research papers J. Appl. Cryst. (2008). 41, 729–737 doi:10.1107/S0021889808011898 729 Journal of Applied Crystallography ISSN 0021-8898 Received 10 February 2008 Accepted 24 April 2008 # 2008 International Union of Crystallography Printed in Singapore – all rights reserved Absorption correction based on a three-dimensional model reconstruction from visual images Ricardo M. F. Leal, a,b,c Susana C. M. Teixeira, b,c Vicente Rey, a V. Trevor Forsyth b,c and Edward P. Mitchell a,c * a ESRF, Rue Jules Horowitz, Grenoble, France, b Institut Laue–Langevin, Rue Jules Horowitz, Grenoble, France, and c EPSAM and ISTM, Keele University, Staffordshire ST5 5BG, England. Correspondence e-mail: mitchell@esrf.fr The results are presented of a feasibility study for the application of absorption corrections to macromolecular crystallographic X-ray diffraction data using a three-dimensional crystal model generated photographically. The model allows path lengths through the crystal, the solvent and the crystal mount system to be determined. The approach has been tested on the macromolecular crystallography beamline ID23-1 at the ESRF in Grenoble using a model insulin system with the standard mini diffractometer facilities, which incorporate high- quality camera systems for sample alignment. Data from the insulin crystal at low incident beam energy (6.0 keV or 2.1 A ˚ ) were recorded and processed using this approach. The resulting data are compared against those treated using an empirical method and show significant improvement. The methods described here are of general interest, particularly for long-wavelength X-ray work, and may also be applied to account for absorption effects in neutron crystallography. 1. Introduction Absorption effects have always concerned crystallographers. The first approaches to reduce the effects of absorption were made by reshaping the sample to simple geometries, such as spherical or cylindrical, so that tabulated corrections could be applied easily (Bradley, 1935; Evans & Ekstein, 1952). When the crystal could not be reshaped, Albrecht’s (1939) method for determining the correction graphically was widely used. Rogers & Moffett (1956) and Henshaw (1958) later published aids to facilitate the procedure. The principles underlying the application of absorption corrections in single-crystal diffraction experiments are well established (Busing & Levy, 1957). The transmission factor to be computed for every reflection is given by T hkl ¼ V 1 R V exp½ðr a þ r b Þ dV; ð1Þ where  is the linear absorption or attenuation coefficient, r a and r b are the path lengths of the incident beam and of the diffracted beam, respectively, and V is the volume of the crystal. Various methods have been proposed to evaluate this integration either in an analytical (de Meulenaer & Tompa, 1965; Alcock et al., 1972) or in a numerical way (Busing & Levy, 1957; Wells, 1960), usually dependent upon indexing the faces of the crystal. Driven by the needs of the macro- molecular crystallography (MX) community, DeTitta (1985) developed a program, ABSORB, based on a Gaussian numerical approximation and using the calculations of Wells (1960) for cylindrical shapes, to calculate the absorption correction for crystals enclosed in capillaries with trapped mother liquor. Difficulties associated with geometrical sample character- ization led to the development of semi-empirical and empirical methods (North et al., 1968; Flack, 1974; Walker & Stuart, 1983; Katayama, 1986; Blessing, 1995). Semi-empirical corrections are based on an analysis of either the intensities of symmetrically equivalent reflections or an azimuthal scan (É scan; North et al., 1968; Huber & Kopfmann, 1969), whilst empirical methods exploit available data redundancy, model- ling an empirical transmission surface, to maximize the consistency amongst the measured data (Blessing, 1995; Katayama, 1986; Bricogne et al. , 2005). Empirical approaches are implemented in programs such as SCALA (Evans, 2006), XDS (Kabsch, 1993), SADABS (Sheldrick, 2002) and SCALEPACK (Otwinowski et al., 2003). MX has been a continuous driving force for the optimiza- tion of absorption corrections. This has become particularly evident in recent years with increasing use of sulfur and phosphorous phasing methods (Yang et al., 2003; Weiss et al. , 2004; Phillips et al. , 2004; Chen et al., 2004; Mueller-Dieck- mann et al., 2004, 2005, 2007; Micossi et al., 2002), as well as increasing numbers of studies involving fragile and radiation- sensitive crystals that are rapidly damaged in strong undulator X-ray beams (Flot et al., 2006). Most of the absorption correction methods summarized above have significant prac- tical problems. The indexing of crystal faces is time consuming and difficult to perform accurately. Moreover, macro- molecular crystals can be highly irregular in shape, and it is difficult to account for absorption effects associated with the