Using an aliasing operator and a single discrete Fourier transform to down-sample the Fresnel transform

In Digital Holography there are applications where computing a few samples of a wavefield is sufficient to retrieve an image of the region of interest. In such cases, the sampling rate achieved by the direct and the spectral methods of the discrete Fresnel transform could be excessive. A few algorithmic methods have been proposed to numerically compute samples of propagated wavefields while allowing down-sampling control. Nevertheless, all of them require the computation of at least two 2D discrete Fourier transforms which increases the computational load. Here, we propose the use of an aliasing operator and a single discrete Fourier transform to achieve an efficient method to down-sample the wavefields obtained by the Fresnel transform.