Tables for
Volume F
Crystallography of biological macromolecules
Edited by E. Arnold, D. M. Himmel and M. G. Rossmann

International Tables for Crystallography (2012). Vol. F, ch. 11.4, p. 289   | 1 | 2 |

Section 11.4.7. Integration of diffraction maxima by profile fitting

Z. Otwinowski,a* W. Minor,b D. Boreka and M. Cymborowskib

aUT Southwestern Medical Center at Dallas, 5323 Harry Hines Boulevard, Dallas, TX 75390–9038, USA, and bDepartment of Molecular Physiology and Biological Physics, University of Virginia, 1300 Jefferson Park Avenue, Charlottesville, VA 22908, USA
Correspondence e-mail:

11.4.7. Integration of diffraction maxima by profile fitting

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To accurately integrate diffraction peaks, the spot position has to be predicted accurately. Each integration program has its own procedure for predicting and fitting diffraction profiles. In DENZO, profile-shape prediction is defined by a weighted average of other reflection profiles present within some radius from the spot of interest. Each spot has its own prediction, which is continuously adjusted to variations of spot shapes over the detector. The profiles are added by shifting them to the same position, generating a normalized profile Pi, where [\textstyle\sum_i P_i=1]. In the second step, the measured pixels' values are fitted to a function[B_i+IP_i,\eqno(]where Bi is the predicted value for the background in pixel i and I is the diffraction intensity of the spot. The profile-fitting procedure minimizes the function[\displaystyle\sum\limits_i{[M_i-(B_i+IP_i)]^2\over V_i},\eqno(]where Mi are the measured pixel values and Vi are the variances of these measurements. The minimum of this function defines the value of the profile-fitted intensity (Otwinowski & Minor, 1997[link]):[I={\textstyle\sum_iP_i(M_i-B_i)/V_i\over \textstyle\sum_iP_i^2/V_i}.\eqno(]


Otwinowski, Z. & Minor, W. (1997). Processing of X-ray diffraction data collected in oscillation mode. Methods Enzymol. 276, 307–326.

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