How to model an LCD backlight

In this article, a wedged LCD backlight is modeled, analyzed, and optimized for illumination output criteria.

Authored By Akash Arora


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Liquid crystal displays (LCDs) are ubiquitous nowadays as a display technology. The most prominent applications in the commercial sector include computer monitors, cellular phones, televisions, and handheld digital devices.

The majority of LCDs are illuminated from the rear to provide lighting when ambient conditions are insufficient. The two illumination schemes employed are bottom-lit and edge-lit. While OpticStudio has the capability to model either illumination scheme, the edge-lit configuration poses a more involved design problem and will be the focus of the article. 

LCD illumination schemes

The bottom-lit LCD configuration uses an array of sources, such as light emitting diodes, or one uniform source, such as an electro-luminescent panel, placed behind the LCD. This configuration gives excellent uniformity and brightness, but requires more energy and thicker housing.


See here for reference.

The edge-lit design is the focus of this article. It uses a wedged guide to distribute light from a source placed beside the LCD display. This configuration uses less energy and can be housed in a thinner package, but sacrifices uniformity and brightness.


See here for reference.

We will ignore the actual liquid crystal layer and consider only the backlight design in this article.

Modeling the backlight

A detailed layout of the edge-lit LCD is shown below:


The source is usually a cold-cathode fluorescent lamp (CCFL) or a series of light-emitting diodes (LED). A reflector is placed behind the source to increase the efficiency of the system. A wedged light guide exploits total internal reflection (TIR) to distribute light more evenly across the display area. Mirrored surfaces surround the light guide, also for the purpose of increasing efficiency. A patterned array, referred to as brightness enhancement film (BEF), is used to control the luminous intensity and polarization of the emitted light.

In this design case, we will assume certain constraints. The area of the display will be based upon a standard cellular phone. The light guide thickness will be chosen to limit the overall package height. 

Display area: 75 mm x 75 mm

Wedge thickness: 4 mm input face, 1 mm end face

BEF: Vikuiti™ T-BEF 90/24

Download the necessary files located on the last page of this article. Place the glass catalog in the {Zemax}\Glasscat directory. This catalog contains modified acrylic and PMMA to model the approximate internal transmission values (93% over 25 mm) of these plastics. The basic design and parameters are defined in the “Starting Point.zmx” file. Note the source/object types in the Non-Sequential Component Editor (NSCE) used to model the different backlight components.


A CCFL emits light when excited electrons strike the coating material on the tube surface. The “source tube” is ideal for this type of source emission. We could alternately use the “source diode” to model a 1D array of diodes as the source.

The wedged light guide is modeled with a rectangular volume object made of acrylic material. This object allows different end face dimensions and tilts. Note that we want to keep the upper face of the light guide parallel to the X-Z plane and must tilt the object to do so. A slight positional change in Y is also needed because we are rotating about the center of the input face, not the top edge. Pickup solves on the tilt of the front and rear faces ensure that they remain parallel to the Y-Z plane.


The BEF is the most complex component in the system. Replicating the parent prism by hand would be time-consuming and require extensive memory during ray tracing. The array object is a much better choice because it requires only as much memory as the parent object, and the entire array can be altered by adjusting the parameters of the parent. Note the ray tracing speed of the array even though it is still a geometry object.

Determining initial performance

Now that the basic system is modeled, let’s take a look at the initial performance. The criteria often used in determining design merit are energy efficiency and uniformity (illuminance and luminous intensity). Energy efficiency is defined as the ratio of energy emitted by the display to the energy emitted by the source. In position space, the desired output should be uniform across the display (minimum flux per pixel deviation). In angle space, the output should be uniform within a small (~30 deg) half-cone angle. Remember that we are using this design for a small digital device. If the design application was a television or computer monitor, we would want a much larger half-cone angle (~90 degrees).

Trace rays with the following Ray Trace Control settings and notice the energy lost due to thresholds.


Looking at the detector viewer we can see that about 40% of the source energy is getting to the detector; this value may vary up to a few percent based upon the random nature of the Monte Carlo ray-trace. There is some energy lost due to ray errors, but this is insignificant in this application. Most of the energy is lost due to bulk absorption in the waveguide, however, almost 10% is lost due to thresholds. This is common in systems where rays undergo multiple reflections. Eliminating this loss requires reducing the minimum relative ray intensity by a few orders of magnitude. This can be done if the lost energy is significant, but it will noticeably slow down the ray trace. Reducing the threshold to 1E-6 reduces the lost energy to 1% and increases the efficiency to about 46%.


Take a look at the illuminance and luminous intensity distributions. The illuminance is highest on the side of the display opposite the source. This is a consequence of the light guide causing high angles of incidence, and thus TIR, close to the source. The luminous intensity plot shows several peaks rather than the desired uniform distribution at smaller angles. As we will see, this intensity distribution is characteristic of the wedged light guide and BEF.


