  For field electron emission (FE), an empirical equation for measured current
I_m as a function of measured voltage V_m has the form I_m =
C*(V_m)^k*exp[-B/(V_m)], where B is a constant and C and k are constants or
vary weakly with V_m. Values for k can be extracted (a) from simulations based
on some specific FE theory, and in principle (b) from current-voltage
measurements of sufficiently high quality. This paper shows that comparison of
theoretically derived and experimentally derived k-values could provide a
sensitive and useful tool for comparing FE theory and experiment, and for
choosing between alternative theories. Existing methods of extracting k-values
from experimental or simulated current-voltage data are discussed, including a
modernised "least residual" method, and existing knowledge concerning k-values
is summarised. Exploratory simulations are reported. Where an analytical result
for k is independently known, this value is reliably extracted. More generally,
extracted k-values are sensitive to details of the emission theory used, but
also depend on assumed emitter shape; these two influences will need to be
disentangled by future research, and a range of emitter shapes will need
examination. Other procedural conclusions are reported. Some scientific issues
that this new tool may be able to help investigate are indicated.
