[en] We present the theory in broadly the same way as for visible holography, specializing to the Gabor, in-line case with plane-wave illumination, but allowing phase and amplitude contrast and a fairly general transfer function. Much of this theory is treated by a number of earlier authors but none with the particular choice of issues that we wish to address. These are those mentioned plus numerical reconstruction from a digitized hologram and of course application to the soft x-ray spectral range. For simplicity and clarity, we consider first an amplitude and phase object consisting of a single, on-axis pixel and an ideal, perfect transfer function. (12 refs., 4 figs.)