I know this question has been answered and Dirk has waved off further
discussion but... I have an answer from a different than usual perspective
that I've been dieing to try out on someone.
Assume you have a one dimensional crystal with a 10 Angstrom repeat.
Someone has told you the value
Assume you have a one dimensional crystal with a 10 Angstrom repeat.
Someone has told you the value of the electron density at 10 equally
spaced points in this little unit cell, but you know nothing about the
value of the function between those points. I could spend all night
with a
Dear colleagues,
I just stumbled across a simple question and a seeming paradox for me in
crystallography, that puzzles me. Maybe, it is also interesting for you.
The simple question is: is the discrete sampling of the continuous
molecular Fourier transform imposed by the crystal lattice
Hi Dirk
I think you're confusing the sampling of the molecular transform with
the sampling of the electron density. You say In the 1-dimensional
crystal, we sample the continuous molecular transform at discrete
reciprocal lattice points according to the von Laue condition, S*a =
h. In fact the
Is the simplest answer that we indeed do not get all of the
information, and are accordingly missing phases? My understanding is
that if we were able to sample with higher frequency, we could get
phases too. For example, a lone protein in a huge unit cell would
enable phase determination. Taken
Hi Dirk,
If you have a N points of a 1D real discrete function, there will be Fourier
coefficients indexed h=0,1,2,...,N-1. Taking N as odd, there will be
int(N/2)+1 independent Fourier coefficients but your h(max) will in fact
be 'N-1'. In crystallography we write h(N-1) as h(-1) etc and
Dear Ian,
oh, yes, thank you - you are absolutely right! I really confused the
sampling of the molecular transform with the sampling of the electron
density in the unit cell! Sometimes I don't see the wood for the trees!
Let me then shift my question from the sampling of the molecular
Dear Dirk,
The factor of 2 comes from the fact that the diameter of a sphere is
twice its radius. The radius of the limiting sphere for data to a certain
resolution in reciprocal space is d_star_max. If you sample the electron
density at points distant by delta from each other, you periodise
Dear Dirk,
You are getting confused about where the sampling occurs, and this is
perhaps because we usually learn about the Shannon criterion from a
certain way around (sampling in real/time space - periodicity of the
signal transform in frequency/reciprocal space). To see the Shannon
criterion in
Dear colleagues of the CCP4BB,
many thanks for all your replies - I really got lost in the trees (or
wood?) and you helped me out with all your kind responses!
I should really leave for the weekend ...
Have a nice weekend, too!
Best regards,
Dirk.
Am 15.04.11 13:20, schrieb Dirk Kostrewa:
Hi Dirk,
My interpretation of your question is what is the impact of resolution given
by the individual diffraction spots from the electron density sampling and
the Nyquist theorem. My explanation would be that the Nyquist theorem gives
an upper limit to the frequency information that can be
2011 12:20
To: CCP4BB@JISCMAIL.AC.UK
Subject: [ccp4bb] Lattice sampling and resolution - a seeming paradox?
Dear colleagues,
I just stumbled across a simple question and a seeming paradox for me
in
crystallography, that puzzles me. Maybe, it is also interesting for
you.
The simple
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