  A major bottleneck in nanoparticle measurements is the lack of comparability.
Comparability of measurement results is obtained by metrological traceability,
which is obtained by calibration. In the present work the calibration of
dimensional nanoparticle measurements is performed through the construction of
a calibration curve by comparison of measured reference standards to their
certified value. Subsequently, a general approach is proposed to perform a
measurement uncertainty evaluation for a measured quantity when no
comprehensive physical model is available, by statistically modelling
appropriately selected measurement data. The experimental data is collected so
that the influence of relevant parameters can be assessed by fitting a mixed
model to the data. Furthermore, this model allows to generate a probability
density function (PDF) for the concerned measured quantity. Applying this
methodology to dimensional nanoparticle measurements leads to a PDF for a
measured dimensional quantity of the nanoparticles. A PDF for the measurand,
which is the certified counterpart of that measured dimensional quantity, can
then be extracted by reporting a PDF for the measured dimensional quantity on
the calibration curve. The PDF for the measurand grasps its total measurement
uncertainty. Working in a fully Bayesian framework is natural due to the
instrinsic caracter of the quantity of interest: the distribution of size
rather than the size of one single particle. The developed methodology is
applied to the particular case where dimensional nanoparticle measurements are
performed using an atomic force microscope (AFM). The reference standards used
to build a calibration curve are nano-gratings with step heights covering the
application range of the calibration curve.
