Predicted Behavior of the Corrector

The values for the paraxial focal lengths predicted by Zemax at all wavelengths were taken to be the "f'' terms in the predicted OFAD. Values for d₃ and d₅ were then obtained by fitting the OFAD model to the positions given by Zemax for the centroids of a number of images distributed uniformly throughout the field. This procedure yields models which predict Zemax's theoretical image locations with an rms error of less than 4µ in U and 2µ in all other colors.

As previously mentioned, the parameters given in Table 2 are not those of the corrector as it was designed, but come from measurements made after construction. To estimate the effect of any error in these measurements, Monte Carlo (MC) calculations were done during which the mechanical and optical parameters of the system were varied at random within the tolerances which were maintained during manufacture and final assembly. Every MC iteration creates a new, slightly different optical system which represents the way the corrector might have been put together. Each MC design was modeled in the same way as the nominal configuration, optimizing the image quality by refocussing after each iteration.

Image quality after a MC perturbation always remained within or very near to the design specifications, i.e. with the monochromatic D₇₀ not exceeding .25'' in the center and .50'' at the edge. The image center moved by as much as several hundred µs as a result of tilts introduced by the Monte Carlo process, but after recentering, a new OFAD model could always be found which was able to predict the new theoretical positions to an rms precision of 6µ or less. The system focal length varied from the nominal value by an average of +/-5mm from after each Monte Carlo calculation. The MC perturbations changed d₅ by an average of 30,000 units. Increases of d₅ were seen more often than decreases. Changes in d₅ were usually accompanied by changes of d₃ in the opposite sense.