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In free space optical (FSO) communication, atmospheric turbulence will introduce aberration to the laser wavefront, which will reduce the coupling efficiency of space light to optical fiber. The system based on blind optimization principle can realize wavefront aberration compensation by using actuators such as fast steering mirror (FSM) and deformable mirror (DM), combined with blind optimization control algorithms. Stochastic parallel gradient descent (SPGD) algorithm is widely used in this kind of system. The disadvantages of SPGD algorithm are possibly local convergence and slow convergence. In order to improve the convergence performance of the SPGD algorithm, we proposed improved SPGD algorithms called Adagrad & Staged SPGD algorithm (AS-SPGD). Specifically, to accelerate SPGD algorithm, the Adagrad SPGD algorithm (A-SPGD) integrated Adagrad's adaptive gain strategy is proposed firstly in wavefront tip–tilt aberration compensation using FSM. Then, we consider compensating the wavefront high-order aberration using DM. By adopting the strategy of using SPGD algorithm with different settings in different stages, the Staged SPGD algorithm (S-SPGD) is proposed to improve the local convergence of the traditional SPGD algorithm. The simulation results show that the Adagrad SPGD algorithm converges faster than the traditional SPGD algorithm in the compensation of tip–tilt aberrations of different amplitude; the Staged SPGD algorithm has better global convergence ability than the traditional SPGD algorithm in high-order aberration compensation. • The blind optimization control is used to realize wavefront aberration compensation. • The Adagrad SPGD algorithm is proposed to improve the convergence speed. • The Staged SPGD algorithm is proposed to improve the local convergence. • Simulation results verify the modified SPGD methods have better performance. [ABSTRACT FROM AUTHOR]

• We propose a simple but efficient pre-processing algorithm capable of extracting translation positions of the structure light directly from raw images of Incoherent pattern-illumination Fourier ptychography (IFP), termed translation position extracting (TPE). • TPE removes the requirement of IFP for prior knowledge of translation positions, thus further relaxing the practical conditions. Both simulation and experiment are performed to demonstrate its effectiveness. • The calculation cost of the TPE algorithm is similar to the cross-correlation, which is far lower than the existing translation extraction algorithm based on iterative optimization. Incoherent Pattern-illuminated Fourier ptychography (IFP) is a newly developed super-resolution method, where accurate prior knowledge of translation positions is essential for image reconstruction. To release this limitation, we propose a pre-processing algorithm capable of extracting translation positions of the structure light directly from raw images of IFP, termed translation position extracting (TPE). TPE mainly involves two steps. First, the speckle parts mixed in the acquired raw images, in which the illumination motion is encoded, are isolated by intensity averaging and division. Then the cross-correlations of the speckle dataset are computed to determine the shift positions. TPE-IFP improves the previous IFP by removal of the requirement for prior knowledge of translation positions. Its effectiveness is demonstrated by obtaining high-quality super-resolution images in absence of location information in both simulations and experiments. By further relaxing the practical conditions, the proposed TPE may accelerate the applications of IFP. What's more, as a pre-processing approach, TPE might also contribute to the estimation of pattern positions for the similar speckle-based imaging. [ABSTRACT FROM AUTHOR]