Plots for only the most important crystal systems and orientations are present. To assist those workers with no computing facilities, Preuss, Krahl-Urban & Butz (1974) have published a large number of plotted Laue back-reflection diagrams. (1973) and Preuss (1979) programs can, from the input of data for three indexed spots, calculate the crystal direction which is anti- parallel to the X-ray beam. The structure factors must be either taken from a ten-structure-factor library, which is part of the program, or read in via cards. The Preuss (1979) program calculates and plots Laue-spot angular relationships and intensities and also produces a stereographic projection. However, apart from 'on-off' reflection intensities, no graduation in intensity appears to be calculated. (1973) program is designed for 'white' radiation and any crystal structure. (1975) is a precision technique and can only be used for cubic symmetry and monochromatic radiation. CORNELIUS 431 Urban, Butz & Preuss (1973), Christiansen, Gerward & Alstrup (1975) and Preuss (1979) which simulate to various degrees the reflections expected for Laue back-reflection and transmission X-ray photographs. Computer programs have been published by Krahl- 0567-7330-07501.00 © 1981 International Union of Crystallography C. This is particularly the case when the crystal structure has symmetry lower than cubic, or orientations with low-symmetry directions are required. Introduction Orientation of single crystals or indexing of crystal faces via the Laue back-reflection X-ray technique can be a difficult and very time-consuming task. The procedure incorporating use of the program requires only minimal knowledge of crystallography or computer methods. The program may ultimately be used to index an orientation from the identification of at least *Present address: Department of Physics, University of Southampton, Southampton SO9 5NH, England. Comparison of com- puter plots of the calculated patterns with the photo- graphs enables rapid identification of approximate orientation. CORNELIUS Department of Physics, Monash University, Clayton, Victoria 3168, Australia* (Received 9 July 1980 accepted 3 December 1980) Abstract A simple computer program for the simulation and analysis of X-ray back-reflection Laue photographs of a single crystal with any structure and orientation has been developed in Fortran IV. A37, 430-436 A Simple Computer Method for the Orientation of Single Crystals of Any Structure Using Laue Back-Reflection X-ray Photographs BY C. Some Statistical Applications in X-ray Crystallography, p. Crystal- lographic Computing, edited by F. Abstracts, Sixth European Crystallographic Meeting, Barcelona, p. On the other hand, computational aspects often speak in favor of reciprocal-space procedures. The use of the VS programs requires some skill which, in the present test case, leads to slightly better results. The function uses difference structure factors which are refined by the DIRDIF procedure in space group P1 (see Beurskens, van den Hark & Beurskens, 1976), with three or four refinement cycles. The function (ILl 2 I Epl 2) was calculated using various I EI cut-off values the best results were obtained using I EI > 1.0. The programs were executed using a variety of selection parameters to find the best results (a posteriori). Comments on the calculations and discussion of the results (1) VS. Table 3 gives the sequence numbers of the peaks that indicate the correct position of the fragments. The Hough transform is a function over the accumulator space.430 A STATISTICAL INTERPRETATION OF ROTATION FUNCTIONS The fragments were shifted by (0-1 0-0 0.2) and input to the various calculations. Each line on the image is represented by two line parameters which represent a pixel in the ‘accumulator space’. In digital image analysis, the discrete form of the Radon transform in \(R^2\) is known as the Hough transform. The integration over lines is seen as an accumulation (or voting) procedure. The standard technique for line detection is the Radon transformation. In this case, reflections of zones are projected on straight lines.
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