Section 2.2.1.5. Gnomonic and stereographic transformations

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. 2.2.1.5 shows the graphical relationships involved [taken from International Tables, Vol. II (Evans & Lonsdale, 1959)], 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 S_p, S_t and G and the stereographic projection S_r 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

Figure 2.2.1.5| top | pdf | Geometrical principles of the spherical, stereographic, gnomonic, and Laue projections. From Evans & Lonsdale (1959).