The computer simulation of the Talbot Effect and carpet via the iterative Fresnel integrals method

The Talbot effect was first experimentally observed by Henry Talbot in 1836. It is the repeated self-imaging of a diffraction grating at regular distances in the near-field behind the grating. The corresponding selfrepeating distance is now known as the Talbot distance. If the observed diffraction images are laid out as a function of the distance, a beautiful and repetitive pattern is observed; this is known as the Talbot carpet. Apart from a considerable theoretical interest, the Talbot effect has found many applications in diverse areas of optics, for example, in imaging, refractive index measurements, displacement sensors, lithography and array illumination, to name a few. In this Chapter, we have applied the Iterative Fresnel Integrals Method (IFIM) to the simulation of the Talbot effect, and consequently, to the generation of Talbot carpets. The methodology of how the IFIM method was applied for the simulation of the Talbot effect is described explicitly, followed by a systematic synthesis of the Talbot carpet from the generated data. All the data were generated without recourse to any experimental apparatus. Finally, examples of Talbot carpets are presented at two different resolutions, and suggestions are made as to how the whole process of Talbot carpet synthesis can be automated to generate carpets of higher resolutions.