  The dispersed fixed-delay interferometer (DFDI) represents a new instrument
concept for high-precision radial velocity (RV) surveys for extrasolar planets.
A combination of Michelson interferometer and medium-resolution spectrograph,
it has the potential for performing multi-object surveys, where most previous
RV techniques have been limited to observing only one target at a time. Because
of the large sample of extrasolar planets needed to better understand planetary
formation, evolution, and prevalence, this new technique represents a logical
next step in instrumentation for RV extrasolar planet searches, and has been
proven with the single-object Exoplanet Tracker (ET) at Kitt Peak National
Observatory, and the multi-object W. M. Keck/MARVELS Exoplanet Tracker at
Apache Point Observatory. The development of the ET instruments has
necessitated fleshing out a detailed understanding of the physical principles
of the DFDI technique. Here we summarize the fundamental theoretical material
needed to understand the technique and provide an overview of the physics
underlying the instrument's working. We also derive some useful analytical
formulae that can be used to estimate the level of various sources of error
generic to the technique, such as photon shot noise when using a fiducial
reference spectrum, contamination by secondary spectra (e.g., crowded sources,
spectroscopic binaries, or moonlight contamination), residual interferometer
comb, and reference cross-talk error. Following this, we show that the use of a
traditional gas absorption fiducial reference with a DFDI can incur significant
systematic errors that must be taken into account at the precision levels
required to detect extrasolar planets.
