ZEMAX Development Corporation thanks Optima Research Ltd for permission to use the brightness enhancement filter POB object used in this article.

When light travels from one refractive index to another, a partial reflection occurs because the speed of light is different in the two media. This means that some fraction of the energy is transmitted, and some fraction is reflected. Additionally, some energy may be lost (absorbed) especially if the interface has a metallic coating on it.

Partial reflections are sometimes known as Fresnel reflections. ZEMAX has sophisticated models of Fresnel reflections from bare and coated surfaces, including complex multi-layer coatings.

When a ray intersects the surface of an object, ZEMAX computes the fraction of energy transmitted, reflected and absorbed at the interface. It can then split the ray into two: a reflected and a transmitted ray, with the correct relative energy.

For example, open the sample file contained in {zemaxroot}/samples/ray splitting/beam splitter.zmx:

The initial ray (drawn in dark blue) hits the front of the beamsplitter cube and 1% (approximately) of the energy is reflected. ZEMAX generates a new ray that takes that 1% of energy. This ray then hits the detector object and is terminated.

The transmitted ray now carries 99% of the energy, and it hits the 50/50 beamsplitter coating at the intersection of the two prisms. Another new ray is generated to take away the reflected 49.5% of the ray energy, and 49.5% is transmitted. These rays then hit the exit face of the prism, and 1% is reflected again. This process of ray-splitting continues until all rays have hit a detector, or until the energy in the ray is less than some user-defined threshold:

In this case, we continue tracing rays until the energy in a segment has fallen below the minimum relative ray intensity threshold of 10^-7. This is the recommended and most accurate method of tracing rays and accounting for the energy in all directions.

In some cases -and in particular in illumination systems- a simpler approach can be adopted: Simple Ray Splitting. In this case, the ray either reflects or transmits, but it does not split. The probability of reflection/transmission is defined by the reflectivity/transmission coefficients of the ray. In this case, each ray sees one defined path, as shown below:

In this particular case, simple splitting is not a good idea, as we want to get good data on the back reflections. But in illumination systems we are not usually concerned with ghosts of ghosts of ghosts, and so the simpler approach can bring speed benefits.