Tunable, Nonmechanical, Fractional Talbot Illuminators

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Inside an optical Fourier processor, we inserted a varifocal system to continuously magnify the frequency of a master grating. The proposed system does not involve any mechanical compensation for scaling the Fourier spectrum. As the magnification, M, varies, the Fourier spectrum remains at the same initial location. We identified a previously unknown quadratic phase factor for generating, in the fixed output plane, Talbot images of any fractional order. We applied this result to setting a structured illumination beam, which does not have occluding regions. This illuminating beam can be useful for Talbot interferometry.