Bessel functions, time averaged fringes and dynamical systems

Abstract

Bessel functions play a primary role in experimental mechanics whenever the mathematical description of time-averaged optical processes is considered. Nevertheless, numerical modelling of time-averaged fringes is a complex task usually involving the Finite Element Method, the physical model describing interference effects, and a graphical model comprising all interacting objects. We propose a simplified approach for visualization of time-averaged geometric moire fringes which can have a definite educational value and can complement courses comprising Bessel functions and exemplify the role of these functions in experimental mechanics.