Abstract: Methods for controlling light transmission through a medium by transmitting light from a single spatial portion of an input optical field through the medium creating an output optical field, superposing the output optical field with a reference optical field creating an optical interference field, detecting an intensity of a spatial portion of a polarization component of the optical interference field and using the detected intensity to determine a value of an optical field amplitude and of an optical field phase for each of a plurality of spatial portions of the input optical field and for each of first and second orthogonal input polarization states of transmitted light entering the medium. The method may be used in the control of the transmission of light 1) through a medium, which is randomizing in amplitude, phase and/or polarization or 2) through a multi-mode fiber or for beam shaping, optical trapping and/or optical manipulation.