Real-time Imaging System Based On Spatial Light Modulator And Fast Phase Retrieval

The optical wave field contains intensity and phase information.The research data show that about 75% of the information in the optical wave field is encoded in the phase.However,due to the high oscillation frequency of the optical wave field,existing optical detection devices can only record its intensity information.The intensity is proportional to the square of the amplitude.Therefore,how to recover the “lost” phase information from the intensity information of the field has important research value,and this problem is called phase retrieval.At present,the problem of phase retrieval widely exists in the fields of X-ray crystallography,optics,astronomy,biomedicine,and speech processing.At present,there are many solutions to the phase retrieval problem,which can be roughly divided into three categories: traditional non-convex phase retrieval algorithms,phase retrieval methods based on convex optimization,and new non-convex optimized phase retrieval methods.Traditional non-convex phase retrieval algorithms include Gerchberg-Saxton(GS)algorithm,Error-Reduction(ER)algorithm,Hybrid Input-Output(HIO)algorithm,and Yang-Gu(YG)algorithm,etc.This type of non-convex algorithms converges slowly and easily falls into a “stagnation” state,and usually only converges to a local optimal solution.Inspired by these shortcomings,Candès et al.proposed a phase retrieval method based on convex optimization.Commonly used are PhaseLift algorithm,PhaseCut algorithm,and PhaseMax algorithm.This kind of convex method can converge to a global optimal solution(up to a global phase factor).Due to the matrix lifting strategy,the signal dimension to be processed is exponentially increased,which has great limitations in practical applications.To make up for their shortcomings,new non-convex phase retrieval algorithms have been born,such as Wirtinger Flow algorithm,Truncated Wirtinger Flow algorithm,and Truncated Amplitude Flow algorithm.This type of algorithm first uses an effective adaptive method to obtain the initial spectral estimation,and then selects a suitable gradient descent algorithm to finally obtain a convergence result.Experimental results show that this new class of non-convex algorithm not only improves the convergence speed,but also has lower computational complexity.The main study work and innovations of this paper are as follows:(1)Aiming at the problem that the single-intensity phase retrieval method has poor reconstruction quality and low probability of successful recovery,an improved two-step phase retrieval(TSPR)method based on single-intensity measurement is proposed in this paper.Ourmethod divides the phase retrieval into two steps: firstly,the GS algorithm is used to recover the amplitude in the spatial domain from the single-spread Fourier spectrum,and then the classical GS algorithm using two intensity measurements(one is recorded and the other is estimated from the first step)measurements is used to recover the phase.Finally,the effectiveness of the proposed method is verified by numerical experiments.Compared with the single-intensity phase retrieval method,the TSPR method proposed in this paper can significantly improve the quality of phase establishment and the possibility of successful recovery.(2)The convex phase retrieval method represented by PhaseLift transforms the non-convex constraint into a convex constraint through matrix lifting,which can obtain a global optimal solution up to a global phase factor.Aiming at the problem that the PhaseLift method does not consider how the actual imaging system performs multiple measurement records,a physically realistic optical imaging system is proposed in this paper.The imaging system can achieve the design of different masks using the optical field modulation characteristics of the spatial light modulator,which can achieve the random modulation of complex optical field and the recording of different coded diffraction patterns.Numerical experiments verify the effectiveness and robustness of the proposed imaging system.(3)A 4f imaging system based on an electrically tunable lens(ETL)is proposed in this paper,which can be used for real-time acquisition of multiple-shot coded diffraction patterns for high-speed and large-scale phase retrieval scenario,and has the advantages of high-speed,high-resolution,extended deth-of-field,high-sensitivity and low-cost imaging.And the ETL allow variable-distance focusing of imaging and display systems without mechanical structures,which reduce the mechanical complexity and power consumption,improve acquisition speed.Numerical experiments verify the effectiveness and superiority of the improved imaging system proposed in this paper.