International
Tables for Crystallography Volume C Mathematical, physical and chemical tables Edited by E. Prince © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. C, ch. 2.2, pp. 3134

The main modern book dealing with the rotation method is that of Arndt & Wonacott (1977).
The purpose of the monochromatic rotation method is to stimulate a reflection fully over its rocking width via an angular rotation. Different relp's are rotated successively into the reflecting position. The method, therefore, involves rotation of the sample about a single axis, and is used in conjunction with an area detector of some sort, e.g. film, electronic area detector or image plate. The use of a repeated rotation or oscillation, for a given exposure, is simply to average out any timedependent changes in incident intensity or sample decay. The overall crystal rotation required to record the total accessible region of reciprocal space for a single crystal setting, and a detector picking up all the diffraction spots, is 180° + . If the crystal has additional symmetry, then a complete asymmetric unit of reciprocal space can be recorded within a smaller angle. There is a blind region close to the rotation axis; this is detailed in Subsection 2.2.3.5.
Figs. 2.2.3.1(a) to (d) are taken from IT II (1959, p. 176). They neatly summarize the geometrical principles of reflection, of a monochromatic beam, in the reciprocal lattice for the general case of an incident beam inclined at an angle (μ) to the equatorial plane. The diagrams are based on an Ewald sphere of unit radius.
With the nomenclature of Table 2.2.3.1:

Fig. 2.2.3.1(a) gives Fig. 2.2.3.1(b) gives, by the cosine rule, and and Figs. 2.2.3.1(a) and (b) give
The following special cases commonly occur:
In this section, we will concentrate on case (a), the normalbeam rotation method (μ = 0). First, the case of a plane film or detector is considered.
The notation now follows that of Arndt & Wonacott (1977) for the coordinates of a spot on the film or detector. is parallel to the rotation axis and ζ. is perpendicular to the rotation axis and the beam. IT II (1959, p. 177) follows the convention of y being parallel and x perpendicular to the rotationaxis direction, i.e. . The advantage of the notation is that the xaxis direction is then the same as the Xray beam direction.
The coordinates of a reflection on a flat film are related to the cylindrical coordinates of a relp (ξ, ζ) [Fig. 2.2.3.2(a)] by which becomes where D is the crystaltofilm distance.

