  The use of Nye's dislocation tensor for calculating the density of
geometrically necessary dislocations (GND) is widely adopted in the study of
plastically deformed materials. The curl operation involved in finding the Nye
tensor, while conceptually straightforward has been marred with inconsistencies
and several different definitions are in use. For the three most common
definitions, we show that their consistent application leads to the same
result. To eliminate frequently encountered confusion, a summary of expressions
for Nye's tensor in terms of elastic and plastic deformation gradient, and for
both small and large deformations, is presented. A further question when
estimating GND density concerns the optimization technique used to solve the
under-determined set of equations linking Nye's tensor and GND density. A
systematic comparison of the densities obtained by two widely used techniques,
L1 and L2 minimisation, shows that both methods yield remarkably similar total
GND densities. Thus the mathematically simpler, L2, may be preferred over L1
except when information about the distribution of densities on specific slip
systems is required. To illustrate this, we compare experimentally measured
lattice distortions beneath nano-indents in pure tungsten, probed using
3D-resolved synchrotron X-ray micro-diffraction, with those predicted by 3D
strain-gradient crystal plasticity finite element calculations. The results are
in good agreement and show that the volumetric component of the elastic strain
field has a surprisingly small effect on the determined Nye tensor. This is
important for experimental techniques, such as micro-beam Laue measurements and
HR-EBSD, where only the deviatoric strain component is measured.
