mode flag in the parameters of the Birefringent In surface tells ZEMAX which ray to trace:

• if mode = 0, then ZEMAX traces the ordinary ray;
• if mode = 1, then ZEMAX traces the extraordinary ray

This layout plot is computed by using one configuration of the design with mode = 0, and another with mode = 1, and overlaying the plots for the two configurations: