Rainbow techniques permit measurement of refractive indices, and hence the temperatures of liquid droplets through determination of the absolute angular position of a rainbow interference image in space. The Airy theory, which is commonly used to explain the rainbow effect, permits the determination of a unique refractive-index value, even in the presence of nonuniformities in the droplet. An extension of this theory to spheres that exhibit internal refractive-index gradients is proposed. The case of burning droplets is considered as an example of such spheres, and the results obtained are successfully compared with those presented in the literature.
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