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 Fourier
summation', Acta Cryst. 4, 362-367) and were dealt with in a landmark paper
by Lynn Ten Eyck in 1977 ('Efficient Structure-Factor Calculation for Large
Molecules by the Fast Fourier Transform', Acta Cryst. A33, 486-492) with a
follow-up by Jorge Navaza in 2002 ('On the computation of structure factors
by FFT techniques', Acta Cryst. (2002). A58, 568-573). All the ideas needed
to understand the phenomenon you describe (i.e. aliasing errors) are already
presented with remarkable clarity in David Sayre's paper.
With best wishes,
Gerard.
--
On Sun, Apr 30, 2023 at 02:15:54PM -0700, James Holton wrote:
> 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 of 4. Is 4 a scale
> factor? or a B factor?
>
> Cheers, and I hope you had a pleasant weekend,
>
> -James
>
> On 4/28/2023 5:29 PM, Paul Emsley wrote:
> >What fun!
> >
> >super-sampled by a factor of 2 then sharpen/blur with a factor of
> >4 gives a superposition
> >
> >Paul.
> >
>
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