Abstract
The coherent wave field, which is the ensemble average of the solution of the wave equation, is studied. The approach is similar to that used in the previous theory on extinction [Kato (1976). Acta Cryst. A32, 453–457, 458–466]. Here it is extended to deal with general cases where the single average and the second-order correlation of lattice phase factors are mixed. The Laplace transforms of the coherent wave fields are derived first and integro-differential equations (IDEs) are formulated for them. The latter are identical to the previous ones derived directly from the wave equation. A controversial problem of IDEs is explained by the interpretation of IDEs.
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