B63 Comparison with Published Patterns

Perhaps the most severe test of the approximation here was the comparison of patterns generated by ASYMM with published contour plots for coma and astigmatism. The coma contour plots were figured analytically by R. Kingslake

(1948), but they are most commonly available as reprinted in Born and Wolf (6th ed., 1980). The astigmatism contour plot was published by Nienhuis and Nijboer

The expressions for aberration differ somewhat from the primary aberrations used to derive these contour plots, but if we trace through the details, we find that 3.2 and 6.4 wavelengths of primary coma translate to 2.13 and 4.27 wavelengths of peak-to-valley coma aberration as defined at Zernike diffraction focus. In other words, coma as defined here is 2/3 the coefficient appearing in Born and Wolf. Likewise, the amount of astigmatism used there was 0.64 wavelengths, which translates to 1.28 wavelengths peak-to-valley astigmatism. The patterns as drawn by ASYMM appear in Fig. B-5. They match the overall shapes of the contour plots very well (axes were relabeled in Born and Wolf pp. 478, 480).

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