Section 11.4.6.3. Detector distortions

The design of detectors results in pixels not being positioned on an exact square or rectangular grid. A correct understanding of the detector distortions is essential to accurate positional refinement. The types of distortions are detector-specific. The primary sources of error include misalignment of the detector position sensors and optical or magnetic distortion in CCD-based detectors. If the detector distortion can be parameterized, then these parameters should be added to the refinement. For example, in the case of spiral scanners, there are two parameters describing the end position of the scanning head. In a perfectly adjusted scanner, these parameters would be zero. In practice, however, they may deviate from zero by as much as 1 mm. Such misalignment parameters can correlate very strongly with other detector and crystal parameters, particularly for low-symmetry lattices or in the case of low-resolution data. If the distortions are stable, it is better to determine them in a separate experiment optimized for that task.

Fibre-optic tapers used in many CCD detectors have distortion that has to be individually determined for each instrument. The distortion is stable over time and its spatial characteristics are dominated by a smooth component and a small local shear. In high-quality tapers used in X-ray instruments, the small local shear can be ignored. The smooth component can be parameterized in a number of ways, for example by splines (Hammersley, 1998) or polynomials (Messerschmidt & Pflugrath, 1987). DENZO uses two-dimensional Chebyschev polynomials (Press et al., 1989) in {x, y} or {p, q} coordinates, normalized to the range , . Typically, fifth- or seventh-order polynomials result in a positional error (r.m.s.) lower than 7 µm (about one tenth of the detector pixel). DENZO can use either a grid mask pattern or the X-ray diffraction pattern to refine the coefficients of the Chebyschev polynomials. If a grid mask is used, it has to be precisely made and positioned. The use of crystallographic data requires precise knowledge of detector and crystal parameters that are not known a priori with the required precision. The crystal and detector parameters can be determined in the same experiment as detector distortion. However, this experiment needs to be designed to minimize the impact of correlations between the parameters involved. The data analysis requires the description of the distortion function and its inverse. In DENZO, both are approximated in terms of Chebyschev polynomials. The magnitude of the approximation error is the same for the distortion function and its inverse.