  It has been shown that spectroscopy of transiting extrasolar planets can
potentially provide a wealth of information about their atmospheres. Herein, we
set up the inverse problem in spectroscopic retrieval. We use non-linear
optimal estimation to retrieve the atmospheric state (pioneered for Earth
sounding by Rodgers 1976, 2000). The formulation quantifies the the
degrees-of-freedom and information content of the spectrum with respect to
geophysical parameters; herein, we focus specifically on temperature and
composition. First, we apply the technique to synthetic near infrared spectra,
and explore the influence of spectral signal-to-noise ratio and resolution (the
two important parameters when designing a future instrument) on the information
content of the data. As expected, we find that the number of retrievable
parameters increase with increasing signal-to-noise and resolution, although
the gains quickly asymptote for large values. Second, we apply the methods to
the previously studied atmosphere of HD198733b, and compare the results of our
retrieval with those obtained by others.
