An updated equation for the refractive index of air

Laser has been widely used in spectroscopic and metrological measurement. High-precision laser metrology is affected by the refractive index of air. In order to apply the algorithm for the refractive index of air in some situation where low calculation complexity and high-precision are needed, the algorithm of the refractive index of Rueger is updated. As the errors of Rueger's algorithm are mainly affected by temperature, humidity, and the concentration of carbon dioxide in the atmosphere as well as laser wavelength, we do some revisions about these effects of the factors of atmosphere in Rueger's algorithm. The conditions of standard air is redefined in this paper because of the average concentration of carbon dioxide in the atmosphere has been changed in the past few decades. As the concentration of carbon dioxide in the air is not constant, the effect of carbon dioxide on the refractive index of air is taken into consideration in the updated algorithm. The updated algorithm adapts to the real atmosphere well. The effects of dry air and humid air on the algorithm are also corrected, and the refractive index of air calculated by the updated algorithm is much closer to that of Philip E. Ciddor's algorithm defined as reference algorithm in the paper because of its high-precision. The performance of the updated algorithm is also analyzed in this paper. It is compared to that of the reference algorithm and the real measured data. Comparing results show that the performance of the algorithm has been improved after the correction. Comparing to the reference algorithm, the performance of the updated algorithm is a little bit lower, but the updated algorithm is much simpler and easier to be applied. Comparing to Rueger's algorithm, the performance of the updated algorithm is much higher and the complexity of the updated algorithm increases very small. The updated algorithm meets low calculation complexity and high-precision requirements.