A new method for information retrieval in two-dimensional grating-based X-ray phase contrast imaging

Grating-based X-ray phase contrast imaging has been demonstrated to he an extremely powerful phase-sensitive imaging technique. By using two-dimensional （2D） gratings, the observable contrast is extended to two refraction directions. Recently, we have developed a novel reverse-projection （RP） method, which is capable of retrieving the object information efficiently with one-dimensional （1D） grating-based phase contrast imaging. In this contribution, we present its extension to the 2D grating-based X-ray phase contrast imaging, named the two-dimensional reverse- projection （2D-RP） method, for information retrieval. The method takes into account the nonlinear contributions of two refraction directions and allows the retrieval of the absorption, the horizontal and the vertical refraction images. The obtained information can be used for the reconstruction of the three-dimensionak phase gradient field, and for an improved phase map retrieval and reconstruction. Numerical experiments are carried out, and the results confirm the validity of the 2D-RP method.

ISAR imaging based on improved phase retrieval algorithm

Traditional inverse synthetic aperture radar(ISAR)imaging methods for maneuvering targets have low resolution and poor capability of noise suppression. An ISAR imaging method of maneuvering targets based on phase retrieval is proposed,which can provide a high-resolution and focused map of the spatial distribution of scatterers on the target. According to theoretical derivation, the modulus of raw data from the maneuvering target is not affected by radial motion components for ISAR imaging system, so the phase retrieval algorithm can be used for ISAR imaging problems. However, the traditional phase retrieval algorithm will be not applicable to ISAR imaging under the condition of random noise. To solve this problem, an algorithm is put forward based on the range Doppler(RD) algorithm and oversampling smoothness(OSS) phase retrieval algorithm. The algorithm captures the target information in order to reduce the influence of the random phase on ISAR echoes, and then applies OSS for focusing imaging based on prior information of the RD algorithm. The simulated results demonstrate the validity of this algorithm, which cannot only obtain high resolution imaging for high speed maneuvering targets under the condition of random noise, but also substantially improve the success rate of the phase retrieval algorithm.

Phase retrieval algorithm for optical information security

As a typical technology for optical encryption,phase retrieval algorithms have been widely used in optical information encryption and authentication systems.This paper presents three applications of two-dimensional(2D)phase retrieval for optical encryption and authentication:first,a hierarchical image encryption system,by which multiple images can be hidden into cascaded multiple phase masks;second,a multilevel image authentication system,which combines(t,n)threshold secret sharing(both t and n are positive integers,and t≤n)and phase retrieval,and provides both high-level and low-level authentication;and finally,a hierarchical multilevel authentication system that combines the secret sharing scheme based on basic vector operations and the phase retrieval,by which more certification images can be encoded into multiple cascaded phase masks of different hierarchical levels.These three phase retrieval algorithms can effectively illustrate phase-retrievalbased optical information security.The principles and features of each phase-retrieval-based optical security method are analyzed and discussed.It is hoped that this review will illustrate the current development of phase retrieval algorithms for optical information security and will also shed light on the future development of phase retrieval algorithms for optical information security.

A general phase retrieval algorithm based on a ptychographical iterative engine for coherent diffractive imaging

Coherent diffractive imaging （CDI） is a lensless imaging technique and can achieve a resolution beyond the Rayleigh or Abbe limit. The ptychographical iterative engine （PIE） is a CDI phase retrieval algorithm that uses multiple diffraction patterns obtained through the scan of a localized illumination on the specimen, which has been demonstrated successfully at optical and X-ray wavelengths. In this paper, a general PIE algorithm （gPIE） is presented and demonstrated with an He-Ne laser light diffraction dataset. This algorithm not only permits the removal of the accurate model of the illumination function in PIE, but also provides improved convergence speed and retrieval quality.

USING TWO-DIMENSIONAL TIME RESOLVED LIGHT SCATTERING TO STUDY THE CURE REACTION INDUCED PHASE SEPARATION PROCESS OF EPOXY-AMINE-POLYETHERSULFONE BLEND WITH SECONDARY PHASE SEPARATION

The generalized two-dimensional correlation analysis based on time-resolved light scattering patterns （2D TRLS） has been employed to study the phase separation process of an epoxy-amine-polyethersulfone blend in which the secondary phase separation takes place. The results of the 2D TRLS provided more detailed information that was not readily observed in the 1D TRLS patterns. （i） During the first process of phase separation, the sequential order of coarsening in size of the domains among the larger and smaller ones has been reversed between the diffusion regime and the hydrodynamic regime. （ii） The change of the larger domains in size, due to the hydrodynamic flow in the late stage of the first phase separation process, keeps on taking place earlier than that of the new domains appeared in the secondary phase separation process. （iii） During the secondary phase separation process the size growth of the smaller domains takes place earlier than that of the larger ones, probably due to the assumption that the coarsening mode could decrease the interface tension more quickly.

Algorithm for phase contrast X-ray tomography based on nonlinear phase retrieval

A new algorithm for phase contrast X-ray tomography under holographic measurement was proposed in this paper. The main idea of the algorithm was to solve the nonlinear phase retrieval problem using the Newton iterative method. The linear equations for the Newton directions were proved to be ill-posed and the regularized solutions were obtained by the conjugate gradient method. Some numerical experiments with computer simulated data were presented. The efficiency, feasibility and the numerical stability of the algorithm were illustrated by the numerical experiments. Compared with the results produced by the linearized phase retrieval algorithm, we can see that the new algorithm is not limited to be only efficient for the data measured in the near-field of the Fresnel region and thus it has a broader validity range.

