Generating near-field fresnel diffraction patterns by iterative fresnel integrals method: Acomputer simulation approach

Recently the concept of computer-based virtual experiments in all branches of physics has generated wide spread interests among the researchers. In this Chapter, we describe the Iterative Fresnel Integrals Method (IFIM), which is essentially a computer-based simulation method employing repeated calculation of Fresnel integrals to obtain the complete near-field Fresnel diffraction patterns or images from rectangular-shaped apertures in any given experimental configuration. The images observed in the far-field (the Fraunhofer regime) can be considered as a special case in this IFIM method. MATLAB codes are used to perform this Fresnel simulation in any personal computer, with a program execution time of the order of a minute. The IFIM method simulates a real diffraction experiment in a PC, and can also be a useful pedagogic tool to understand the details of the diffraction process. Here, we discuss the theoretical background of the method, as well as the complete implementation of the technique in MATLAB codes. Three specific applications of the iterative Fresnel integral method are considered in this Chapter: (a) single rectangular or square apertures, (b) double apertures and slits with arbitrary separations, and (c) square apertures tilted at an arbitrary angle to the optical axis. In each of these cases, the transition to the far-field (the Fraunhofer regime) is also simulated and discussed. Quantitative comparisons of the far-field intensity distributions with the analytic expressions from the Fraunhofer theory are made whenever possible. Double apertures in two dimensions, and apertures tilted simultaneously around two orthogonal axes are also briefly considered and simulated. Future possible extensions of the method to more complicated problems, such as multiple slits and diffraction gratings are also mentioned therein.