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, ZEMAX 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 ZEMAX 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 afterwards 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, ZEMAX 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.