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Ron 
I don't think you should knock what the EM people do (at least for the reason 
you give!).

The grid they pick will be decided by all sorts of practical criteria 
determined by factors like tilt requirements/constraints, radiation damamge 
(not that again) etc. They will often oversample the data and this is good 
practise. The question you raise is however relevent.  

The Niquist-Shannon sampling theorem should provide the answer regarding the 
number of unique observations if you know the thickness perpedicular to the 2D 
crystal. If the thickness is A and you are measuring intensities the minimum 
sampling interval is 1/2A (1/A if measuring amplitudes with phases). This 
interval essentially defines the number of unique observations (with phases the 
real and imaginary components can each be regarded as unique observations) and 
we can compare what they have with the 3D crystallographic case.

Note that for the crystallographic case (1D, 2D or 3D), the sampling given by a 
reciprocal lattice (real lattice dimension A) is 1/A - fine if you have phases 
but undersampled if you only have intensities.

Of course if they quoted the large  number of (oversampled)observations as 
being unique that would be misleading. 

Colin
-----Original Message-----
From: [EMAIL PROTECTED] [mailto:[EMAIL PROTECTED] Behalf Of
R. Stenkamp
Sent: 28 April 2006 15:59
To: Bart Hazes
Cc: [EMAIL PROTECTED]; [email protected]
Subject: Re: [ccp4bb]: Acceptable Rmerge values in last resolution shell


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Three comments about "observations" (just to point out a few
other aspects of "observations", etc):

1.  Reflections with zero intensities are useful in refinement, even
if they don't contribute much to Fo maps.  They provide important
restraints on the electron density.

2.  I've slowly discovered that some data reduction programs count
partials as "measurements".  I understand why you'd do that, but
it's a tad confusing when the number of measured reflections gets
so large.

3.  And another slow realization on my part is that our cryo-EM
colleagues have a wonderful way to increase their number of
observations.  They pick an arbitrary (or at least it looks that way
to my un-trained eyes) grid in reciprocal space to sample their
diffraction pattern perpendicular to the 2-d crystals.  There must
be some guidelines for acceptable choices for that sampling interval,
but if they change it a little, they can change their number of
observations by large numbers.

Ron


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