Determination of optical fiber layer parameters by inverse evaluation of lateral scattering patterns

Step-index fibers consisting of two (or more) concentric layers of different transparent materials are common in optical telecommunication technology. Our aim is to establish algorithms allowing for the determination of the parameters (e.g., diameters) of these layers by evaluation of the lateral scattering pattern originating under planewave monochromatic illumination perpendicular to the fiber axis. We investigate numerical simulations only, i.e. applying the corresponding parameter estimation algorithms to numerically generated scattering patterns with known geometry and optical parameter values. We consider three algorithms for parameter determination. The first is the iteratively regularized GaussNewton (IRGN) algorithm, which minimizes the norm ||F(q) − u∞||2 of the difference between the pattern for the parameters qn and the input u∞, but only locally. However, local minima in the norm “landscape” are spaced periodically, which we utilize. The second approach treats parameter determination as the optimization problem of minimizing ||F(q)−u∞||2 globally, subject to the Dividing Rectangles (DiRect) algorithm. The third approach hybridizes both optimization methods. The results show that the modified IRGN algorithm is considerably faster for cases where the scattering intensities are superimposed with no or little noise. In terms of precision, the DiRect algorithm and its hybrid variant perform slightly better. These algorithms also terminate quicker for increasing noise. This, however, highlights the general trade-off between calculation times and precision.