Brightness Enhancement Film (BEF) is widely used in the design and manufacture of LCD screens and large-screen TVs. It is generally used to provide maximum brightness towards the on-axis viewer.

BEF uses a microreplicated prismatic structure to control the exit angle of the light. In this schematic diagram, rays from the source may undergo multiple total internal reflections, before emerging at close to on-axis angles with respect to the viewer. More details can be found here. Light within the viewing cone (approxinately 35° off the perpendicular) is transmitted out and light outside this angle is TIRed back into the film and recycled until it is within this cone angle.


In this article we will model the Vikuiti™ Thin Brightness Enhancement Film (T-BEF) 90/24 microreplicated prism film. From the manufacturer's datasheet, the nominal film properties are:

Thickness: 62µ
Prism Angle: 90°
Prism Pitch: 24µ

As the BEF is a micro-replicated prism array, we will use the Array object to model it. This is an ideal application of the Array object. A single object is replicated on an (x,y,z) grid. (In this case, we will only need the (x,y) grid.) Because of how this object is implemented in ZEMAX, an array of any size can be created without using more memory than the original parent object. Also, ray-tracing speed is largely unaffected by the size of the array. This makes the Array object vastly superior to alternate methods of modeling the BEF, such as CAD objects, which quickly become huge when you must model a 24µ prism pitch over a 50 inch TV screen diagonal!

The first thing to consider is which object to use to describe the 'primitive' prism which is to be replicated. Some possibilities are:

• A Polygon object (.pob object) as these are often used in prism modeling
• A Rectangular Volume object, which can be easily configured to model a wide range of prisms
• A CAD object

and others exist too. For this design, there is no reason to use CAD, the object is very simple and can be represented directly inside ZEMAX without recourse to STL or NURBS-based geometry. A .pob object would be easy to write and fast to trace, but loses the parametric control that is so useful in complex system design. As a result, in this article we model the primitive prism object using a Rectangular Volume object, configured as follows

Parameter Number	Parameter Description	Value	Comments
1: X1 half-width	half-width in x of the front face of the prism	12µ	Set from T-BEF 90/24 datasheet
2: Y1 half-width	half-width in x of the front face of the prism	12µ	Set from datasheet, pickup from parameter 1 enforces this condition
3: Z-Length	the height of the prism	12µ	Prism angle is 90° from datasheet, so prism height = X1 half width by definition: pickup from parameter 1 enforces this condition
4: X2 half-width	half-width in x of the rear face of the prism	12µ	Set to make a 'square faced' prism, see discussion below. Pickup from parameter 1 enforces this condition
5: Y2 half-width	half-width in y of the rear face of the prism	0	Forms a triangle with 90° apex angle given z-length and X1, X2 half-heights

The object looks like so:



This models the prism perfectly, but it ignores the substrate of the film. The prism has a height of 12µ, but the BEF has a total thickness of 62µ, so an extra thickness of 50µ is required.  A second Rectangular Volume object is used to provide the 'backing' material of the BEF:



This aspect ratio looks a little different to what is usually drawn for a BEF: the thickness of the backing is usually not drawn fully.

Now T-BEF 90/24 film is used in many applications, from mobile phones and PDA screens to LCD monitors and plasma TV screens. It is therefore used in many different sizes. It is convenient to use the x and y thickness parameters of the backing sheet to define the size of the piece of film used. We will then fill the film with as many prisms as are required.

To do this, we first set the size of the backing (in this screenshot it is set to 0.1 mm square) and set the (x,y) location of the prism object to be at the bottom left-hand size of the backing:



In this case the backing object is object number 1 in the NSC editor. It has X and Y half-widths defined by its parameter 1 and 2 columns. The X-position of the prism is picked up from the X-width of the backing like so:



The small offset is so that the prism is always on the 'inside' of the backing.

The file at this point is saved as 'BEF_Intermediate.zmx' in the zip archive that can be downloaded from the last page of this article.

Now that we have a single prism object correctly located on the backing material, we can now add an Array object as object number 3. This object has as its parent object the prism object, and it is positioned exactly co-located with it. As we do not need the parent object for ray-tracing, its 'rays ignore this object' and 'do not draw this object' settings are selected on, so that all ray-tracing is done with the array object.

