Rainbow refractrometry: On the validity domain of Airy’s and Nussenzveig’s theories

To measure the temperature of individual droplets or the average temperature in a section of a spray, the analysis of the light scattered around the rainbow angle provides an attractive approach. Up to now, the analysis of recorded rainbow signals has been carried out in the framework of the full Lorenz–Mie theory or of the Airy theory. In this paper, we consider four approaches (Lorenz–Mie, Debye, Airy and Nussenzveig approaches) to compute the light scattered around the rainbow angle, and we compare them in terms of accuracy and time-consumption. It is shown that the Complex Angular Momentum (CAM) theory proposed by Nussenzveig, modified by using empirical coefficients, allows one to accurately compute the light scattered around the rainbow angle in a large angular domain for particles with diameters as small as 10 μm.