A stacked system of phase Fourier holograms on which binary information is recorded has been built and its performance studied. The properties of the zero-order beam propagating through the stack have been investigated. The results show how the energy and intensity distributions of the read-out beam change as the beam propagates through the system, and the values of the imaging efficiency ηnof successive holograms and the signal-to-noise ratio (S/N) are measured in successive reconstructed images. The evolution of the zero-order beam is described mathematically.