where , ∆ , and Δ is the frequency fluctuation at time , the amplitude of frequency fluctuations, decay constant, and the static inhomogeneity components, respectively. is the constant giving rise to the homogeneous width and is the waiting time between pump and probe pulses. The FFCF decay constant for the ester carbonyl stretch is determined to be approximately 1.07 ps for the 1:9 POPS:DMPC vesicles.