Optimization of pure non-sequential (NS) systems is inherently more difficult than optimization of sequential systems. This difficulty stems from defining a merit function and computing the derivative of it with respect to variable parameters. If the energy in a given ray is assigned to only one pixel, there is no quantitative difference when a system change causes the ray to shift anywhere within that pixel. As a result, optimization is difficult, with discontinuous derivatives in the merit function occurring when a ray crosses the boundary into a new pixel; this is a very inefficient method for optimization.

ZEMAX contains several tools that significantly improve the optimization of NS systems. The first is “pixel interpolation” which solves the problem of discontinuous derivatives in the merit function.

Instead of 100% of a ray’s energy being assigned to the single pixel struck, a fraction of the energy is spread to adjacent pixels based upon the location of the ray intercept inside the pixel. As a result, there is a noticeable change in the merit function as a system change causes a ray to move across a pixel. We will see the difference this makes on optimization efficiency in the following example.

Also, the NSDD optimization operand has received added capabilities: computation of standard deviation and mean of all non-zero pixel values, intensity or irradiance centroid coordinates, and RMS distributions of pixel data from the centroid. For a detailed description of the new NSDD capabilities, see the Optimization chapter in the ZEMAX user’s guide. These features allow more efficient optimization for focus (minimize RMS spatial width), collimation (minimize RMS angular width), and uniformity (best signal to noise).