  This paper presents a detailed, numerical study on the performance of the
standard phasing algorithms with random phase illumination (RPI). Phasing with
high resolution RPI and the oversampling ratio $\sigma=4$ determines a unique
phasing solution up to a global phase factor. Under this condition, the
standard phasing algorithms converge rapidly to the true solution without
stagnation. Excellent approximation is achieved after a small number of
iterations, not just with high resolution but also low resolution RPI in the
presence of additive as well multiplicative noises. It is shown that RPI with
$\sigma=2$ is sufficient for phasing complex-valued images under a sector
condition and $\sigma=1$ for phasing nonnegative images. The Error Reduction
algorithm with RPI is proved to converge to the true solution under proper
conditions.
