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We study the capabilities of time-modulated diffraction gratings as imagingdevices. It is shown that a time-dependent but transversally homogeneous slabcan be used to make a perfect image of an object in the far-field, since allthe evanescent modes couple to propagative time-diffracted orders. It is foundthat, if the image to be obtained is axially symmetric, it can be recovered bymeasuring the time-signal at a single point, without the need of performing aspatial scan, so that time gratings can act as well as single-pixel imagingdevices. In the case of having an object without axial symmetry, thetime-grating can be combined with a spatial grating, and then the full imagecan be recovered again with a measurement at a single point. We apply thetheory of compressive sensing to optimize the recovery method and numericalexamples are provided. We show therefore that time-modulated gratings can beused to perfectly recover the image of an object in the far field and aftermeasuring at a single point in the space, being therefore a promising approachto superesoloution and ultra-fast imaging.

Far-field Perfect Imaging with Time Modulated Gratings