  We consider the problem of recovering a signal from the magnitudes of affine
measurements, which is also known as {\em affine phase retrieval}. In this
paper, we formulate affine phase retrieval as an optimization problem and
develop a second-order algorithm based on Newton method to solve it. Besides
being able to convert into a phase retrieval problem, affine phase retrieval
has its unique advantages in its solution. For example, the linear information
in the observation makes it possible to solve this problem with second-order
algorithms under complex measurements. Another advantage is that our algorithm
doesn't have any special requirements for the initial point, while an
appropriate initial value is essential for most non-convex phase retrieval
algorithms. Starting from zero, our algorithm generates iteration point by
Newton method, and we prove that the algorithm can quadratically converge to
the true signal without any ambiguity for both Gaussian measurements and CDP
measurements. In addition, we also use some numerical simulations to verify the
conclusions and to show the effectiveness of the algorithm.
