International
Tables for Crystallography Volume B Reciprocal space Edited by U. Shmueli © International Union of Crystallography 2006 
International Tables for Crystallography (2006). Vol. B. ch. 2.5, p. 287

Reciprocity was introduced into the subject of electron diffraction in stages, the essential theoretical basis, through Schrödinger's equation, being given by Bilhorn et al. (1964), and the Nbeam diffraction applications being derived successively by von Laue (1935), Cowley (1969), Pogany & Turner (1968), Moodie (1972), Buxton et al. (1976), and Gunning & Goodman (1992).
Reciprocity represents a reverseincidence configuration reached with the reversed wavevectors and , so that the scattering vector is unchanged, but is changed in sign and hence reversed (Moodie, 1972). The reciprocity equation, is valid independently of crystal symmetry, but cannot contribute symmetry to the pattern unless a crystalinverting symmetry element is present (since belongs to a reversed wavevector). The simplest case is centrosymmetry, which permits the righthand side of (2.5.3.1) to be complexconjugated giving the useful CBED pattern equation Since K is common to both sides there is a pointbypoint identity between the related distributions, separated by 2g (the distance between g and reflections). This invites an obvious analogy with Friedel's law, , with the reservation that (2.5.3.2) holds only for centrosymmetric crystals. This condition (2.5.3.2) constitutes what has become known as the ±H symmetry and, incidentally, is the only reciprocityinduced symmetry so general as to not depend upon a disc symmetrypoint or line, nor on a particular zone axis (i.e. it is not a point symmetry but a translational symmetry of the pattern intensity).
References
Bilhorn, D. E., Foldy, L. L., Thaler, R. M. & Tobacman, W. (1964). Remarks concerning reciprocity in quantum mechanics. J. Math. Phys. 5, 435–441.Google ScholarBuxton, B., Eades, J. A., Steeds, J. W. & Rackham, G. M. (1976). The symmetry of electron diffraction zone axis patterns. Philos. Trans. R. Soc. London Ser. A, 181, 171–193.Google Scholar
Cowley, J. M. (1969). Image contrast in transmission scanning electron microscopy. Appl. Phys. Lett. 15, 58–59.Google Scholar
Gunning, J. & Goodman, P. (1992). Reciprocity in electron diffraction. Acta Cryst. A48, 591–595.Google Scholar
Laue, M. von (1935). Die Fluoreszenzrontgenstrahlung von Einkristallen. Ann. Phys. (Leipzig), 23, 703–726.Google Scholar
Moodie, A. F. (1972). Reciprocity and shape function in multiple scattering diagrams. Z. Naturforsch. Teil A, 27, 437–440.Google Scholar
Pogany, A. P. & Turner, P. S. (1968). Reciprocity in electron diffraction and microscopy. Acta Cryst. A24, 103–109.Google Scholar