Аннотация:The theory of diffraction microscopy is completed and extended in different directions. In this two-step method of image formation the object is reconstructed by optical means from a diffraction diagram, taken in coherent illumination with light or with electrons. The `projection method', originally described, and the `transmission method', recently proposed by Haine and Dyson, are two variants which can be treated by one theory. The Proc.ess of image formation, the coherence requirements, and the conditions for a good reconstruction are discussed in detail It is shown that the reconstructed image of extended objects suffers from some spurious detail, but this can be largely suppressed in the `dark-field' method of reconstruction, in which the illuminating wave is cut out after it has passed through the diffraction diagram.