Section 2.2.3.4. Maximum oscillation angle without spot overlap

For a given oscillation photograph, there is maximum value of the oscillation range, , that avoids overlapping of spots on a film. The overlap is most likely to occur in the region of the diffraction pattern perpendicular to the rotation axis and at the maximum Bragg angle. This is where relp's pass through the Ewald sphere with the greatest velocity. For such a separation between successive relp's of a*, then the maximum allowable rotation angle to avoid spatial overlap is given by where Δ is the sample reflecting range (see Section 2.2.7). is a function of , even in the case of identical cell parameters. This is because it is necessary to consider, for a given orientation, the relevant reciprocal-lattice vector perpendicular to . In the case where the cell dimensions are quite different in magnitude (excluding the axis parallel to the rotation axis), then is a marked function of the orientation.

In rotation photography, as large an angle as possible is used up to . This reduces the number of images that need to be processed and the number of partially stimulated reflections per image but at the expense of signal-to-noise ratio for individual spots, which accumulate more background since . In the case of a CCD detector system, is chosen usually to be less than Δ so as to optimize the signal-to-noise ratio of the measurement and to sample the rocking-width profile.

The value of Δ, the crystal rocking width for a given hkl, depends on the reciprocal-lattice coordinates of the hkl relp (see Section 2.2.7). In the region close to the rotation axis, Δ is large.

In the introductory remarks to the monochromatic methods used, it has already been noted that originally the rotation method involved 360° rotations contributing to the diffraction image. Spot overlap led to loss of reflection data and encouraged Bernal and Weissenberg to devise improvements. With modern synchrotron techniques, the restriction on (equation 2.2.3.30) can be relaxed for special applications. For example, since the spot overlap that is to be avoided involves relp's from adjacent reciprocal-lattice planes, the different Miller indices hkl and h + l, k, l do lead in fact to a small difference in Bragg angle. With good enough collimation, a small spot size exists at the detector plane so that the two spots can be resolved. For a standard-sized detector, this is practical for low-resolution data recording. This can be a useful complement to the Laue method where the low-resolution data are rather sparsely stimulated and also tend to occur in multiple Laue spots. Alternatively, a much larger detector can be contemplated and even medium-resolution data can be recorded without major overlap problems. These techniques are useful in some time-resolved applications. For a discussion see Weisgerber & Helliwell (1993). For regular data collection, however, narrow angular ranges are still generally preferred so as to reduce the background noise in the diffraction images and also to avoid loss of any data because of spot overlap.