  The Atmospheric Chemistry Experiment's Fourier Transform Spectrometer on the
SCISAT satellite has been measuring infrared transmission spectra of Earth
during Solar occultations since 2004. We use these data to build an infrared
transit spectrum of Earth. Regions of low atmospheric opacity, known as
windows, are of particular interest, as they permit observations of the
planet's lower atmosphere. Even in the absence of clouds or refraction,
imperfect transmittance leads to a minimum effective thickness of $h_{min}
\approx 4$ km in the 10--12$\mu$m opacity window at a spectral resolution of
$R=10^3$. Nonetheless, at $R=10^5$, the maximum transmittance at the surface is
around 70%. In principle, one can probe the troposphere of an Earth-like planet
via high-dispersion transit spectroscopy in the mid-infrared; in practice
aerosols and/or refraction likely make this impossible. We simulate the transit
spectrum of an Earth-like planet in the TRAPPIST-1 system. We find that a
long-term near-infrared campaign with JWST could readily detect CO$_2$,
establishing the presence of an atmosphere. A mid-IR campaign or longer NIR
campaign would be more challenging, but in principle could detect H$_2$O and
the biosignatures O$_3$ and CH$_4$.
