Dear Bernhard,
You are being charmingly modest and self-critical: your philosophical
discourse has always contributed to broadening an initially narrow question
in an enlightening way :-) .
In this case, it seems to me that Rohit's narrow question itself has
only been touched upon. Clearly, we know what is meant by the "redundancy"
he mentions in his question, independently of the extent to which it can or
not help reduce errors in the final merged data: it is the number of times
that unique reflections are measured through symmetry equivalence, and
perhaps Friedel equivalence if no anomalous differences are to be ignored.
Kay's gives an outline of a formula, but I would say that it is a very
"noisy" outline, in the sense that it suggests a linearity that applies only
in the limit of very high multiplicity. The main thing is that when one is
far from that limit, redundancy can be very uneven across the set of unique
reflections (it can even be zero for a subset of them if the available
frames do not achieve completeness) and that this pattern depends not only
on the space group but on the orientation of the symmetry axes with respect
to the rotation axis. Of course, as you add frames, you add more reflections
and something is bound to increase; but the way in which that increase is
distributed between completeness and redundancy can be quite capricious.
This was the motivation for Raimond Ravelli's beautiful work on his STRATEGY
program (http://www.crystal.chem.uu.nl/distr/strategy.html). In the days
when people alway tried to collect a complete dataset in a minimum number of
frames, one moment of inattention caused by synchrotron fatigue could easily
lead to collecting half the data with a multiplicity of 2 instead of
complete data with a redundancy of 1, e.g. if one forgot about a 2-fold axis
perpendicular to the rotation axis that perversely related the second half
of the dataset to the first. Raimond told me that he was once bitten in this
way, and promised to himself that he would never be again - so he wrote his
program!
I am digressing (into history rather than philosophy) myself ... . The
short answer to your question, Rohit, is ... that there is no short answer
to it in the guise of a simple formula, unless you have a very large
redundancy. Talking about "redundancy" as a single number is also
misleading: it is a distribution, whose magnitude can vary a lot across the
set of unique reflections - unless, again, it is very large everywhere. All
data processing programs will give you an idea of that distribution, at
least as a function of resolution (although it would often be useful to be
able to examine it in 3D).
With best wishes,
Gerard.
--
On Sun, Jan 18, 2015 at 02:12:51PM +0100, Bernhard Rupp wrote:
> In defense of redundancy:
>
> While the IUCr online dictionary is notably silent about multiplicity, the
> term itself seems
> already oversubscribed and used differently in various crystallographic
> contexts.
>
> (i) Each general or special position in a crystal structure has a certain
> multiplicity, defined by symmetry.
>
> (ii) General reflection multiplicity M is usually is defined by reflection
> symmetry, and
> when reflections are affected by special operations, the resulting
> corresponding
> lower multiplicity because they map onto themselves is accounted for in the
> epsilon factor e.
>
> Btw a useful table of M and e is Iwasaki & Ito Acta Cryst. (1977). A33,
> 227-229
>
> (iii) In case of Laue patterns, overlap of higher order reflections is also
> called Multiplicity afaik
> (various Helliwell/Moffat et al papers explain this).
>
> So expanding the term multiplicity to include multiple instances of
> measurements of the same reflections
> - while admittedly avoiding the connotation of obsolescence - adds to its
> promiscuous meaning,
> where context becomes part of the definition....
>
> I abstain from making any suggestions because in the past this has led to
> interesting
> but time-consuming philosophical discourse, proving in general the
> multiplicity of my reflections
> and positions redundant if not obsolete.
>
> Best, BR
>
> -----Original Message-----
> From: CCP4 bulletin board [mailto:CCP4BB@JISCMAIL.AC.UK] On Behalf Of Kay
> Diederichs
> Sent: Sonntag, 18. Januar 2015 09:28
> To: CCP4BB@JISCMAIL.AC.UK
> Subject: Re: [ccp4bb] Redundancy vs no of frames
>
> Dear Rohit Kumar,
>
> I prefer the term "multiplicity" instead of "redundancy" because the latter
> has a connotation of "not really needed any more".
>
> The relation then is
>
> multiplicity = c * number_of_frames * oscillation_range
>
> where the constant c depends mainly on the space group.
>
> HTH,
>
> Kay
>
> On Sun, 18 Jan 2015 02:35:46 +0530, rohit kumar <rohit...@gmail.com> wrote:
>
> >Dear all,
> >
> >Can anyone tell me how to calculate number of frames from redundancy or
> >vica versa
> >
> >Thank you
> >
--
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