A new method for obtaining digital Fourier holograms, under spatially incoherent white-light illumination and in a single camera shot, is presented. Multiple projections of the 3-D scene are created in the image plane of a microlens array, and a digital camera acquires the entire projections in a single shot. Then, each projection is computer processed to yield a single point in a Fourier hologram. The new method, designated as integral holography, is proved for the general case and demonstrated experimentally for a simple case.