We will perform the same optimization using instead the added capabilities of the NSDD optimization operand and pixel interpolation. In the previous method for optimizing the mirror, the merit function was defined to increase the brightness (luminous intensity) of the central pixel in angle space. Using this method ZEMAX will attempt to make changes to the mirror that only increase intensity of the central pixel. If a change decreases the vergence of the beam in general, but does not increase central pixel intensity, the optimization algorithm sees the change as ineffectual. However, reduction of beam vergence is clearly beneficial if our goal is to attain a high degree of beam collimation. A better set of operands to use would be centroid position and RMS width of the beam in angular space. We will specify the criteria in the merit function editor:

NSDD operands 6 and 7 specify the target centroid coordinates of the luminous intensity and NSDD operand 8 specifies the target RMS radius of the luminous intensity data. Using these criteria, any change that causes an increase in central pixel luminous intensity will shift the centroid closer to (0,0). Additionally, a reduction in vergence of the beam will cause the RMS radius to move closer to 0. These criteria more accurately describe what we are attempting to achieve and our results will show improved performance as a consequence.

Before we begin to optimize the system, let’s take a look at the universal plot to see how the modified merit function improves optimization efficiency.



The new merit function shows greater continuity even without pixel interpolation. The optimization algorithm can converge on a solution very quickly in such a solution space, and the optimization we perform will confirm this.

In the same manner as previous optimizations, we begin with a radius value of -100. Using this step wise optimization (radius; radius & conic; all coefficients), the DLS algorithm is able to come to a superior design in an astonishing 1/100th of the time it takes the global search optimizing for central pixel luminous intensity. The luminous intensity plot below shows the optimized distribution using the new NSDD operands.



The central pixel luminous intensity of 260 Cd is higher than that attained with the previous optimization method (~250 Cd), and the RMS width is vastly improved; all in a fraction of the time. If pixel interpolation is disabled for this optimization, the central pixel brightness is even higher (265 Cd) because all the energy hitting the central pixel is assigned to it. A final hammer optimization would further improve this result.