A merit function defines the 'quality' of an optical design, in terms of how well the design meets its specified operating characteristics. In this case, we want to get the largest brightness (luminous intensity) at zero degrees angle. This is easily achieved with the NSDD and NSTR operands.

NSDD stands for Non-Sequential Detector Data. It is fully described in the Optimization chapter of the ZEMAX User's Guide. It takes as arguments the object number of the detector we want to read out, the pixel we want to read out, and a flag that defines where it returns the total power in the pixel, the power/unit area (illuminance) or power/unit solid angle (luminous intensity).

In this design, the detector is object number 3, and we want to obtain the luminous intensity at zero degrees. The detector viewer shows this:

This shows the angular range of the rays that are incident on the detector from the range -90° to +90° in both x and y. No rays land with angles beyond about 35° because the LED does not emit beyond this angle. Peak intensity occurs at around 27 degrees. We are interested in the power landing at angles close to zero. This is the central pixel in the display. The detector has 101 pixels in both x and y, so the central pixel is pixel number 5100 (out of 10201 total pixels). The following merit function retrieves the luminous intensity seen at this angle:

The first NSDD operand reads out detector object 0, which does not exist. This is a special usage of the operand: no object 0 can exist. ZEMAX instead clears all detectors.

Then, the NSTR operand tells ZEMAX to trace rays. The last NSDD operand reads out detector object 3, pixel number 5100, data item 2 which is power/unit solid angle. This value is approximately 25 Cd. Please see the User's Guide for full documentation on the usage of NSDD.

So, we know that near zero angle the luminous intensity is 25 Cd, and we want to optimize this number to be as large as possible. Because when we optimize we try to drive the merit function to zero, rather than trying to optimize the luminous intensity to be infinite, we will instead optimize the reciprocal of the luminous intensity to be zero. This is numerically a more stable approach. The last two lines of the merit function take the reciprocal and target it to zero.