On Phase Retrieval Via Amplitude Flow

The characteristics of the optical field can be described in terms of amplitude,wavelength and phase.According to statistics show that about three-quarters of the information is encoded in the phase,so the phase is particular important relative to other information.However,the human eyes or the existing optical detector used to record the intensity or amplitude of the optical field cannot acquire the phase information of the light wave field directly.This is due to the high frequency of light wave(oscillates at a frequency of 1015 Hz),which is much larger than the human eye(about 30 Hz)and the existing highest speed light detector(about 108 Hz).Therefore,it is necessary to use the measured amplitude or intensity to calculate the phase of the object,which is named phase retrieval.In recent years,phase retrieval has been widely used in many fields such as X-ray crystallography,holographic display,optics,astronomy,diffraction imaging and electron microscopy.At present,there are roughly three kinds of methods for phase retrieval:phase retrieval based on transport of intensity equation(TIE),phase retrieval based on convex optimization and phase recovery based on non-convex optimization.The phase retrieval methods based on the TIE needs to use the intensity difference to approximate the intensity differential when solving the equation,and there will be some error,and the selection of the defocus distance is difficult to achieve a balance between the nonlinear error and the noise in the image acquisition process.Although the phase retrieval methods based on convex optimization can get better recovery results,the computational complexity of the algorithm is relatively high,which leads to low recovery efficiency and is not suitable for two-dimensional image phase recovery.Besides the commonly used Gerchberg-Saxton iterative algorithm,the Wirtinger flow algorithm is a popular phase retrieval method based on non convex optimization,which uses spectral initialization to obtain an ideal initial value and can obtain an ideal recovery result through gradient iteration.This paper first summarizes three kinds of common phase retrieval algorithms,and then the phase retrieval method based on non convex optimization is studied in detail.The main research work and innovation are as following:(1)Phase retrieval algorithms based on Wirtinger flow,truncated amplitude flow and incremental truncated Wirtinger flow are studied.The experimental results show that when the signal to be recovered is a large-scale signal,the Wirtinger flow algorithm and the truncated amplitude flow algorithm have the disadvantage of low efficiency and the incremental truncation of the Wirtinger flow and other algorithm recovery results is not very satisfactory when the number of measurements is insufficient.Therefore,this paper proposes an Incremental Truncated Amplitude Flow(ITAF)algorithm.The proposed algorithm firstly preprocesses the original measured data and then initializes it by using orthogonal truncation,finally,an incremental truncated gradient is used to obtain the initial value.The simulation results show that the proposed algorithm can accurately recover the original signal with fewer measurement times and faster convergence rate,which verifies the effectiveness and robustness of the proposed algorithm.(2)The problem of mask setting and image acquisition in phase recovery was studied.Starting from the actual imaging process,an optical imaging system based on coded diffraction pattern acquisition was designed by using the optical field modulation characteristics.of the spatial light modulator(SLM),an octanary phase mask with "more structured" and "less random" characteristics is loaded on the SLM to modulate the input signal,than the frequency intensity information is acquired at the back focal plane of Fourier lens,finally,the ITAF algorithm is used to obtain the phase recovery results.Simulation experiments verified the effectiveness of the image acquisition system,indicated that Octanary masks can achieve better recovery results than traditional binary masks.At the same time,contrast experiments verified further the effectiveness and robustness of the ITAF algorithm for two-dimensional signals.