# What is Simple Splitting?

This article explains what the “Simple Splitting” feature is and when it should be used.

Authored By Mark Nicholson

## Introduction

When a ray hits a surface, it is partially reflected, transmitted, and absorbed upon the surface properties. This energy splitting is modelled in two ways within OpticStudio.

The first consists of splitting the incident ray into two, one reflected and one transmitted. Once a ray splits, each of the “child” rays will strike another object, and the rays may split again and again, usually resulting in a large amount of rays.

The second method - Simple Ray Splitting - consists of choosing the ray path based on the probability of reflection or transmission at the surface. Whichever path is selected, the reflected or refracted ray will be assigned all the energy that would have propagated down both paths. This article will focus on this method.

## What is Simple Splitting?

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. OpticStudio 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, OpticStudio 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, see the figure below:

The initial ray (drawn in dark blue) hits the front of the beamsplitter cube and 1% (approximately) of the energy is reflected. OpticStudio 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 beam splitter 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 particularly 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. The advantage to using Simple Ray Splitting is that fewer rays are traced, so computations are faster. The disadvantage is that the rays traced contain less detailed information.

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.

## Using Simple Splitting

Open the sample file {Zemax}\Samples\Non-Sequential\Ray Splitting\a simple brightness enhancement filter.zmx:

A brightness enhancement filter (BEF) is used in LCD backlighting to improve the coupling of light to the outside world. It is made up of a series of prisms on the rear side of a plastic sheet. In this file, the BEF is modelled as a polygon object (POB):

The ray bending produced by the BEF causes light to flow out of the filter on the opposite side, and therefore improved brightness and illumination uniformity. Note that the plastic sheet is being illuminated by a single cylindrical source (inside a parabolic mirror) along one edge only.

Now this is a good case where Simple Splitting improves ray-tracing speed with little loss of accuracy. Because we are interested only in the out-coupled light, we get a ray-tracing speed improvement of a factor of 6, with no loss of accuracy.

Therefore, in illumination systems, Simple Splitting can often give big productivity gains. However, the results should always be tested against full splitting, in order to establish confidence. In stray light work, where ghosts of ghosts of ghosts are important, full sampling will be both faster and more accurate.

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