Accurate measurement of droplet size, temperature and concentration in sprays is of great importance but still challenging in applications. The secondary rainbow refractometry is investigated in this work to measure refractive index and size of transparent spherical droplets, with better sensitivity than the first rainbow. Inversion algorithm of the secondary rainbow is used and validated through processing the secondary rainbow signals simulated by the Lorenz-Mie theory. The secondary rainbow refractometry is applied to measure monodispersed spherical droplets of ethanol and N-heptane with different diameters in the isothermal conditions. Measured refractive indices of both liquids are 1.3621 and 1.3950 with diameter of about 145 µm and uncertainty of size measurement is down to $1\mu \mathrm{m}$ with RMS error of $0.3\mu \mathrm{m}$. Compared with results from the microscopic imaging, the maximum of deviation as well as the relative error are within several microns and 4$\%$. This work confirms the feasibility and high accuracy of the secondary rainbow refractometry in spherical droplet size and refractive index measurement at room temperature of about $300K$.

准确测量喷雾中的液滴尺寸、温度和浓度非常重要，但在应用中仍然具有挑战性。在这项工作中研究了二次彩虹折射法来测量透明球形液滴的折射率和大小，其灵敏度比第一彩虹更好。通过对Lorenz-Mie理论模拟的次虹信号进行处理，使用并验证了次虹反演算法。二次虹折射法用于测量等温条件下不同直径的乙醇和正庚烷的单分散球形液滴。两种液体的测量折射率分别为 1.3621 和 1.3950，直径约为 145 µm，尺寸测量的不确定度低至$1\mu \mathrm{米}$ RMS 误差为 $0.3\mu \mathrm{米}$. 与显微成像结果相比，最大偏差和相对误差在几微米和4$\%$. 这项工作证实了二次虹折射法在室温下约$300钾$.