Research On Single Frame Deep Learning Phase Retrieval Method Based On Four-quadrant Discrete Phase Modulation

Phase retrieval(PR)method can reconstruct incident wavefront based on a singleframe focal plane intensity image through multiple iterations.PR method has a simple system structure,high energy utilization,while PR method is easy to realize.However,in a point source system,a pair of incident wavefronts that rotat 180 degrees and flip symmetrically have same far-field intensity distribution,that is,a focal plane intensity image corresponds to multiple incident wavefronts.Traditional single-frame image PR method(such as the Gerchberg-Saxton algorithm)is susceptible to the multi-solution problem mentioned above,algorithm converges to a false solution,the iteration stagnates,and wavefront reconstruction accuracy is low.R.A.Gonsalves et al.proposed phase diversity(PD)method to deal with multi-solution problem.However,PD method requires CCD to measure multiple times on focal plane and defocus plane respectively in each iteration.CCD measuring on defocus plane is equivalent to adding a defocus constraint to system.PD method avoids multiple solutions at a cost of increasing system structure complexity,actual applications of PD method are strictly limited.In addition,PR method requires multiple iterations to reach local optima,thus algorithm has poor real-time performance.Nowadays PR method is mostly used to reconstruct static incident wavefronts.To eliminate the influence of the multi-solution problem,this paper introduces four-quadrant discrete phase modulation(FQDPM)to break the far-field consistency of a pair of incident wavefronts that rotate 180 degrees and flip symmetrically.In addition,to reduce the time-consuming calculation of PR method,we introduce convolutional neural network(CNN)to replace the primitive iteration optimization process of PR method.Well-trained CNN can reconstruct incident wavefront after one calculation based on a single-frame focal plane intensity image,while calculation time is greatly reduced.Main research contents of this paper are as follows.Firstly,the multi-solution problem is analyzed in this paper.Applying discrete phase modulation can overcome multi-solution problem,while ? should satisfy the condition that -?(x,y)?-(-x,-y).This paper proposes FQDPM as a special form of .FQDPM divides the unit circle into four quadrants,the first and third quadrants both have a -?/4 phase step,while the second and fourth quadrants have a ?/4 phase step respectively.Numerical simulation verifies that FQDPM can overcome the multi-solution problem.Then,using Maxwell's equations as a starting point,using Zernike polynomials as a medium,simulation model is established according to the Fresnel diffraction formula.In a point source system,focal plane far-field intensity distribution is equal to square of modulus of Fourier transform of complex amplitude of incident wavefront.Randomly generate a set of Zernike coefficients,obtain incident wavefront according to Zernike polynomial,perform four-quadrant discrete phase modulation on,and square modulus of Fourier transform of new complex amplitude of incident wavefront,then we can obtain modulated far-field intensity distribution .The modulated far-field intensity distribution here is sample,its corresponding Zernike coefficients are labels,CNN is used to fit the mapping relationship between and its corresponding Zernike coefficients.Finally,the working principle of the single-frame deep learning PR method based on FQDPM is introduced,while numerical simulation and experimental research are carried out.Simulation and experimental results indicate that the proposed method eliminates the influence of multiple solutions,can quickly and accurately retrieve phase information from a single-frame focal plane intensity image.Average root mean square(RMS)of residual wavefronts is only 6.3% of that of incident wavefronts,time required for proposed method to converge can be less than 0.6 milliseconds.