There are few geometry parameters in the system as it is currently defined that will correct these distributions. The most effective means of doing so is to introduce scattering properties to the wedged light guide. The input, top, and bottom faces have the greatest effect on the illuminance and luminous intensity distribution.

Apply a Lambertian scattering profile to the input face of the light guide with the following settings.


Trace rays and observe the difference in output characteristics. Make sure “Scatter Rays” is checked in the Ray Trace Control dialog!


The efficiency of the system increases a few percent and the illuminance uniformity is much improved. The luminous intensity is slightly better, but some hotspots remain that must be resolved.

Now, remove the scatter profile from the front face of the light guide and apply one to the top face. The rectangular volume is defined by default with three face groups, so we cannot set only the top or bottom face to be diffuse. Instead, we will place a scattering rectangular volume coincident with the top face that effectively adds a scatter profile just to this surface. The nesting rule will give precedence to this new volume at the interface if this object follows the rectangular volume in the NSCE. Insert a rectangular volume object at Object 7 with the following parameters:

Y-Pos = 2

Z-Pos = 38.5

X-Tilt = -90

Material: Blank (Air)

X1, X2, Y1, Y2 Half Widths = 37.5

Z Length = 0.01

Lambertian scattering profile: front face only

Leave all other parameters as their defaults. Trace rays and note the change in output.


The illuminance uniformity is degraded, but the luminous intensity hotspots are resolved; the efficiency is also drastically increased. It appears that there is a tradeoff between the spatial and angular distribution of the output. If a similar scattering function is applied to just the bottom face we find that the efficiency is reduced.

Based on our results, it would seem the ideal scattering profile would be on the top face of the light guide and would scatter less light near the source and more towards the opposite end. The array object has the capability to model just such a non-linear pattern.

Optimizing the backlight

The most common microstructures used in wedged light guides today are molded extrusions/intrusions. These have the advantage of not requiring extra processing steps, such as printing scattering dots onto the light guide. For this design, we will use spherical shapes for the individual microstructures, although any object (native, imported, boolean, etc.) could be used. This is accomplished by placing an array of spheres in contact with the upper face of the light guide. By placing these objects after the light guide in the NSCE and defining their material as air, the effect is to model spheres embossed on the light guide (remember the nesting rule). The parent sphere and array object are added to “Mid Point..zmx” in the attachments of this article.

Upon opening the file, note the draw limit parameter on array object 12 is set very low because of the large number of elements in the array; drawing all the elements would require extensive rendering time. Instead, OpticStudio draws a bounding box around the entire array.

We want to optimize the parameters of the array to achieve the best performance criteria as stated on the previous page. The needed merit function is already defined in the current file. Open the merit function editor.


Operands 5 and 8 are used to maximize spatial uniformity and total flux, respectively. Operands 10 and 11 are used to control the centroid of the luminous intensity distribution. Operand 13 is used to control RMS radius of the intensity distribution. We don’t want the output to be perfectly collimated, but rather limited to some range of viewing angles; as such a target of 30 degrees has been specified. The last sets of operands (15-18) are boundary constraints to prevent the array from becoming too large or small; these are necessary because optimization has a tendency to produce extreme solutions if unbounded. Note the negative weightings on these operands. These act as Lagrangian multipliers that force the target to be met.

The variables to allocate for optimization are as follows:

Sphere object: radius

Array object: Number X’ & Y’, Delta1 X’ & Y’, Delta2 Y’

The array only needs to be non-linear in the y-direction due to symmetry considerations. As such, we only allocate the linear array spacing (Delta1 X’) in the x-direction. Also, we most likely will not need 3rd and 4th order variability for the array, so we will not allocate these as variables.

Optimization is generally more efficient if you give OpticStudio a finite starting value for variables rather than beginning with zero. To determine a good starting point for the 2nd order y-spacing, we will look at a universal plot of spacing versus merit function value. Open a 1D universal plot (Analysis...Universal Plot) and apply the following settings.


Press OK and allow the plot to update; this may take a few minutes depending on the speed of your computer. Based upon the following plot, we will set the “Delta2 Y’” parameter on the array object to 5E-3.


The backlight design form is constant and we only need to optimize the array parameters. Given this fact, hammer optimization using the orthogonal descent (OD) algorithm is a good choice for our needs. Hammer performs best with extended runs, and afterward, we can be relatively certain there is not a better design very similar to our starting point. After running the hammer optimizer for approximately 20 hours, OpticStudio arrives at a solution with excellent spatial uniformity and acceptable luminous intensity. Be aware that the intensity emission is characteristic of this type of light guide and cannot be altered significantly without drastically changing design parameters. The optimized system is provided in the attachments: “End Point.zmx”.


Also, note that system efficiency has risen to approximately 60%. If we decrease the minimum relative ray intensity threshold we find that the efficiency is closer to 62%. Further improvements might be possible by adding additional scattering and/or coating properties in the system.


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