  Detection dead zones and heading errors induced by light shifts are two
important problems in optically pumped scalar magnetometry. We introduce an
atomic orientation based single-beam magnetometry scheme to simultaneously
solve these problems, using a polarization-reversing and path-bending Herriott
cavity. Here, a reflection mirror is inserted into the cavity to bend the
optical paths in the middle, and divide them into two separated orthogonal
regions to avoid the detection dead zone. Moreover, half-wave plates are added
in the center of each optical region, so that the light polarization is flipped
each time it passes the wave plates and the light shift effects are spatially
averaged out. This operation is demonstrated to eliminate the unnoticed heading
errors induced by ac light shifts. The methods developed in this paper are
robust to use, and easy to be applied in other atomic devices.
