The quality of images computed from digital holograms or heterodyne array imaging is degraded by phase errors in the object and/or reference beams at the time of measurement. This paper describes computer simulations used to compare the performance of digital shearing laser interferometry and various sharpness metrics for the correction of such phase errors when imaging a diffuse object. These algorithms are intended for scenarios in which multiple holograms can be recorded with independent object speckle realizations and a static phase error. Algorithm performance is explored as a function of the number of available speckle realizations and signal-to-noise ratio (SNR). The performance of various sharpness metrics is examined in detail and is shown to vary widely. Under ideal conditions with $>15$ speckle realizations and high SNR, phase corrections better than $\lambda ∕50$ root-mean-square (RMS) were obtained. Corrections better than $\lambda ∕10$ RMS were obtained in the high SNR regime with as few as two speckle realizations and at object beam signal levels as low as 2.5 photons/speckle with six speckle realizations.