  Fourier ptychography is a new computational microscopy technique that
provides gigapixel-scale intensity and phase images with both wide
field-of-view and high resolution. By capturing a stack of low-resolution
images under different illumination angles, a nonlinear inverse algorithm can
be used to computationally reconstruct the high-resolution complex field. Here,
we compare and classify multiple proposed inverse algorithms in terms of
experimental robustness. We find that the main sources of error are noise,
aberrations and mis-calibration (i.e. model mis-match). Using simulations and
experiments, we demonstrate that the choice of cost function plays a critical
role, with amplitude-based cost functions performing better than
intensity-based ones. The reason for this is that Fourier ptychography datasets
consist of images from both brightfield and darkfield illumination,
representing a large range of measured intensities. Both noise (e.g. Poisson
noise) and model mis-match errors are shown to scale with intensity. Hence,
algorithms that use an appropriate cost function will be more tolerant to both
noise and model mis-match. Given these insights, we propose a global Newton's
method algorithm which is robust and computationally efficient. Finally, we
discuss the impact of procedures for algorithmic correction of aberrations and
mis-calibration.
