When a plane electromagnetic wave is scattered by an optically transparent object, whose size is much larger than the wavelength, a series of bright and dark fringes forms the primary rainbow, which is one of the most splendid phenomena in nature. In this work, an optical technique is discussed for simultaneous measurement of the diameter and refractive index of an axisymmetric and dielectric fiber by studying some rainbow features. This noncontact optical technique uses a beam of light exhibiting low temporal coherence, which enabled us to reduce the detrimental sensitivity of the rainbow features to variations of the fiber properties, thus allowing for high-precision estimates. Approximate mathematical formulas for the diameter and refractive index measurements were derived from the lowest-order complex angular momentum correction to Airy theory of rainbow. Furthermore, sensitivity of the measurement data to small deformation of the fiber's cross section into an ellipse was discussed. Preliminary empirical results provide a qualitative verification.
The aim of this paper is to discuss the possibility of a noninvasive, optical characterization of a transparent (glass) fiber on the basis of scattered light in the vicinity of a primary rainbow. Computational studies show that with the use of a spectrally adjusted incident beam of light, it is possible to form a rainbow with no strong nonlinearities typical for coherent light and that may be interpreted in terms of Airy's theory of rainbow. An inverse analysis is applied to obtain the fiber diameter with the help of a straightforward mathematical formula based on the Airy integral, corrected by comparison with the solution according to the complex angular momentum method.
The objective of this paper is to discuss the possibility of noninvasive optical characterization of a transparent (glass) fiber by means of low-coherent light scattering. It will be shown that, by adjusting the temporal coherence of incident light, it is possible to select these specific orders of scattering, which are related to diffraction. Discussion will be devoted to the direct scattering and the inverse problem, where an inference about the diameter of a multilayered and transparent fiber is accomplished.
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