MTF v I I p J0 2ncpvpdpB7

M0 j0

The number M0 is a normalization at zero spatial frequency.

A problem with this calculation is not apparent from casual inspection. The upper limit of the integral assumes that the intensity is known out to an arbitrarily high angle. We can calculate the intensity out to any angle, of course, but there must be energy beyond that angle that we know nothing about. High angles are represented by very low spatial frequencies. Thus, at first glance it would seem that this energy would be automatically taken into account by forcing the normalization M0 to be the integral evaluated at v = 0.

This approximation throws a wrench into the works. A modulation transfer function calculated this way does have the proper value (i.e., 1) at a spatial frequency of 0, but at higher spatial frequencies, the calculated transfer function is too high. The inescapable conclusion is that the truncation of the angle causes a numerically diminished MTF at low spatial frequencies. In other words, if we have not gathered that distant energy in our intensity calculation, we had better not take tally of it in Eq. B.7. Therefore, the computational algorithm is slightly modified:

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