Lensless Fourier-Transform Digital Holography through an aperture has been demonstrated some years ago. This technique allows to record and reconstruct images of large objects placed at short distances from the camera. In this paper we show that the distance between the aperture plane and the camera can be used to control the field of view and, therefore, moving the camera away from or towards the aperture has an effect similar to zooming a lens in and out, respectively. We also show that the F/# number of the aperture must be kept constant to hold the relative lateral resolution, i.e., to have a constant speckle size while zooming. With this improvement, Lensless Fourier-Transform Digital Holography provides a functionality similar to Image-Plane Digital Holography. Both involve practically the same computational cost. The former has the benefit of its experimental simplicity but has the drawback of not providing a real-time image of the object, which is useful for alignment, as the latter does.
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