This paper describes a new relative technique developed at LNE-Cnam, for the determination of the thermodynamic temperature of blackbodies without recourse to a radiometric reference. This technique is referred to as the ‘synthetic double wavelength technique’ (SDWT) as it is considered to be a particular case of the ‘double wavelength technique’ (DWT). It offers a new experimental technique for the determination of the thermodynamic temperature at high temperature and as such a new means for the mise-en-pratique of the new definition of the kelvin achievable by any national metrology institute provided a multi-wavelength radiation thermometer combining large and narrow bandwidths is available. In this work, a first experimental implementation of this technique based on a wavelength-tuneable spectroradiometer providing both narrowband and broadband signals with the particularity of the broadband signal being virtually synthesised from the spectral distribution of the narrowband signals sampled over a wide spectral range. SDWT determination of the thermodynamic temperature of a blackbody at 2760 K was performed with a level of uncertainty that confirms the promising capabilities of this technique.

A new least-squares method for the circle using a set of coordinate data (x(i), y(i)) is presented. This method provides analytical expressions for the coordinates ((X) over cap(0), (Y) over cap(0)) of the central point of a circle and its radius (R) over cap(0). Expressions for the variances V((X) over cap)(0), V((Y) over cap)(0) and V((R) over cap(0)), and the covariances cov((X) over cap(0), (Y) over cap(0)), cov((X) over cap(0), (R) over cap(0)) and cov((Y) over cap(0)(R) over cap(0)) are also presented. The method is applied to two problems, one in interferometry and the other in radiometry.