Modeling of structured light projection on vibrating surfaces: Amplitude and phase mapping by fringe visibility evaluation

Abstract

Vibration analysis is an extremely important issue in many fields of production systems like quality control as well as maintenance procedures. In this work it is theoretically studied the behavior of structured light in the form of straight sinusoidal fringes projected on vibrating objects. It was shown that by time averaging the moving fringes on the vibrating surface the resulting light pattern can be described with the help of the zero-order Bessel function of the vibration amplitude and constant factors related to the optical setup geometry. A simple formula was derived allowing to determine the Bessel function by combining the projected light patterns in different object configurations. The amplitude distribution in turn was retrieved from the Bessel function with the help of the explicit Euler method. It was also demonstrated that the phase mapping can be carried out by illuminating the object with a properly oscillating light pattern. The vibration analyses of a rectangular bar and of a square plate was simulated and its possible applications were pointed out.