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A weak scattering potential imposed on a $CuO_2$ layer of a cupratesuperconductor modulates the local density of states $N(x,\omega)$. In recentlyreported experimental studies scanning-tunneling maps of $N(x,\omega)$ havebeen Fourier transformed to obtain a wave-vector power spectrum. Here, for thecase of a weak scattering potential, we discuss the structure of this powerspectrum and its relationship to the quasi-particle spectrum and the structurefactor of the scattering potential. Examples of quasi-particle interferences innormal metals and $s$- and d-wave superconductors are discussed.Comment: 22 pages, 21 figures; enlarged discussion of the d-wave response, to  be published in Physical Review

Wave-vector power spectrum of the local tunneling density of states: Ripples in ad-wave sea