Simulating Fourier Optics Using Mathematica®

This book introduces the reader to many aspects of Fourier optics, using Mathematica as a simulation tool. A brief discussion of Mathematica's symbolic and numerical computation capabilities is introduced. Starting from the wave equation, several simulations of Fresnel and Fraunhofer diffraction problems are treated symbolically. Diffraction by an arbitrary linear optical system using ABCD matrices includes several symbolic examples. Recognizing that many diffraction problems cannot be solved symbolically, the discrete Fourier transform (DFT) is introduced and used to calculate many diffraction problems numerically. Three different numerical methods are used: numerical convolution, the Fresnel transform, and the Fresnel transfer function, with examples for each. Simulations of imaging with both coherent and incoherent light are covered both symbolically and numerically. Simulations of Gabor holography, Leith–Upatnieks holography, and phase-stepping holography are treated numerically. Finally, simulations of spatial filtering by manipulating the Fourier spectrum of an object are presented.