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The Talbot effect is a phenomenon that is also often known as self-images or images without a lens. Such an effect is manifested by a periodic repetition of optical field distributions at certain distances from an aperture. We present a mathematical development, based on the Fourier transform in polar coordinates to solve this case.
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Alitzel G. Ortiz, Alfonso P. Vivanco, Carina Toxqui-Quitl, "Talbot effect from structures with periodic Bessel and sinusoidal profiles," Proc. SPIE 11814, Current Developments in Lens Design and Optical Engineering XXII, 118140I (1 August 2021); https://doi.org/10.1117/12.2596428