  Scanning tunneling spectroscopy (STS) is a useful probe for studying the
cuprates in the superconducting and pseudogap states. Here we present a
theoretical study of the Z-map, defined as the ratio of the local density of
states at positive and negative bias energies, which frequently is used to
analyze STS data. We show how the evolution of the quasiparticle interference
peaks in the Fourier transform Z-map can be understood by considering different
types of impurity scatterers, as well as particle-hole asymmetry in the
underlying bandstructure. We also explore the effects of density wave orders,
and show that the Fourier transform Z-map may be used to both detect and
distinguish between them.
