Weak lensing by large-scale mass inhomogeneities in the Universe induces correlations in the observed ellipticities of distant sources .
We first review the harmonic analysis and statistics required of these correlations and discuss calculations for the predicted signal .
We consider the ellipticity correlation function , the mean-square ellipticity , the ellipticity power spectrum , and a global maximum-likelihood analysis to isolate a weak-lensing signal from the data .
Estimates for the sensitivity of a survey of a given area , surface density , and mean intrinsic source ellipticity are presented .
We then apply our results to the FIRST radio-source survey .
We predict an rms ellipticity of roughly 0.011 in 1 ^ { \circ } \times 1 ^ { \circ } pixels and 0.018 in 20 ^ { \prime } \times 20 ^ { \prime } pixels if the power spectrum is normalized to \sigma _ { 8 } \Omega ^ { 0.53 } = 0.6 , as indicated by the cluster abundance .
The signal is significantly larger in some models if the power spectrum is normalized instead to the COBE anisotropy .
The uncertainty in the predictions from imprecise knowledge of the FIRST redshift distribution is about 25 % in the rms ellipticity .
We show that FIRST should be able to make a statistically significant detection of a weak-lensing signal for cluster-abundance–normalized power spectra .