  We investigate weak lensing by large-scale structure using ray tracing
through N-body simulations. Photon trajectories are followed through high
resolution simulations of structure formation to make simulated maps of shear
and convergence on the sky. Tests with varying numerical parameters are used to
calibrate the accuracy of computed lensing statistics on angular scales from
about 1 arcminute to a few degrees. Various aspects of the weak lensing
approximation are also tested. For fields a few degrees on a side the shear
power spectrum is almost entirely in the nonlinear regime and agrees well with
nonlinear analytical predictions. Sampling fluctuations in power spectrum
estimates are investigated by comparing several ray tracing realizations of a
given model. For survey areas smaller than a degree on a side the main source
of scatter is nonlinear coupling to modes larger than the survey. We develop a
method which uses this effect to estimate the mass density parameter Omega from
the scatter in power spectrum estimates for subregions of a larger survey. We
show that the power spectrum can be measured accurately from realistically
noisy data on scales corresponding to 1-10 Mpc/h. Non-Gaussian features in the
one point distribution function of the weak lensing convergence (reconstructed
from the shear) are also sensitive to Omega. We suggest several techniques for
estimating Omega in the presence of noise and compare their statistical power,
robustness and simplicity. With realistic noise Omega can be determined to
within 0.1-0.2 from a deep survey of several square degrees.
