Assessment of refractive index gradients by standard rainbow thermometry

Up to now the application of rainbow thermometry has been limited to particle systems possessing a uniform refractive index. This is mostly due to the absence of an appropriate data inversion algorithm that takes into account the presence of a refractive index gradient. In this paper, for the first time to our knowledge, exploiting a generalization of the Airy theory, a data inversion algorithm for a single droplet, presenting a parabolic refractive index gradient, is proposed. This data inversion algorithm is used to compute the diameter and the refractive index at the core and at the surface of a simulated burning droplet. The results are compared to the analytical solutions showing a satisfactory agreement.