Inverse analysis of the rainbow for the case of low-coherent incident light to determine the diameter of a glass fiber.

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.