  High precision measurements of stellar spectroscopic line profiles and their
changes over time contain very valuable information about the physics of the
stellar photosphere (stellar activity) and can be used to characterize
extrasolar planets via the Rossiter-McLaughlin effect or from reflected light
from the planet.
  In this paper we present a new method for measuring small changes in the mean
line profile of a spectrum by performing what we call differential Least
Squares Deconvolution (dLSD). The method consists in finding the convolution
function (or kernel) required to transform a high signal-to-noise ratio
template of the star into each observed spectrum. Compared to similar
techniques, the method presented here does not require any assumptions on the
template spectrum (eg. no line-list or cross-correlation mask required).
  We show that our implementation of dLSD is able to perform -at least- as good
as other techniques by applying it to star-planet obliquity measurements of
exoplanet HD183799 during its transit. Among other things, the method should
enable model independent detection of light reflected by an exoplanet.
