Modeling the Concentric Fiber Optic Bundle Displacement Sensor Using a Quasi-Gaussian Beam Approach

In the design and analysis of a fiber optic displacement sensor, modeling of the modulation function is important as it leads to accurate descriptions of several important parameters that are to be taken into consideration of the sensor design. Furthermore, it is also important for the experimental verification. Here, the design of a reflective-based intensity modulation mechanism for displacement measurements, employing a concentric fiber optic bundle acting as the fiber optic probe, with a planar reflector is presented. The aim is to develop a new theoretical model for analyzing the modulation function of the sensor using a quasi-Gaussian approach. In the case of fiber optic bundles, the choice of the emitted beam shape becomes more critical as there will occur partial illumination of the receiving cores for smaller values of displacements. In an attempt to produce a more accurate model for the modulation function, a slightly different angular dependence as presented in the quasi-Gaussian approach is more suitable. Perturbation parameters are used to indicate the variation amount of the actual beam profile from the Gaussian profile. The derivation of the mathematical model developed for describing the characteristics of such sensing mechanisms is demonstrated. The model is subsequently verified using the simulation of the quasi-Gaussian beam approach and validated using the experimental data. A comparison with the simulation of the widely used Gaussian beam approach is made. The quasi-Gaussian approach is proven to be a much better approximation than the Gaussian approach.