The acoustic method for determination of the refractive index of air is a new promising method for improving accuracy of interferometric displacement measurements in air. The method is based on the measurement of the speed of ultrasound over the same distance measured with a laser interferometer. The effectiveness of the method derives from the fact that the relative effect of a change in air temperature is about two thousand times greater on the speed of sound than on the refractive index of air.
During this co-operation in research the device and equations developed at MIKES are compared against PTB’s interferometric nanometer comparator operated in a vacuum. Simultaneously measured displacement with a vacuum interferometer and heterodyne interferometer in air with acoustic measurement for the refractive index along the beam of the heterodyne interferometer will give a good view of the properties of the method and equations in laboratory conditions at temperatures near 20°C.
 A. Lassila, V. Korpelainen, 'An acoustic method for determination of the effective temperature and refractive index of air', in Proc. SPIE, 5190, 2003
 J. Flügge, R. Köning : 'Status of the nanometer comparator at PTB', Proc. SPIE, 4401, 2001
Final Report 2004-12-30
In September between 13th and 24th measurements for the project were carried out at PTB.
Displacement of a corner cube fixed to a measurement stage was measured simultaneously with an interferometer with acoustic wavelength compensation (MIKES) and a vacuum interferometer (PTB nanometer comparator). Angle deviations of the vacuum interferometer were measured by angle interferometer and Abbe error was corrected. The reference temperature was measured by 2 Pt25 thermometers, humidity was measured by a dew point meter and pressure by a reference pressure meter.
During the measurements room temperature was adjusted to some set points and also air humidity and pressure varied. The measurement stage was scanned repeatedly back and forth in ten steps. The acoustic measurement was carried out and displacement data was read from both instruments simultaneously. The refractive index of air was determined by three different ways; nac by acoustic speed of sound measurements, ni by displacements measured with interferometers both without n correction and ne by Edlen equations and measured environmental data. Two of the methods were independent of the acoustic method.
The results measured under 9 different ambient air conditions were analyzed. If data of one series is omitted due to noticed thermal drift, the difference between the interferometers with 0.6 m displacement was -33 nm with standard deviation of 7 nm.
However, it seems that there are some other errors influencing the data since difference between ni and ne was around 1.3x10-7, which corresponds to 80 nm in length with STD of 10 nm. The difference between ne and nac was 1.0x10-7 or 64 nm with STD of 5 nm.
Separate analysis shows that acoustically measured temperature and reference temperature followed slow temperature changes equally within a few mK. Different time constants were believed to be the main reason for the variations. However, there was approximately 100 mK difference in the measured air temperature. The reason for that is still unclear but the temperature difference corresponds with the measured discrepancy of the refractive indices and must therefore be studied in more detail. Another possible source for the discrepancy could be bending effects in the granite base due to the translation of the measurement slide which could cause a lateral shift of one interferometer beamsplitter.
The comparison showed that acoustic method has high sensitivity to air temperature and refractive index measurements. However, when working over short distances with the current set-up there seems to be some increase in uncertainty maybe due to non-linear burst propagation or echoes.