Light field phase retrieval based on extended Nijboer–Zernike polynomials

The phase of a light field carries a significant amount of information and is therefore often used for mode characterization. Accurate acquisition of the phase information of different modes is essential for evaluating the communication performance of mode-division (MDM) multiplexing systems. In this work, we proposed a phase retrieval method based on the Extended Nijboer–Zernike (ENZ) polynomials, which are derived from the Zernike polynomials framework. Based on this phase retrieval method, we designed and implemented a light field measurement system. The system acquires intensity information of the light field at the focal plane and at multiple parallel defocused planes. The phase of the light field at the pupil plane can be reconstructed by combining the measured data with the point spread function (PSF) and the ENZ polynomials. We applied this phase retrieval method to commonly used communication modes at the 1550 nm wavelength, including linearly polarized (LP) modes LP01, LP11, LP21, achieving successful reconstruction of their light field phases.