Facile Phase Retrieval with Vector Angular Momentum Beams

Solutions to the "phase problem" are broadly classified into phase retrieval using masks, interferometry and ptychography, which generally involve moving parts or iterative algorithms. Iterative algorithms, such as Gerchberg–Saxton and Yang–Gu, are reliable but slow to converge and often computational demanding. Interferometric methods are computationally simpler but require a more complex experimental setup. Ptychographic methods involve a more developed experimental setup with a probe beam and typically an iterative algorithm. In this paper we demonstrate a non-interferometric, non-iterative, experimentally and computationally simple method for phase retrieval using an elliptically-polarized vortex vector beam. Light from different locations of the illuminating vortex beam are phase locked and interfere in the diffraction measurement to produce differentiation in the Fourier plane. As a result, the phase calculation may be reduced to simple addition and subtraction of gradient terms from filtered intensity patterns of the vortex profile. We derive partial differential equations consisting of spatial gradients corresponding to the vortex illumination for phase retrieval calculations. This makes our non-interferometric method among the simplest to date.