  We report direct measurements of the magnetic field screening at the limits
of the Meissner phase for two superconducting Nb samples. The samples are
processed with two different surface treatments that have been developed for
superconducting radio-frequency cavity applications -- a "baseline" treatment
and an oxygen-doping ("O-doping") treatment. The measurements show: 1) that the
screening length is significantly longer in the "O-doping" sample compared to
the "baseline" sample; 2) that the screening length near the limits of the
Meissner phase increases with applied field; 3) the evolution of the screening
profile as the material transitions from the Meissner phase to the mixed phase;
and 4) a demonstration of the absence of any screening profile for the highest
applied field, indicative of the full flux entering the sample. Measurements
are performed utilizing the $\beta$-detected nuclear magnetic resonance
($\beta$-NMR) technique that allows depth resolved studies of the local
magnetic field within the first 100 nm of the surface. The study takes
advantage of the $\beta$-SRF beamline, a new facility at TRIUMF, Canada, where
field levels up to 200 mT are available parallel to the sample surface to
replicate radio frequency (RF) fields near the Meissner breakdown limits of Nb.
