  Optical pump-probe spectroscopy is a powerful tool for the study of
non-equilibrium electronic dynamics and finds wide applications across a range
of fields, from physics and chemistry to material science and biology. However,
a shortcoming of conventional pump-probe spectroscopy is that photoinduced
changes in transmission, reflection and scattering can simultaneously
contribute to the measured differential spectra, leading to ambiguities in
assigning the origin of spectral signatures and ruling out quantitative
interpretation of the spectra. Ideally, these methods would measure the
underlying dielectric function (or the complex refractive index) which would
then directly provide quantitative information on the transient excited state
dynamics free of these ambiguities. Here we present and test a model
independent route to transform differential transmission or reflection spectra,
measured via conventional optical pump-probe spectroscopy, to changes in the
quantitative transient dielectric function. We benchmark this method against
changes in the real refractive index measured using time-resolved Frequency
Domain Interferometry in prototypical inorganic and organic semiconductor
films. Our methodology can be applied to existing and future pump-probe data
sets, allowing for an unambiguous and quantitative characterisation of the
transient photoexcited spectra of materials. This in turn will accelerate the
adoption of pump-probe spectroscopy as a facile and robust materials
characterisation and screening tool.
