  A primary aim of the Nuclear Spectroscopic Telescope Array (NuSTAR) mission
is to find and characterize heavily obscured Active Galactic Nuclei (AGNs).
Based on mid-infrared photometry from the Wide-Field Infrared Survey Explorer
(WISE) and optical photometry from the Sloan Digital Sky Surveys, we have
selected a large population of luminous obscured AGN (i.e., obscured quasars).
Here we report NuSTAR observations of four WISE-selected heavily obscured
quasars for which we have optical spectroscopy from the Southern African Large
Telescope and W. M. Keck Observatory. Optical diagnostics confirm that all four
targets are AGNs. With NuSTAR hard X-ray observations, three of the four
objects are undetected, while the fourth has a marginal detection. We confirm
that these objects have observed hard X-ray (10-40 keV) luminosities at or
below ~ 10^43 erg s^-1. We compare X-ray and IR luminosities to obtain
estimates of the hydrogen column densities (N_H) based on the suppression of
the hard X-ray emission. We estimate N_H of these quasars to be at or larger
than 10^25 cm^-2, confirming that WISE and optical selection can identify very
heavily obscured quasars that may be missed in X-ray surveys, and do not
contribute significantly to the cosmic X-ray background. From the optical
Balmer decrements, we found that our three extreme obscured targets lie in
highly reddened host environments. This galactic extinction is not adequate to
explain the more obscured AGN, but it may imply a different scale of
obscuration in the galaxy.
