Simple wave function of optical diffraction connecting the near- and far-field regimes

We present a simple wave function that seamlessly connects the near-field and far-field regimes of optical diffraction within a single analytical formulation. Starting from the classical description of the Talbot effect, we extend the theoretical treatment to encompass far-field diffraction, revealing both regimes as limiting cases of the same underlying physical principle. The derived expressions recover the Fresnel and Fraunhofer diffraction patterns without invoking separate approximations, thereby offering a continuous transition between near-field self-imaging and far-field interference patterns. The study shows that, at the same propagation distance, varying the number of grating slits allows the observed diffraction pattern to evolve from a far-field–like interference pattern for a small number of slits ( N =2) to a near-field regime exhibiting sharper and higher-contrast interference fringes as the number of slits increases. Experimental verification was performed using a laser diffraction setup, where both the Talbot images and far-field patterns were recorded and compared with theoretical predictions. The results show reasonable agreement, validating the unified model and providing new insights, to our knowledge, into the nature of optical wave propagation. This approach not only deepens the conceptual understanding of diffraction phenomena but also offers some advanced optics applications.