On combining lensing shear information from multiple filters

We consider the possible gain in the measurement of lensing shear from imaging data in multiple filters. Galaxy shapes may differ significantly across filters, so that the same galaxy offers multiple samples of the shear. At the other extreme, if galaxy shapes are identical in different filters, one can combine them to improve the signal-to-noise ratio and thus increase the effective number density of faint, high redshift galaxies. We use the GOODS dataset to test these scenarios by calculating the covariance matrix of galaxy ellipticities in four visual filters (B,V,i,z). We find that galaxy shapes are highly correlated, and estimate the gain in galaxy number density by combining their shapes.