  Fourier transform scanning tunneling spectroscopy (FTSTS) is a useful
technique for extracting details of the momentum-resolved electronic band
structure from inhomogeneities in the local density of states due to
disorder-related quasiparticle scattering. To a large extent, current
understanding of FTSTS is based on models of Friedel oscillations near isolated
impurities. Here, a framework for understanding many-impurity effects is
developed based on a systematic treatment of the variance Delta rho^2(q,omega)
of the Fourier transformed local density of states rho(q,\omega). One important
consequence of this work is a demonstration that the poor signal-to-noise ratio
inherent in rho(q,omega) due to randomness in impurity positions can be
eliminated by configuration averaging Delta rho^2(q,omega). Furthermore, we
develop a diagrammatic perturbation theory for Delta rho^2(q,omega) and show
that an important bulk quantity, the mean-free-path, can be extracted from
FTSTS experiments.
