  We investigate interferometric techniques to estimate the deflection angle of
an optical beam and compare them to the direct detection of the beam
deflection. We show that quantum metrology methods lead to a unifying treatment
for both single photons and classical fields. Using the Fisher information to
assess the precision limits of the interferometric schemes, we show that the
precision can be increased by exploiting the initial transverse displacement of
the beam. This gain, which is present for both Sagnac and Mach-Zehnder-like
configurations, can be considerable when compared to non-interferometric
methods. In addition to the fundamental increase in precision, the
interferometric schemes have the technical advantage that (i) the precision
limits can be saturated by a sole polarization measurement on the field, and
that (ii) the detection system can be placed at any longitudinal position along
the beam. We also consider position-dependent polarization measurements, and
show that in this case the precision increases with the propagation distance,
as well as the initial transverse displacement.
