We measured the absolute lengths of three single crystal silicon samples by means of an imaging Twyman-Green interferometer in the temperature range from 7 K to 293 K with uncertainties of about 1 nm. From these measurements we extract the coefficient of thermal expansion with uncertainties in the order of 1 × 10 −9 /K. To access the functional dependence of the length on the temperature usually polynomials are fitted to the data. Instead we use a physically motivated model equation with 7 fit parameters for the whole temperature range. The coefficient of thermal expansion is obtained from the derivative of the best fit. The measurements conducted in 2012 and 2014 demonstrate a high reproducibility and the agreement of two independently produced samples supports single crystal silicon as reference material for thermal expansion. Although the results for all three samples agree with each other and with measurements performed at other institutes, they significantly differ from the recommended values for thermal expansion of crystalline silicon.

A new Ultra Precision Interferometer (UPI) was built at Physikalisch-Technische Bundesanstalt. As its precursor, the precision interferometer, it was designed for highly precise absolute length measurements of prismatic bodies, e.g. gauge blocks, under well-defined temperature conditions and pressure, making use of phase stepping imaging interferometry. The UPI enables a number of enhanced features, e.g. it is designed for a much better lateral resolution and better temperature stability. In addition to the original concept, the UPI is equipped with an external measurement pathway (EMP) in which a prismatic body can be placed alternatively. The temperature of the EMP can be controlled in a much wider range compared to the temperature of the interferometer's main chamber. An appropriate cryostat system, a precision temperature measurement system and improved imaging interferometry were established to permit absolute length measurements down to cryogenic temperature, demonstrated for the first time ever. Results of such measurements are important for studying thermal expansion of materials from room temperature towards less than 10 K.

Gauge blocks (GBs) are very important material standards that provide industry with reliable and traceable standards of length. At the highest accuracy level, the measurement of GBs must be performed by interferometry. The double ended interferometer (DEI) offers an alternative to obtain traceable measurements of the absolute length of GB shaped objects without the need for a platen to be wrung to one of the faces. In spite of this general advantage, there is no reliable DEI system being used at any National Metrology Institute (NMI). PTB, as the NMI of Germany, is developing a dedicated DEI which will be situated in a temperature-stabilized vacuum chamber. This paper describes a preliminary prototype DEI that was built firstly to study the measurement principle, and secondly to learn about the challenges and limitations to be taken into consideration for the final design. A comparison of results from the DEI measurements and those from PTB's existing single ended GB interferometers (SEI) indicates that the present prototype is a basis for the final version.

The refractive index of air is a major limiting factor in length measurements by interferometry, which are mostly performed under atmospheric conditions. Therefore, especially in the last century, measurement and description of the air refractive index was a key point in order to achieve accuracy in the realisation of the length by interferometry. Nevertheless, interferometric length measurements performed in vacuum are much more accurate since the wavelength of the light is not affected by the air refractive index. However, compared with thermal conditions in air, in high vacuum heat conduction is missing. In such a situation, dependent on the radiative thermal equilibrium, a temperature distribution can be very inhomogeneous. Using a so-called contact gas instead of high vacuum is a very effective way to enable heat conduction on nearly the same level as under atmospheric pressure conditions whereby keeping the effect of the air refractive index on a small level. As physics predicts, and as we have demonstrated previously, helium seems like the optimal contact gas because of its large heat conduction and its refractive index that can be calculated from precisely known parameters. On the other hand, helium gas situated in a vacuum chamber could easily be contaminated, e.g. by air leakage from outside. Above the boiling point of oxygen (−183 °C) it is therefore beneficial to use dry air as a contact gas. In such an approach, the air refractive index could be calculated based on measured quantities for pressure and temperature. However, existing formulas for the air refractive index are not valid in the low-pressure regime. Although it seems reasonable that the refractivity (n − 1) of dry air simply downscales with the pressure, to our knowledge there is no experimental evidence for the applicability of any empirical formula. This evidence is given in the present paper which reports on highly accurate measurements of the air refractive index n for the wavelengths 532 nm, 633 nm and 780 nm in the low-pressure regime from 0 Pa to 1300 Pa. In our approach, using a vacuum cell, n − 1 is obtained from the comparison of optical path lengths in vacuum and air along the same path by imaging interferometry. These measured values are compared with the ones obtained from Bönsch's formula. An agreement of ±10 −9 is found in the low-pressure regime. Accordingly, this formula could be applied for the accurate determination of the refractive index of dry air even at low pressures, provided that the pressure is measured with high accuracy.

Humidity is the most problematic parameter for the accurate determination of the refractive index of air. Besides the fact that the humidity measurement can be limiting, the existing empirical equations for the refractive index of moist air are either restricted to 20 degrees C or are based on insufficient knowledge of the refractivity of water vapor. To overcome this problem, a new kind of measurement method for the refractivity of water vapor is suggested that is based on the accurate measurement of the absolute length of a step length by interferometry under vacuum conditions and subsequent measurements at different well-defined absolute water vapor pressures.