Automatic unit for measuring refractive index of air based on Ciddor equation and its verification using direct interferometric measurement method

Abstract

In scanning probe microscopy laser interferometers are usually used for measuring the position of the probe tip with a metrological traceability. As the most of the AFM setups are designed to work under standard atmospheric conditions the changes of the refractive index of air have an influence to measured values of the length with 1.0 × 10 −4 relatively. In order to achieve better accuracies the refractive index of air has to be monitored continuously and its instantaneous value has to be used for compensating the lengths measured by all of the interferometric axes. In the presented work we developed a new concept of an electronic unit which is able to monitor the refractive index of air on basis of measurement of ambient atmospheric conditions: temperature, humidity, pressure of the air and the CO2 concentration. The data processing is based on Ciddor equation for calculating the refractive index of air. The important advantage of the unit is a very low power consumption of the electronics so the unit causes only negligible temperature effects to the measured environment. The accuracy of the indirect measuring method employed by the unit was verified. We tested the accuracy in comparison with a direct method of measuring refractive index of air based on an evacuatable cell placed at the measuring arm of a laser interferometer. An experimental setup used for verification is presented together with a set of measurements describing the performance. The resulting accuracy of the electronic unit falls to the 4.1 × 10 −7 relatively.

Thermally compensated common-path differential interferometer with reduced long-term zero-drifts

“…The environmental interrogation unit E.I.U. (originally an indirect refractometer [23]) handles a set of environmental sensors: three temperature sensors with the resolution of 3 mK were calibrated with U = 0, 08 K (range from 20 • C to 29 • C, k = 2), the pressure sensor (resolution > 1 Pa, range from 85 kPa to 102 kPa, U = 0, 01 kPa) and sensor for the relative humidity (U = 1, 5 %). The triplet of temperature sensors is used to measure the temperature inside the enclosure (reference temperature T ref at the same point as the servo thermometer, which is not calibrated on an absolute scale), external temperature T external and the vertical temperature gradient T gradient .…”

A review of state-of-the-art 1D length scale calibration instruments

“…Ciddor [51] developed equations for refractive index for wavelengths in the visible and near infrared. A custom refractive index measurement unit [52] which uses these equations was utilised by Rerucha et al [53] in development of their new diode based stabilised laser source.…”

Linearized and compensated interferometric system for high-velocity traceable length calibration on a metre scale

“…The most significant influence of changing ambient conditions is the fluctuations of the refractive index of air, that influences the effective wavelength of the laser in air. In our system, the temperature, pressure and relative humidity are monitored 6 and used for a real-time correction of the effective laser wavelength so that the influence is mitigated down to the approximately 10 −8 level.…”