The task considered is to measure the diameter of a cylindrical fiber by examining the angular profile of light scattered from the fiber. For this problem, the contrast mechanism (or forward model) is rigorously understood and is described by Lorenz-Mie theory. However, the inverse problem is complicated by phenomena that vary significantly and non-linearly with the fiber geometry. For example, with monochromatic illumination the angular dependence of the signal can vary rapidly with observation angle, and in a way that may change significantly with very small changes in fiber diameter. So while scattering from the fiber can be accurately modeled as a function of diameter, in certain diameter ranges recovering the fiber size is impractical in the presence of noise and small experimental uncertainties. Here the authors show that the stability of the inverse problem can be improved by using an illumination source with a broader spectral profile. Doing so results in many of the contrast sensitivities averaging out, and means that the system can be modeled with the simpler Airy’s theory of rainbows (albeit augmented with a correction) rather than the full Lorenz-Mie solution. This provides a computational simplification but, more importantly, reduces the detrimental sensitivity of the data to small changes in fiber properties. This is shown to allow high precision diameter estimates which, interestingly, are robust even to some un-modeled refractive index variations within the fiber. By exploring the physical relationship between the data collection instrumentation and the inverse problem, the authors have shown a clear route to improving the measurement process.
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