The optimal weighting function for cosmic magnification measurement
  through foreground galaxy-background galaxy (quasar) cross correlation
  Cosmic magnification has been detected through cross correlation between
foreground and background populations (galaxies or quasars). It has been shown
that weighing each background object by its $\alpha-1$ can significantly
improve the cosmic magnification measurement \citep{Menard02,Scranton05}. Here,
$\alpha$ is the logarithmic slope of the luminosity function of background
populations. However, we find that this weighting function is optimal only for
sparse background populations in which intrinsic clustering is negligible with
respect to shot noise. We derive the optimal weighting function for general
case including scale independent and scale dependent weights. The optimal
weighting function improves the S/N (signal to noise ratio) by $\sim 20%$ for a
BigBOSS-like survey and the improvement can reach a factor of $\sim 2$ for
surveys with much denser background populations.
