Recently proposed lensless object scanning holography (LOSH) [Opt. Express 20, 9382 (2012)] is a fully lensless method capable of improving the image quality in digital Fourier holography applied to one-dimensional (1D) reflective objects and it involves a very simplified experimental setup. LOSH is based on the recording and digital postprocessing of a set of digital lensless Fourier transform holograms, which finally results in a synthetic image with improved resolution, field-of-view (FOV), signal-to-noise ratio (SNR), and depth of field. In this paper, LOSH is extended to the cases of two-dimensional (2D) mirror-like and 1D diffuse-based objects. For 2D mirror-like objects, the experimental results show an impressive image quality improvement over a factor of 3 in FOV, SNR, and resolution, as good as that obtained for the 1D case but in two dimensions. For 1D diffuse-based objects, in general the speckle affects the image resolution, which will not be only a function of the aperture size. In this case, increasing the aperture produces a decrease of the speckle size. Moreover, due to the overlapping of speckles between successive images, different types of digital processing can be applied to obtain the final synthetic image: fully incoherent, fully coherent, and partially coherent. The last, arising from the incoherent sum of several independent sets of coherently added images, provides the best improvement in the resolution. Experimental results for both types of objects are presented.
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