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

International Tables for Crystallography (2006). Vol. F, ch. 11.3, p. 219   | 1 | 2 |

## Section 11.3.2.4. Spot centroids and partiality

W. Kabscha*

aMax-Planck-Institut für medizinische Forschung, Abteilung Biophysik, Jahnstrasse 29, 69120 Heidelberg, Germany
Correspondence e-mail: kabsch@mpimf-heidelberg.mpg.de

#### 11.3.2.4. Spot centroids and partiality

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The intensity of a reflection can be completely recorded on one image, or distributed among several adjacent images. The fraction of total intensity recorded on image j, the `partiality' of the reflection, can be derived from the distribution function as The integral is evaluated by using a numerical approximation of the error function, erf (Abramowitz & Stegun, 1972).

While the spot centroids in the detector plane are usually good estimates for the detector position of the diffraction maximum, the angular centroid about the rotation axis, can be a rather poor guess for the true ϕ angle of the maximum. Its accuracy depends strongly on the value of ϕ and the size of the oscillation range relative to the mosaicity of the crystal. For a reflection fully recorded on image j, the value will always be obtained, which is correct only if ϕ accidentally happens to be close to the centre of the rotation range of the image. In contrast, the ϕ angle of a partial reflection recorded on images j and is closely approximated by . If many images contribute to the spot intensity, is always an excellent approximation to the ideal angular position ϕ when the Laue equations are satisfied; in fact, in the limiting case of infinitely fine-sliced data, it can be shown that .

Most refinement routines minimize the discrepancies between the predicted ϕ angles and their approximations obtained from the observed Z centroids, and must therefore carefully distinguish between fully and partially recorded reflections. This distinction is unnecessary, however, if observed Z centroids are compared with their analytic forms instead, because the sensitivity of the centroid positions to the diffraction parameters is correctly weighted in either case (see Section 11.3.2.8).

### References

Abramowitz, M. & Stegun, I. A. (1972). Handbook of mathematical functions. New York: Dover Publications.Google Scholar