  Optical phase determination is an important and established tool in diverse
fields such as astronomy, biology, or quantum optics. There is increasing
interest in using a lower number of total photons. However, different noise
sources, such as electronic readout noise in the detector, and shot noise,
hamper the phase estimation in regimes of very low illumination. Here we report
a study on how the quality of phase determination is affected by these two
sources of noise. To that end, we experimentally reconstruct different
wavefronts by means of a point diffraction interferometer for different mean
intensities of illumination, up to $15\ \mathrm{phot/px}$. Our interferometer
features a Skipper-CCD sensor, which allows us to reduce the readout noise
arbitrarily, thus enabling us to separate the effect of these two sources of
noise. For two cases of interest: a spatial qudit encoding phase, consisting of
d = 6 uniform phase regions, and a more general continuous phase, we see that
reducing the readout noise leads to a clear improvement in the quality of
reconstruction. This can be explained by a simple noise model that allows us to
predict the expected fidelity of reconstruction and shows excellent agreement
with the measurements.
