B61 Comparison of Aperture and ASYMM

Two dissimilar procedures were used to generate diffraction patterns in the symmetric and asymmetric programs. Even though both programs have a pedigree that traces back to Eq. B.3, very little resemblance between them can be easily seen. They use different routines and are written in different languages. We can calculate the same situations using these two separate procedures and verify that the answers are indeed the same.

Taking a circularly-symmetric pupil and cranking it through the slow, direct-integration program ASYMM, one should obtain the same answer as APERTURE does. Tests were done for a number of pupils, and good comparisons resulted. Two such images appear in Fig. B-3; the point spread functions appear in Fig. B-4.

The pictures are virtually identical except for a slight azimuthal structuring of the ASYMM output. A possible reason for this image difference is discussed below in section B.8.

Had these programs generated markedly different patterns, we would not have known whether either was correct. But because two quite dissimilar routines generate the same answer, they are either coded correctly or an unlikely accident has occurred—an error that exhibits itself identically in both procedures. Lacking evidence to the contrary, we will assume that they are correct for now and proceed with other checks.

This verification does not support the original theory contained in Eq. B.3. It merely says that the programs seem to be calculating Eq. B.3 correctly. A partial confirmation of the theory has been performed experimentally, but diffraction patterns from real apertures are exceedingly compact. Hence, their brightnesses are difficult to measure quantitatively (Taylor and Thompson 1958, Burch 1985).

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