Humidity coefficient correction in the calculation equations of air refractive index by He-Ne laser based on phase step interferometry

The refractive index of air (RIA) is an important parameter in precision measurement. The revisions to Edlen's equations by Boensch and Potulski [Metrologia 35, 133 (1998)] are mostly used to calculate the RIA at present. Since the humidity correction coefficients in the formulas were performed with four wavelengths of a ¹¹⁴Cd lamp (644.0, 508.7, 480.1, and 467.9 nm) and at the temperature range of 19.6°C-20.1° C, the application is restricted when an He-Ne laser is used as the light source, which is mostly applied in optical precision measurement, and the environmental temperature is far away from 20°C as well. To solve this problem, a measurement system based on phase step interferometry for measuring the effect of the humidity to the RIA is presented, and a corresponding humidity correction equation is derived. The analysis and comparison results show that the uncertainty of the presented equation is better than that of Boensch and Potulski's. It is more suitable in present precision measurements by He-Ne laser, and the application temperature range extends to 14.6°C-24.0°C as well.