  It is a common practice in the solar physics community to test whether or not
measured photospheric or chromospheric vector magnetograms are force-free,
using the Maxwell stress as a measure. Some previous studies have suggested
that magnetic fields of active regions in the solar chromosphere are close to
be force-free whereas there is no consistency among previous studies on whether
magnetic fields of active regions in the solar photosphere are force-free or
not. Here we use three kinds of representative magnetic fields (analytical
force-free solutions, modeled solar-like force-free fields and observed
non-force-free fields) to discuss on how the measurement issues such as limited
field of view, instrument sensitivity and measurement error could affect the
estimation of force-freeness based on observed magnetograms. Unlike previous
studies that focus on discussing the effect of limited field of view or
instrument sensitivity, our calculation shows that just measurement error alone
can significantly influence the results of force-freeness estimate, due to the
fact that measurement errors in horizontal magnetic fields are usually ten
times larger than that of the vertical fields. This property of measurement
errors, interacting with the particular form of force-freeness estimate
formula, would result in wrong judgments of the force-freeness: a truly
force-free field may be mistakenly estimated as being non-force-free and a true
non-force-free field may be estimated as being force-free. Our analysis calls
for caution when interpreting the force-freeness estimates based on measured
magnetograms, and also suggests that the true photospheric magnetic field may
be further away from being force-free than they currently appear to be.
