  We investigate the performance of ptychography with noisy data by analyzing
the Cram\'{e}r Rao Lower Bound. The lower bound of ptychography is derived and
numerically computed for both plane wave and structured illumination. The
influence of Poisson noise on the ptychography reconstruction is discussed. The
computation result shows that, if the estimator is unbiased, the minimum
variance for Poisson noise is mostly determined by the illumination power and
the transmission function of the object. Monte Carlo analysis is conducted to
validate our calculation results for different photon numbers. The performance
of the maximum likelihood method and the approach of amplitude-based cost
function minimization is studied in the Monte Carlo analysis also.