Geometrical principles of recording the pattern on (a) a plane detector, (b) a Vshaped detector, (c) a cylindrical detector. 
For the case of a Vshaped cassette with the V axis parallel to the rotation axis and the film making an angle α to the beam direction [Fig. 2.2.3.2(b)], then This situation also corresponds to the case of flat electronic area detector inclined to the incident beam in a similar way.
Note that Arndt & Wonacott (1977) use ν instead of α here. We use α and so follow IT II (1959). This avoids confusion with the ν of Table 2.2.3.1. D is the crystal to V distance. In the case of the V cassettes of Enraf–Nonius, α is 60°.
For the case of a cylindrical film or image plate where the axis of the cylinder is coincident with the rotation axis [Fig. 2.2.3.2(c)] then, for in degrees, which becomes Here, D is the radius of curvature of the cylinder assuming that the crystal is at the centre of curvature.
In the three geometries mentioned here, detectormisalignment errors have to be considered. These are three orthogonal angular errors, translation of the origin, and error in the crystaltofilm distance.
The coordinates and are related to filmscanner raster units via a scannerrotation matrix and translation vector. This is necessary because the film is placed arbitrarily on the scanner drum. Details can be found in Rossmann (1985) or Arndt & Wonacott (1977).
The reciprocallattice coordinates, etc. used earlier, refer to an axial system fixed to the crystal, of Fig. 2.2.3.3 . Clearly, a given relp needs to be brought into the Ewald sphere by the rotation about the rotation axis. The treatment here follows Arndt & Wonacott (1977).
The rotation angle required, , is with respect to some reference `zeroangle' direction and is determined by the particular crystal parameters. It is necessary to define a standard orientation of the crystal (i.e. datum) when = 0°. If we define an axial system fixed to the crystal and a laboratory axis system XYZ with X parallel to the beam and Z coincident with the rotation axis then = 0° corresponds to these axial systems being coincident (Fig. 2.2.3.3).
The angle of the crystal at which a given relp diffracts is The two solutions correspond to the two rotation angles at which the relp P cuts the sphere of reflection. Note that , (Subsection 2.2.3.2) are independent of .
The values of x_{0} and y_{0} are calculated from the particular crystal system parameters. The relationships between the coordinates x_{0}, y_{0}, z_{0} and ξ and ζ are X_{0} can be related to the crystal parameters by A is a crystalorientation matrix defining the standard datum orientation of the crystal.
For example, if, by convention, is chosen as parallel to the Xray beam at = 0° and c is chosen as the rotation axis, then, for the general case,
If the crystal is mounted on the goniometer head differently from this then A can be modified by another matrix, M, say, or the terms permuted. This exercise becomes clear if the reader takes an orthogonal case (α = β = γ = 90°). For the general case, see Higashi (1989).
The crystal will most likely be misaligned (slightly or grossly) from the ideal orientation. To correct for this, the misorientation matrices , , and are introduced, i.e. where , , and are angles around the X_{0}, Y_{0}, and Z_{0} axes, respectively.
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 reciprocallattice 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 signaltonoise 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 signaltonoise ratio of the measurement and to sample the rockingwidth profile.
The value of Δ, the crystal rocking width for a given hkl, depends on the reciprocallattice 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 reciprocallattice 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 standardsized detector, this is practical for lowresolution data recording. This can be a useful complement to the Laue method where the lowresolution data are rather sparsely stimulated and also tend to occur in multiple Laue spots. Alternatively, a much larger detector can be contemplated and even mediumresolution data can be recorded without major overlap problems. These techniques are useful in some timeresolved 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.
In normalbeam geometry, any relp lying close to the rotation axis will not be stimulated at all. This situation is shown in Fig. 2.2.3.4 . The blind region has a radius of and is therefore strongly dependent on d_{min} but can be ameliorated by use of a short λ. Shorter λ makes the Ewald sphere have a larger radius, i.e. its surface moves closer to the rotation axis. At Cu Kα for 2 Å resolution, approximately 5% of the data lie in the blind region according to this simple geometrical model. However, taking account of the rocking width Δ, a greater percentage of the data than this is not fully sampled except over very large angular ranges. The actual increase in the blindregion volume due to this effect is minimized by use of a collimated beam and a narrow spectral spread (i.e. finely monochromatized, synchrotron radiation) if the crystal is not too mosaic.

The rotation method. The blind region associated with a single rotation axis. From Arndt & Wonacott (1977). 
These effects are directly related to the Lorentz factor, It is inadvisable to measure a reflection intensity when L is large because different parts of a spot would need a different Lorentz factor.
The blind region can be filled in by a rotation about another axis. The total angular range that is needed to sample the blind region is in the absence of any symmetry or in the case of mm symmetry (for example).
References
Arndt, U. W. & Wonacott, A. J. (1977). The rotation method in crystallography. Amsterdam: NorthHolland.Google ScholarHigashi, T. (1989). The processing of diffraction data taken on a screenless Weissenberg camera for macromolecular crystallography. J. Appl. Cryst. 22, 9–18.Google Scholar
International Tables for Xray Crystallography (1959). Vol. II. Birmingham: Kynoch Press.Google Scholar
Rossmann, M. G. (1985). Determining the intensity of Bragg reflections from oscillation photographs. Methods Enzymol. 114A, 237–280.Google Scholar
Weisgerber, S. & Helliwell, J. R. (1993). Highresolution crystallographic studies of native concanavalin A using rapid Laue data collection methods and the introduction of a monochromatic largeangle oscillation technique (LOT). J. Chem. Soc. Faraday Trans. 89, 2667–2675.Google Scholar