Phase retrieval from the optical vortex scanning microscopy

We consider an optical system in which the optical vortex moves inside the focused Gaussian beam. The vortex movement is due to the vortex lens inserted in front of the focusing objective. We gradually shift the vortex lens along the x-axis which is perpendicular to the axis of laser beam propagation (z-axis). This causes that in the image plane vortex moves along a straight line but the line inclination depends on the position of the observation plane. There is a characteristic position of the observation plane, in which the vortex trajectory is perpendicular to the vortex plate shift. We call this plane a critical plane. The critical plane is sensitive to small phase variations which can be introduce by a transparent sample. We propose a way of retrieving the phase profile (at the critical plane) of such a beam. Our procedure is based on the Fourier transform phase demodulation method. We also investigate how the system reacts to the known phase variations introduced into the critical plane.