Modeling light scattering in the shadow region behind thin cylinders for diameter analysis

Highlights: • Modeling light scattering of circular cylinders. • Sinusoidal model functions for data inversion. • Novel evaluation algorithm for retrieving diameter information of cylindrical products like thin wires or optical fibers. • Test results with synthetic and experimental scattering data. In this paper, the scattered light intensities resulting in the shadow region at an observation plane behind monochromatically illuminated circular cylinders are modeled by sinusoidal sequences having a squared dependence on spatial position in the observation plane. Whereas two sinusoidal components appear to be sufficient for modeling the light distribution behind intransparent cylinders, at least three sinusoidal components are necessary for transparent cylinders. Based on this model, a novel evaluation algorithm for a very fast retrieval of the diameter of thin cylindrical products like metallic wires and transparent fibers is presented. This algorithm was tested in a cylinder diameter range typical for these products ($d\approx 70\dots 150$ µm; n ≈ 1.5). Numerical examples are given to illustrate its application by using both synthetic and experimental scattering data. Diameter accuracies below 0.05 µm could be achieved for intransparent cylinders in the tested diameter range. However, scattering effects due to morphological-dependent resonances (MDRs) are problematical in the diameter analysis of transparent products. In order to incorporate these effects into the model, further investigations are needed.