  Complex Semi-Definite Programming (SDP) is introduced as a novel approach to
phase retrieval enabled control of monochromatic light transmission through
highly scattering media. In a simple optical setup, a spatial light modulator
is used to generate a random sequence of phase-modulated wavefronts, and the
resulting intensity speckle patterns in the transmitted light are acquired on a
camera. The SDP algorithm allows computation of the complex transmission matrix
of the system from this sequence of intensity-only measurements, without need
for a reference beam. Once the transmission matrix is determined, optimal
wavefronts are computed that focus the incident beam to any position or
sequence of positions on the far side of the scattering medium, without the
need for any subsequent measurements or wavefront shaping iterations. The
number of measurements required and the degree of enhancement of the intensity
at focus is determined by the number of pixels controlled by the spatial light
modulator.
