A simple way to visualize what is happening is with UCSF ChimeraX. You can use
the gaussian filter function to select either the frown or the smile from the
“hidden_frown.map”, and then you can visualize the FFT structure factor
magnitudes for each one – here are the commands to do it -
open
Thanks to all who replied both on- and off-list.
A few (such as Charles below) have reported that using general-purpose
FFT algorithms, such as those available in Matlab or NumPy do, in fact,
get the smiley face map back. This is expected because such algorithms
do not have a resolution
Dear James,
The questions of optimally combining oversampling, blurring and
de-blurring to obtain accurate approximations of Fourier transforms by
discrete Fourier transform calculations are old hat: they go back to papers
by David Sayre in 1951 ('The calculation of structure factors by
Thank you Paul. This is interesting!
I have not played with super-sampling yet. I am assuming you mean
creating a new map 8x the size? If so, did you fill the interstitial
grid with zeroes? Local maximum? Linear interpolation? Tricubic spline?
And when you say "sharpen/blur" with a factor
