Chromatic biases. Top: squared relative shifts in PSF centroid, ﹩{({\rm{\Delta }}\bar{R})}^{2}﹩, due to DCR for objects with different SEDs, in LSST r-band (left) and i-band (right) for a zenith angle of 45°. Middle: relative shifts in second central moment, ﹩{\rm{\Delta }}V﹩, due to DCR for objects with different SEDs, in LSST r-band (left) and i-band (right) for a zenith angle of 45°. Bottom: relative fractional shifts in second-moment squared radius, ﹩{\rm{\Delta }}{r}_{\mathrm{PSF}}^{2}/{r}_{\mathrm{PSF}}^{2}﹩, due to chromatic seeing for objects with different SEDs, in LSST r-band (left) and i-band (right). In each panel, the shifts are calculated relative to the mean stellar shift: ﹩{\rm{\Delta }}X=X-\langle X{\rangle }_{\mathrm{stars}}﹩. The blue histograms on the left axes correspond to 4000 stars with ﹩17\lt {i}_{\mathrm{AB}}\lt 22﹩ in the LSST simulated catalog CATSIM. The red projected histograms correspond to 4000 galaxies with ﹩{i}_{\mathrm{AB}}\lt 25.3﹩ in CATSIM. Each galaxy is represented by a colored dot and plotted as a function of redshift, with the color scale (shown on the plot) indicating the observer-frame r − i color of each galaxy. The red (blue) curves indicate the running means (square-root-variances) of the relative galactic shift. The gray bands in the lower panels indicate requirements on the mean shifts such that the resulting systematic uncertainty is less than the expected statistical uncertainty for the entire survey for DES (light gray outer band) and LSST (dark gray inner band). The shaded bands in the upper panels indicate the sufficient (but not necessary) requirements on the square-root-variance. Note that the plotting range is set to highlight the data and thus each requirement band may not be entirely visible.