Realized that my previous entry about gcf's was somewhat missing the point. There I used a map of DASI field A6 to illustrate how close one gets to the direct transform result. Since this field contains a strong point source it makes it look like the exp-sinc gcf gets close to the direct result out until very close to the edge of the image. But in fact there is divergence much closer in. Considering a field of random noise only - extending to infinity - the rms fluctation starts to be suppressed only half way out or so. See the following plot:
Difmap does the FFT (with exp gcf) on a double size grid, and gives you only the central quarter of the area. This produces a result which is for practical purposes identical to the direct FT. I will use it from now on. See the following plot:
Also played with doing just the gcf FFT double size - doesn't really improve.