Accurate characterization and prediction of beam halo has been historically prohibited by an inability to measure beam phase distributions with the required sensitivity level. To address this limitation, a system for measuring transverse beam emittance with very high dynamic range is developed at the Spallation Neutron Source Beam Test Facility. An emittance of a 20 mA H- beam is measured at the 2.5 MeV RFQ exit with the dynamic range larger than 1-part-per-million for the first time. Though no obvious halo is observed within this dynamic range for this particular configuration, the measurement demonstrates a capability to resolve beam distributions at the level required for inspection and characterization of beam halo.