  The electromagnetic calorimeter for the new muon (g-2) experiment at Fermilab
will consist of arrays of PbF2 Cherenkov crystals read out by large-area
silicon photo-multiplier (SiPM) sensors. We report here on measurements and
simulations using 2.0 -- 4.5 GeV electrons with a 28-element prototype array.
All data were obtained using fast waveform digitizers to accurately capture
signal pulse shapes versus energy, impact position, angle, and crystal
wrapping. The SiPMs were gain matched using a laser-based calibration system,
which also provided a stabilization procedure that allowed gain correction to a
level of 1e-4 per hour. After accounting for longitudinal fluctuation losses,
those crystals wrapped in a white, diffusive wrapping exhibited an energy
resolution sigma/E of (3.4 +- 0.1) % per sqrt(E/GeV), while those wrapped in a
black, absorptive wrapping had (4.6 +- 0.3) % per sqrt(E/GeV). The
white-wrapped crystals---having nearly twice the total light
collection---display a generally wider and impact-position-dependent pulse
shape owing to the dynamics of the light propagation, in comparison to the
black-wrapped crystals, which have a narrower pulse shape that is insensitive
to impact position.
