Algorithm for reconstructing complex coefficients of Laguerre–Gaussian modes from the intensity distribution of their coherent superposition

In this paper, we consider a problem of reconstructing complex coefficients of the coherent su-perposition of Laguerre–Gaussian modes from the field intensity in a plane perpendicular to the propagation axis at a given distance using the Levenberg–Marquardt and Brent algorithm. The efficiency of using stage-by-stage optimization to restore complex coefficients of a superposition is demonstrated not only on model, but also on experimental intensity distributions. The algorithm can be used in optical information transmission through a turbulent atmosphere to process the received intensity distribution of the optical signal.