Synthetic aperture enlargement is obtained, in lensless digital holography, by introducing a diffraction grating between the object and the CCD camera with the aim of getting super-resolution. We demonstrate here that the spatial frequencies are naturally self-assembled in the reconstructed image plane when the NA is increased synthetically at its maximum extent of three times. By this approach it possible to avoid the use of the grating transmission formula in the numerical reconstruction process, thus reducing significantly the noise in the final super-resolved image. Demonstrations are reported in 1D and 2D with an optical target and a biological sample, respectively.
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