Measurement error of global rainbow technique: The effect of recording parameters

Rainbow refractometry can measure refractive index and size of spray droplets simultaneously. Recording parameters of global rainbow imaging system, such as recording distance and scattering angle recording range, play a vital role in in-situ high accuracy measurement. In the paper, a theoretical and experimental investigation on the effect of recording parameters on measurement error of global rainbow technique was carried out for the first time. The relation of the two recording parameters, and the monochromatic aberrations in global rainbow imaging system were analyzed. In the framework of Lorenz-Mie theory and modified Nussenzveig theory with correction coefficients, measurement error curves of refractive index and size of the droplets caused by aberrations for different recording parameters were simulated. The simulated results showed that measurement error increased with RMS radius of diffuse spot; a long recording distance and a large scattering angle recording range both caused a larger diffuse spot; recording parameters were indicated to have a great effect on refractive index measurement error, but have little effect on measurement of droplet size. A sharp rise in spot radius at large recording parameters was mainly due to spherical aberration and coma. To confirm some of the conclusions, an experiment was conducted. The experimental results showed that the refractive index measurement error was as high as 1.3× 10−3 for a recording distance of 31 cm. In the case, recording parameters are suggested to be set to as small a value as possible under the same optical elements.