  We present methods for analyzing Beam Emission Spectroscopy (BES) data to
obtain the plasma density evolution associated with rapid sawtooth crash events
at the DIII-D tokamak. BES allows coverage over a 2-D spatial plane, inherently
local measurements, with fast time responses, and therefore provides a valuable
new channel for data during sawtooth events. A method is developed to remove
sawtooth-induced edge-light pulses contained in the BES data. The edge light
pulses appear to be from the $\rm{D}_{\alpha}$ emission produced by edge
recycling during sawtooth events, and are large enough that traditional
spectroscopic filtering and data analysis techniques are insufficient to deduce
physically meaningful quantities. A cross-calibration of 64 BES channels is
performed using a novel method to ensure accurate measurements. For the
large-amplitude density oscillations observed, we discuss and use the
non-linear relationship between BES signal $\delta I/I_{0}$ and plasma density
variation $\delta n_{e}/n_{e0}$. 2-D BES images cover a 8~cm~$\times$~20~cm
region around the sawtooth inversion layer and show large-amplitude density
oscillations, with additional significant spatial variations across the
inversion layer, which grows and peaks near the time of the temperature crash.
The edge light removal technique and method of converting large-amplitude
$\delta I/I_{0}$ to $\delta n_{e}/n_{e0}$ presented here may help analyze other
impulsive MHD phenomena in tokamaks.
