Optical EngineeringSymmetry of the Talbot effect and its applications
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The Talbot effect is one of the most basic optical phenomena that has received extensive investigations both because its new results provide us more understanding of the fundamental Fresnel diffraction and also because of its wide applications. We summarize our recent results on this subject. Symmetry of the Talbot effect, which was reported in Optics Communications in 1995, is now realized as the key to reveal other rules for explanation of the Talbot effect for array illumination. The regularly rearranged-neighboring-phase-differences (RRNPD) rule, a completely new set of analytic phase equations (Applied Optics, 1999), and the prime-number decomposing rule (Applied Optics, 2001) are the newly obtained results that reflect the symmetry of the Talbot effect in essence. We also reported our results on the applications of the Talbot effect. Talbot phase codes are the orthogonal codes that can be used for phase coding of holographic storage. A new optical scanner based on the phase codes for Talbot array illumination has unique advantages. Furthermore, a novel two-layered multifunctional computer-generated hologram based on the fractional Talbot effect was proposed and implemented (Optics Letters, 2003). We believe that these new results should bring us more new understanding of the Talbot effect and help us to design novel optical devices that should benefit practical applications.