  Ptychography is a lensless imaging technique, which considers reconstruction
from a set of far-field diffraction patterns obtained by illuminating small
overlapping regions of the specimen. In many cases, a distribution of light
inside the illuminated region is unknown and has to be estimated along with the
object of interest. This problem is referred to as blind ptychography. While in
ptychography the illumination is commonly assumed to have a point spectrum, in
this paper we consider an alternative scenario with non-trivial light spectrum
known as blind polychromatic ptychography.
  Firstly, we show that non-blind polychromatic ptychography can be seen as a
recovery from quadratic measurements. Then, a reconstruction from such
measurements can be performed by a variant of Amplitude Flow algorithm, which
has guaranteed sublinear convergence to a critical point. Secondly, we address
recovery from blind polychromatic ptychographic measurements by devising an
alternating minimization version of Amplitude Flow and showing that it
converges to a critical point at a sublinear rate.
  Keywords: ptychography, phase retrieval, blind, alternating minimization,
gradient descent.
