A hadron beam with a uniform charge density, elliptical transverse profile,
and small four-dimensional (4D) emittance could mitigate space charge effects
in circular accelerators and improve collider performance. A phase space
painting method to generate such a distribution is being tested in the
Spallation Neutron Source (SNS) accumulator ring. A critical component of these
efforts is to measure the 4D emittance of the beam. Reconstruction of the 4D
emittance from wire-scanner data is a well-known technique. In this paper, we
discuss the implementation of a variant of the multi-optics method using the
four available wire-scanners near the SNS target, as well as the modification
of the wire-scanner region to utilize the fixed-optics method, a method that is
preferred due to its speed but can potentially lead to unacceptable bias and
uncertainty in the reconstructed emittances. We then demonstrate the usefulness
of the fixed-optics method by reconstructing the 4D emittance as a function of
time during accumulation in the SNS ring