Refractive index determination in length measurement by two-colour interferometry

Abstract

A well-known method for compensation of the refractive index of air for length measurements based on the speed of light is a measurement with two different wavelengths and using the dispersion relation. No measurement of temperature, pressure and CO2 content of the air is necessary. However, this method is valid only for dry air and is practically not used. For moist air the partial pressure of water vapour has to be known as the only air parameter for the compensation of the refractive index. In practice it is not possible to measure the partial pressure of water vapour in air directly. Standard hygrometers indicate the relative humidity. To get the partial pressure the temperature has to be known. Experiments were performed with this modified compensation method where the air pressure and the humidity are measured conventionally. A homodyne interferometer was set up with a frequency doubled Nd:YVO4 laser with the wavelengths 1064 nm and 532 nm. The effective temperature in the measurement path is derived from the length results for both wavelengths. Our experiments indicate a length-dependent measurement uncertainty of below 1.2 × 10−7L for distances up to 30 m.