We will re-optimize the free-form mirror that was used in the article "How to Improve the Brightness of an LED Using a Free-Form Mirror". Download and open the “starting point.zmx” file from the last page of this article. The system modeled contains an LED with a flat mirror in the beam path directing light onto a detector plane. The desire is to optimize the mirror to have the highest degree of beam collimation.

To get an idea of a good place to start the design, we’ll take a look at the universal plot. To open this feature go to Analysis>Universal Plot…New Universal Plot 1D. Enter the settings as shown below:



Here is a plot of merit function versus base mirror radius without pixel interpolation:




And the following one is with pixel interpolation:




Pixel interpolation removes the discontinuous derivatives in the merit function that can slow down optimization.

For the first system optimization, we will only enable pixel interpolation. Otherwise, the steps and variables will be identical to the previous optimization article; we set more variables for each optimization attempt. We begin with the mirror radius as the only variable and set it to -100. It is usually a good idea to begin with some non-zero radius value. Asking the optimization algorithm to change the radius from infinite to small and finite in one step is very inefficient and can lead to stagnation.

After all variables have been allocated to the optimization, orthogonal descent has come to a solution with a central pixel brightness of 220 Cd. The distribution as shown below has a much lower vergence than optimization without pixel interpolation.