In the BoxCARS geometry, E3 imparts the phase onto the emitted photon echo, which is heterodyned by the LO field to determine the phase of the signal. The heterodyned signal is phased by matching the probe-axis projection of the 2D IR spectrum to the transient pump-probe spectrum. The 2D IR spectra collected in the fast-scan BoxCARS geometry were phased by taking the real part of the product of the analytic signal and exp( ) i , where  is a constant phase shift in the time domain. Phasing the spectra involved varying  from -π to π and finding the minimum root-mean-square-difference (RMSD) between the pump-probe spectrum and the phased 2D spectrum within the phase shift range. The probe-axis projection was allowed to shift by up to 2 cm -1 during the calculation of RMSD minimization to account for any errors in the probe axis calibration. To correct for LO phase drifts, spectra were recorded with fewer laser shots but with more repetitions, such that each resultant spectrum can be phased individually and then averaged together at a given waiting time. To compare the effects of background noise in two geometries, we analyzed the pump-slice amplitudes (PSAs) for both the fast-scan BoxCARS and pump-probe 2D IR spectra (Figure ). PSA analysis has been described in detail previously. In brief, PSA is the difference between the maximum and minimum amplitudes along ω3 at slices along the excitation (pump) axis, which gives spectra that are comparable to the linear absorption spectra.