  We report on the use of 4.7-$\mu$m-diameter, optically levitated, charged
microspheres to image the three-dimensional force field produced by charge
distributions on an Au-coated, microfabricated Si beam in vacuum. An
upward-propagating, single-beam optical trap, combined with an interferometric
imaging technique, provides optimal access to the microspheres for microscopy.
In this demonstration, the Au-coated surface of the Si beam can be brought as
close as ${\sim}10~\mu$m from the center of the microsphere while forces are
simultaneously measured along all three orthogonal axes, fully mapping the
vector force field over a total volume of ${\sim}10^6~\mu$m$^3$. We report a
force sensitivity of $(2.5 \pm 1.0) \times 10^{-17}~{\rm N / \sqrt{Hz}}$, in
each of the three degrees of freedom, with a linear response to up to
${\sim}10^{-13}~{\rm N}$. While we discuss the case of mapping static electric
fields using charged microspheres, it is expected that the technique can be
extended to other force fields, using microspheres with different properties.
