We use photon-counting to measure nonlinear Thomson scattering from low-density electrons in an intense laser focus. The azimuthal and longitudinal polarization components of the second harmonic are measured across much of the full emission sphere. The data show, for the first time experimentally, emission structure in the ‘Northern’ and ‘Southern’ hemispheres, where the ‘North Pole’ aligns with the direction of laser propagation. To obtain these measurements, we installed an additional power amplifier on our Ti:sapphire laser system at BYU. The upgrade delivers ten times more energy to the laser focus than we had previously. This increase comes partly from the additional amplifier and partly from increased grating efficiency in our pulse compressor. We achieve an on-target pulse energy of 200 mJ at 35 fs. The focal spot size has radius w0 = 4 μm. This corresponds to an available peak intensity of over 1019 W/cm2, an order of magnitude above the onset of strong relativistic effects. The interaction region in the laser focus has a length of approximately 100 μm. Photons scattered from this region are collected using a 5-cm-focal-length lens and then focused onto the end of a 100-μm-diameter fiber by a second identical lens. The imaging system requires precise alignment with the laser focus, which must be maintained when rotating the photon-collection system along the longitudinal direction of the emission sphere. We developed an alignment procedure that ensures that the detector rotation axis aligns with region of space that is imaged onto the fiber. This region is then aligned to the laser focal spot.