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.