The two most fundamental properties of a ray are position and direction.

Position is defined by the vector r = {x, y, z}. The coordinates are measured in units of length commonly called "lens units".

Direction is defined by the vector k = {l, m, n}. The values are the direction cosines of the unit vector that points along the ray.

Both r and k may be measured in surface local coordinates, or in global coordinates relative to some reference frame.

If a ray is propagated a distance t, where t is a length in lens units, the new coordinates are given by r' = r + t k.

For a discussion of how rays are traced to specific types of optical surfaces, see reference 1.

ZEMAX can trace a single ray and create a table of the ray coordinates and cosines, as well as other data, using the Analysis > Calculations > Ray Trace feature.

The coordinates of the ray are listed at each surface, starting from the object. The direction cosines listed for a surface are always after refraction, reflection, or diffraction into the next surface.