A model consisting of a sum of exponential functions is very useful
for the description of time-resolved spectroscopy data. Each exponential
term in the sum can often be associated with a given state of the physical
system underlying the measurement, such as a protein excited by laser light.
Then the exponential decay rate associated with each state describes the time
profile of the contribution of the state to the observed data. The linear coefficients
of the sum represent the relative amplitudes of the contributions of each
state. When time-resolved spectroscopy data represent more than one wavelength,
a linear coefficient is associated with each exponential decay term at
each wavelength. In this chapter sum-of-exponentials models for time-resolved
spectroscopy applications are reviewed. The parameter estimation problem of
fitting the decay rates and linear coefficients of the sum under the least squares
criteria is also reviewed, with attention to implementation of algorithms for
model fitting. Case studies in fitting models to picosecond time-scale spectroscopic
data illustrate the reviewed topics.
Keywords: Sum of exponentials; time-resolved spectroscopy
