Creating arbitrary light patterns finds applications in various domainsincluding lithography, beam shaping, metrology, sensing and imaging. We studythe formation of high-contrast light patterns that are obtained by transmissionthrough an ordered optical element based on self-imaging.By applying thephase-space method, we explain phenomena such as the Talbot and the angularTalbot effects. We show that the image contrast is maximum when the source iseither a plane wave or a point source, and it has a minimum for a source withfinite spatial extent. We compare these regimes and address some of theirfundamental differences. Specifically, we prove that increasing the sourcedivergence reduces the contrast for the plane wave illumination but increasesit for the point source. Also, we show that to achieve high contrast with apoint source, tuning the source size and its distance to the element iscrucial.We furthermore indicate and explore the possibility of realizing highlycomplex light patterns by using a periodic transmission element. These patternscan have more spots in the far field than the number of diffraction orders ofthe periodic element. We predict that the ultimate image contrast is smallerfor a point source compared to a plane wave. Our simulations confirm that thesmallest achievable spot size in the image is imposed by diffraction regardlessof the imaging regime. Our research can be applied to similar domains e.g.quantum systems.
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