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Galaxies are biased tracers of the matter density on cosmological scales. Forfuture tests of galaxy models, we refine and assess a method to measure galaxybiasing as function of physical scale $k$ with weak gravitational lensing. Thismethod enables us to reconstruct the galaxy bias factor $b(k)$ as well as thegalaxy-matter correlation $r(k)$ on spatial scales between $0.01\,h\,{\rmMpc^{-1}}\lesssim k\lesssim10\,h\,{\rm  Mpc^{-1}}$ for redshift-binned lens galaxies below redshift $z\lesssim0.6$.In the refinement, we account for an intrinsic alignment of sourceellipticities, and we correct for the magnification bias of the lens galaxies,relevant for the galaxy-galaxy lensing signal, to improve the accuracy of thereconstructed $r(k)$. For simulated data, the reconstructions achieve anaccuracy of $3-7\%$ (68\% confidence level) over the above $k$-range for asurvey area and a typical depth of contemporary ground-based surveys.Realistically the accuracy is, however, probably reduced to about $10-15\%$,mainly by systematic uncertainties in the assumed intrinsic source alignment,the fiducial cosmology, and the redshift distributions of lens and sourcegalaxies (in that order). Furthermore, our reconstruction technique employsphysical templates for $b(k)$ and $r(k)$ that elucidate the impact of centralgalaxies and the halo-occupation statistics of satellite galaxies on thescale-dependence of galaxy bias, which we discuss in the paper. In a firstdemonstration, we apply this method to previous measurements in theGarching-Bonn-Deep Survey and give a physical interpretation of the lenspopulation.

Scale dependence of galaxy biasing investigated by weak gravitational lensing: An assessment using semi-analytic galaxies and simulated lensing data