Section 2.2.7.4. Geometric effects and distortions associated with area detectors

Electronic area detectors are real-time image-digitizing devices under computer control. The mechanism by which an X-ray photon is captured is different in the various devices available (i.e. gas chambers, television detectors, charge-coupled devices) and is different specifically from film or image plates. Arndt (1986 and Section 7.1.6 ) has reviewed the various devices available, their properties and performances. Section 7.1.8 deals with storage phosphors/image plates.

(a) Obliquity. In terms of the geometric reproduction of a diffraction-spot position, size, and shape, photographic film gives a virtually true image of the actual diffraction spot. This is because the emulsion is very thin and, even in the case of double-emulsion film, the thickness, g, is only ∼0.2 mm. Hence, even for a diffracted ray inclined at = 45° to the normal to the film plane, the `parallax effect', , is very small (see below for details of when this is serious). With film, the spot size is increased owing to oblique or non-normal incidence. The obliquity effect causes a beam, of width w, to be recorded as a spot of width For example, if w = 0.5 mm and = 45°, then w′ is 0.7 mm. With an electronic area detector, obliquity effects are also present. In addition, the effects of parallax, point-spread factor, and spatial distortions have to be considered.

(b) Parallax. In the case of a one-atmosphere xenon-gas chamber of thickness g = 10 mm, the parallax effect is dramatic [see Hamlin (1985, p. 435)]. The wavelength of the beam has to be considered. If a λ of ∼1 Å is used with such a chamber, the photons have a significant probability of fully traversing such a gap and parallax will be at its worst; the spot is elongated and the spot centre will be different from that predicted from the geometric centre of the diffracted beam. If a λ of 1.54 Å is used then the penetration depth is reduced and an effective g, i.e. g_eff, of ∼3 mm would be appropriate. The use of higher pressure in a chamber increases the photon-capture probability, thus reducing g_eff pro rata; at four atmospheres and λ =1.54 Å, parallax is very small.

In general, we can take account of obliquity and parallax effects whereby the measured spot width, in the radial direction, is w′′, where As well as changing the spot size, the spot position, i.e. its centre, is also changed by both obliquity and parallax effects by . The spherical drift-chamber design eliminated the effects of parallax (Charpak, Demierre, Kahn, Santiard & Sauli, 1977). In the case of a phosphor-based television system, the X-rays are converted into visible light in a thin phosphor layer so that parallax is negligible.

(c) Point-spread factor. Even at normal incidence, there will be some spreading of the beam size. This is referred to as the point-spread factor, i.e. a single pencil ray of light results in a finite-sized spot. In the TV-detector and image-plate cases, the graininess of the phosphor and the system imaging the visible light contribute to the point-spread factor. In the case of a charge-coupled device (CCD) used in direct-detection mode, i.e. X-rays impinging directly on the silicon chip, the point-spread factor is negligible for a spot of typical size. For example, in Laue mode with a CCD used in this way, a 200 µm diameter spot normally incident on the device is not measurably broadened. The pixel size is ∼25 µm. The size of such a device is small and it is used in this mode for looking at portions of a pattern.

(d) Spatial distortions. The spot position is affected by spatial distortions. These non-linear distortions of the predicted diffraction spot positions have to be calibrated for independently; in the worst situations, misindexing would occur if no account were taken of these effects. Calibration involves placing a geometric plate, containing a perfect array of holes, over the detector. The plate is illuminated, for example, with radiation from a radioactive source or scattered from an amorphous material at the sample position. The measured positions of each of the resulting `spots' in detector space (units of pixels) can be related directly to the expected position (in mm). A 2D, non-linear, pixel-to-mm and mm-to-pixel correction curve or look-up table is thus established.

These are the special geometric effects associated with the use of electronic area detectors compared with photographic film or the image plate. We have not discussed non-uniformity of response of detectors since this does not affect the geometry. Calibration for non-uniformity of response is discussed in Section 7.1.6 .