Tables for
Volume C
Mathematical, physical and chemical tables
Edited by E. Prince

International Tables for Crystallography (2006). Vol. C, ch. 2.2, p. 29

Section Gnomonic and stereographic transformations

J. R. Helliwella

aDepartment of Chemistry, University of Manchester, Manchester M13 9PL, England Gnomonic and stereographic transformations

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A useful means of transformation of the flat-film Laue pattern is the gnomonic projection. This converts the pattern of spots lying on curved arcs to points lying on straight lines. The stereographic projection is also used. Fig.[link] shows the graphical relationships involved [taken from International Tables, Vol. II (Evans & Lonsdale, 1959[link])], for the case of a Laue pattern recorded on a plane film, between the incident-beam direction SN, which is perpendicular to a film plane and the Laue spot L and its spherical, stereographic, and gnomonic points Sp, St and G and the stereographic projection Sr of the reflected beams. If the radius of the sphere of projection is taken equal to D, the crystal-to-film distance, then the planes of the gnomonic projection and of the film coincide. The lines producing the various projection poles for any given crystal plane are coplanar with the incident and reflected beams. The transformation equations are [P_L=D\tan2\theta\eqno (] [P_G=D\cot\theta\eqno (] [P_S=D{\cos\theta\over(1+\sin\theta)}\eqno (] [P_R=D\tan\theta \eqno (]


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Geometrical principles of the spherical, stereographic, gnomonic, and Laue projections. From Evans & Lonsdale (1959[link]).


Evans, H. T. & Lonsdale, K. (1959). Diffraction geometry. International tables for X-ray crystallography, Vol. II, p. 164. Birmingham: Kynoch Press.Google Scholar
International Tables for X-ray Crystallography (1959). Vol. II. Birmingham: Kynoch Press.Google Scholar

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