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International
Tables for Crystallography Volume F Crystallography of biological macromolecules Edited by M. G. Rossmann and E. Arnold © International Union of Crystallography 2006 |
International Tables for Crystallography (2006). Vol. F. ch. 11.2, p. 216
Section 11.2.6.5. Profile fitting very weak reflections
aMRC Laboratory of Molecular Biology, Hills Road, Cambridge CB2 2QH, England |
For very weak reflections, all pixels will have very similar counts and therefore all the weights will be the same. For simplicity, consider the case where the profile fit is evaluated only for the peak pixels, then equation (11.2.6.15![[link]](/graphics/greenarr.gif)
) reduces to ![[I_{P} \simeq {\textstyle\sum} P_{i} \left(\rho_{i} - ap_{i} - bq_{i} - c\right) {\textstyle\sum} P_{i} \big/ {\textstyle\sum} P_{i}^{2}. \eqno(11.2.6.21)]](/teximages/fach11o2/fach11o2fd33.svg)
The second and third summations in this equation depend only on the shape of the standard profile. This shows that the intensity is a weighted sum of the individual background-corrected pixel counts (rather than a simple unweighted sum, as is the case for summation integration). Because the values of ![[P_{i}]](/teximages/bach2o3/bach2o3fi245.svg)
are a maximum in the centre of the spot, this will place a higher weight on those pixels where the contribution of the Bragg diffraction is greatest, and a very low weight on the peripheral pixels where the Bragg diffraction is weakest. In this way, profile fitting improves the signal-to-noise ratio without the risk of introducing any systematic error that may result by simply reducing the size of the peak region for weak spots.