So at this point, the prism shown below is actually the array object, set to produce a 1 x 1 array of prisms:



Note that the array object inherits all its shape, refractive, diffractive, gradient index etc properties from the parent, except 'rays ignore' and 'do not draw'. The array object's own properties allow you to define the number of replications in x, y and z, and the distances between replications in x, y and z. In this case we do not need to form the array in three dimensions, so the delta_z parameter is set to zero.

The delta_x and delta_y are defined by the size of the prism in x and y. Since we define these by the half-heights, we can just pick up these parameters, and multiply by two to define the x and y separations between the prisms. These are direclty linked to the defining parameters by pick-up solves.

Here for example is a 4x3 array of prisms:



Now, since we know the size of the backing material in x and y, and the size of the prisms in x and y, we can compute the number of prisms required to fill the backing material as just 2*(backing half width)/prism half-width. Pick-up solves allow this to be done automatically, giving:



The file is saved as BEF_model.ZMX. Its worth playing with at this point to understand how the 3 defining parameters:

• X-halfwidth of the backing material
• Y-halfwidth of the backing material
• X1-halfwidth of the prism

control all aspects of geometry the BEF. This is a very elegant demonstration of the power of ZEMAX's parametric-driven editors. The entire BEF can by dynamically regenerated easily with just these parameters. 

Note that if you increase the size of the BEF to a few mm square, ZEMAX will stop drawing the array and replace it with a bounding box instead. ZEMAX counts the number of triangles needed to draw the array, and if this exceeds the limit set in the 'Draw Limit' parameter, ZEMAX will not draw the array. The array still bends rays of course: its just that the drawing routines will take too long to be useful. The draw limit is easily controlled from the user interface to give the exact level of control required fro any given application.

By way of a simple example of the optical perfromance of the BEF, a simple system was built using the BEF_Model.zmx file.

A source object was been placed inside the BEF, at the top of one side. The source used Sobol sampling, and simple splitting was turned on. Neither of these are essential, but they are very useful, and very powerful features to enhance the study of illumination systems.

No attempt was made to make this a realistic model of an LCD illumination screen: rather this is just a simple demonstration of the optical properties of brightness enhancement films. It also shows just how efficient the Array object is in both memory usage and ray-tracing speed: a 5mm x 5mm piece of BEF requires 417² = 173,899 prisms. A 0.5 meter x 0.5 meter square piece (by no means unrealistic) requires 1.7 GIGA-prisms! This would be extremely unweildy to model any other way. As will be seen in this example, ZEMAX handles this with little extra memory requirement and very fast ray-tracing speeds, thanks to the internal architecture of the array object.

All the sides of the backing material object, except the one in contact with the array object, were set to be reflective:


as a result, rays can only escape via the prism face of the BEF. Note that no thin-film coatings were applied, because none are used in the manufacture of the BEF. They can be easily added to the ZEMAX model if needed.

Here is an example of the ray-tracing in the BEF:



note that the 'do not draw' property has been set on the array object so that the bounding box is not drawn either: however the multiple TIR-ing of the rays at the prism array can be clearly seen, even though the prism array is not drawn. The outcoupling of light at near to normal incidence to the BEF object can also be seen. In comparison, if the array object is set to 'rays ignore this object' so that there is no prismatic structure, the ray-trace is as follows:



and light is trapped by total internal reflection.

A detector object was also been defined. In the following screenshots, the detector shows the results of tracing 1 million rays. In the absense of the prismatic strucure, little light escapes the plastic sheet, as shown above, but when the prism structure is turned on, we get:



Here is the illuminance (spatial distribution of power) seen on the detector. The source was set to a nominal 1 Lumen output power:



and so a total of 0.3 lm is coupled onto the detector, with a peak illuminance of 484 Lux. The luminous intensity (angular distribution of power) is



The peak luminous intensity of 0.29 Cd occurs on-axis, and that the distribution is more compressed perpendicular to the prisms than parallel.

Again, note that this is just a simple file demonstrating the optical performance of the BEF array, and is not a model of a full LCD device.

The Array object capability in ZEMAX is ideal for modeling microreplicated arrays like Brightness Enhancement Film. In this case, just three objects are needed to define a BEF film of arbitrary size. The use of pick-up solves locks the three objects togetherr, so a BEF film of any size can be produced quickly and easily.

The memory required to hold the BEF array and the ray-tracing speed are virtually unaffected by the size of the BEF sheet used. Also the ability to automatically replace the prism array with a bounding box allows fast on-screen manipulation of the object.