New results are reported from an ongoing international research effort to accurately determine the Avogadro constant by counting the atoms in an isotopically enriched silicon crystal. The surfaces of two 28 Si-enriched spheres were decontaminated and reworked in order to produce an outer surface without metal contamination and improved sphericity. New measurements were then made on these two reconditioned spheres using improved methods and apparatuses. When combined with other recently refined parameter measurements, the Avogadro constant derived from these new results has a value of N A = 6.022 140 76(12) × 10 23 mol -1 . The X-ray crystal density method has thus achieved the target relative standard uncertainty of 2.0 × 10 -8 necessary for the realization of the definition of the new kilogram.

The need for high-quality aspheres is rapidly growing, necessitating increased accuracy in their measurement. A reliable uncertainty assessment of asphere form measurement techniques is difficult due to their complexity. In order to explore the accuracy of current asphere form measurement techniques, an interlaboratory comparison was carried out in which four aspheres were measured by eight laboratories using tactile measurements, optical point measurements, and optical areal measurements. Altogether, 12 different devices were employed. The measurement results were analysed after subtracting the design topography and subsequently a best-fit sphere from the measurements. The surface reduced in this way was compared to a reference topography that was obtained by taking the pointwise median across the ensemble of reduced topographies on a Cartesian grid. The deviations of the reduced topographies from the reference topography were analysed in terms of several characteristics including peak-to-valley and root-mean-square deviations. Root-mean-square deviations of the reduced topographies from the reference topographies were found to be on the order of some tens of nanometres up to 89 nm, with most of the deviations being smaller than 20 nm. Our results give an indication of the accuracy that can currently be expected in form measurements of aspheres.

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.

The General Conference on Weights and Measures (CGPM) discusses the improvements of a possible revision of the International System of Units (SI). For the new definition of the kilogram apart from an artifact of Platinum-Iridium a suitable fundamental constant seems to be found, to which the kg could be related. Although the Planck constant, h, is being considered for the new definition, its value can currently be determined with less uncertainty from the value of the Avogadro constant, NA. As well the determination of the Avogadro constant is suitable as a primary method for the subsequent realization of the kilogram. The international Avogadro group has reached so far a relative measurement uncertainty of 3×10-8, mainly limited by the interferometric measurement of the volume of the 28Si-spheres, used to count the atoms. The dominant influence on the measurement uncertainty is a contribution which subsumes wavefront aberrations due to surface deviations and irregularities of the spheres polished from our partner at CSIRO, Australia. A new multi-step machining process, developed and realized at PTB, reduces considerably the surface contamination and creates spheres with surface properties which exceed the standards in matters of form deviation and surface roughness. The manufacturing process incorporates highly reproducible multi-step grinding and polishing steps. The surfaces are almost free of scratches and show average roughness values below 0.3 nm. The form shows some regular, long wavelength errors below 30 nm in amplitude, collocated conform to crystal orientation.

A novel device is presented which is designed for in-process measurements of the variation of the diameter of highly reflective spheres. Silicon spheres have been used for the new definition of the International System of Units (SI). Many spheres have to be processed, and the form of these objects, and thus the manufacturing process’s stability, needs to be controlled every day. Commercially available measurement equipment and even state-of-the-art spherical interferometers have reached their limits in terms of resolution, uncertainty, the complexity of their handling routines, measurement time and even financial investment. A novel setup has thus been designed after considering and selecting a special mechanical setup with a minimal measurement loop, stable optical sensors and a handling strategy which avoids collision and contact with the very valuable, superpolished spherical objects. Thus, the design minimizes the influence of the environment and reduces the measurement time at an equator with sub-nanometre resolution to 3 min. In addition, the analysis time is reduced to less than a minute.