Electronically-recorded holography is one technique for 3-dimensional imaging that avoids the requirements of wet-chemical development in conventional photographically recorded holography. It is capable of video-rate recording, and numerical reconstruction permits near real-time imaging. However, the size and pixel pitch of currently available CCD or CMOS sensors restricts its performance, particularly in regard to recordable object volume and spatial resolution. Spatial resolution with in-line recording geometry and collimated illumination is restricted to be no better than the pixel pitch of the recording sensor: however, this limit can be overcome by divergent-beam illumination, at the cost of some further reduction in object volume. We present a number of reconstruction algorithms for electronically recorded holograms, especially those suited to in-line holography using divergent-beam illumination. These algorithms are based on variations of numerical modelling of the diffraction process, as used in the physical reconstruction of conventional holograms. The performances of these algorithms are compared, using simulated and real holograms, and conclusions are drawn for the practical limitations on performance of electronically recorded holography. Applications are demonstrated for the study of sediment transport, and of biologically mediated re-suspension processes (bioturbation) in estuarine sediments, by electronic recording of holographic video.