PHASE RETRIEVAL OF TIME-LIMITED SIGNALS

The problem of reconstructing a signalφ（x） from its magnitude ｜φ（x）] isof considerable interest to engineers and physicists. This article concerns the problem of determining a time-limited signal f with period 2π when ｜f（eix）l is known for x∈[-π,π]. It is shown that the conditions ｜g（eix）｜ = ｜f（eix）｜ and ｜g（ci（x＋b）） -g（eix）｜ =f（ei（x＋b）） - f（eix）｜, b ≠ 27π, together imply that either g = wf or g = v f, where both w and v have period b. Furthermore, if b/2π is irrational then the functions w and v b is rational then w takes the form reduce to some constants c1 and c2, respectively; ifb/2π is rational then w takes the form w=elexB1（e1x）B2（elx）and v takes the form ei（x2πN/b＋a）B1（elx）B2（elx）,where B1 and B2 are Blaschke products.

An Improved Coupled Level Set and Continuous Moment-of-Fluid Method for Simulating Multiphase Flows with Phase Change

An improved algorithm for computing multiphase flows is presented in which the multimaterial Moment-of-Fluid(MOF)algorithm for multiphase flows,initially described by Li et al.(2015),is enhanced addressing existing MOF difficulties in computing solutions to problems in which surface tension forces are crucial for understanding salient flow mechanisms.The Continuous MOF(CMOF)method is motivated in this article.The CMOF reconstruction method inherently removes the"checkerboard instability"that persists when using the MOF method on surface tension driven multiphase(multimaterial)flows.The CMOF reconstruction algorithm is accelerated by coupling the CMOF method to the level set method and coupling the CMOF method to a decision tree machine learning(ML)algorithm.Multiphase flow examples are shown in the two-dimensional(2D),three-dimensional(3D)axisymmetric"RZ",and 3D coordinate systems.Examples include two material and three material multiphase flows:bubble formation,the impingement of a liquid jet on a gas bubble in a cryogenic fuel tank,freezing,and liquid lens dynamics.

Phase retrieval with PhaseLift algorithm

This paper provides a contemporary overview of phase retrieval problem with PhaseLift algorithm and summarizes theoretical results which have been derived during the past few years.Based on the lifting technique,the phase retrieval problem can be transformed into the low rank matrix recovery problem and then be solved by convex programming known as PhaseLift.Thus,stable guarantees for such problem have been gradually established for measurements sampled from sufficiently random distribution,for instance,the standard normal distribution.Further,exact recovery results have also been set up for masked Fourier measurements which are closely related to practical applications.

Temperature-induced phase transition of two-dimensional semiconductor GaTe

GaTe is a two-dimensional Ⅲ-Ⅵ semiconductor with suitable direct bandgap of~1.65 eV and high photoresponsivity,which makes it a promising candidate for optoelectronic applications.GaTe exists in two crystalline phases:monoclinic(m-GaTe,with space group C2/m) and hexagonal(h-GaTe,with space group P63/mmc).The phase transition between the two phases was reported under temperature-varying conditions,such as annealing,laser irradiation,etc.The explicit phase transition temperature and energy barrier during the temperature-induced phase transition have not been explored.In this work,we present a comprehensive study of the phase transition process by using first-principles energetic and phonon calculations within the quasi-harmonic approximation framework.We predicted that the phase transition from h-GaTe to m-GaTe occurs at the temperature decreasing to 261 K.This is in qualitative agreement with the experimental observations.It is a two-step transition process with energy barriers 199 meV and 288 meV,respectively.The relatively high energy barriers demonstrate the irreversible nature of the phase transition.The electronic and phonon properties of the two phases were further investigated by comparison with available experimental and theoretical results.Our results provide insightful understanding on the process of temperature-induced phase transition of GaTe.

Two-Dimensional Electronic Spectroscopy with Active Phase Management

Two-dimensional elec tronic spec troscopy(2DES)is a powerful met hod to probe the coherent electron dynamics in complicated systems.Stabilizing the phase difference of the incident ultrashort pulses is the mos t challenging par t for experimen tal demonstration of 2DES.Here,we present a tuto rial review on the 2DES proto cols based on active phase managements which are originally developed for quantum optics experiments.We introduce the 2DES techniques in box and pump-probe geometries with phase stabilization realized by interferometry,and outline the fully collinear 2DES approach with the frequency tagging by acoustic optical modulators and frequency combs.The combination of active phase managements,ultrashort pulses and other spectroscopic methods may open new opportunities to tackle essential challenges related to excited states.

Broad-band phase retrieval method for transient radial shearing interference using chirp Z transform technique

The transient radial shearing interferometry technique based on fast Fourier transform(FFT)provides a means for the measurement of the wavefront phase of transient light field.However,which factors affect the spatial bandwidth of the wavefront phase measurement of this technology and how to achieve high-precision measurement of the broad-band transient wavefront phase are problems that need to be studied further.To this end,a theoretical model of phase-retrieved bandwidth of radial shearing interferometry is established in this paper.The influence of the spatial carrier frequency and the calculation window on phase-retrieved bandwidth is analyzed,and the optimal carrier frequency and calculation window are obtained.On this basis,a broad-band transient radial shearing interference phase-retrieval method based on chirp Z transform(CZT)is proposed,and the corresponding algorithm is given.Through theoretical simulation,a known phase is used to generate the interferogram and it is retrieved by the traditional method and the proposed method respectively.The residual wavefront RMS of the traditional method is 0.146λ,and it is 0.037λfor the proposed method,which manifests an improvement of accuracy by an order of magnitude.At the same time,different levels of signal-to-noise ratios(SNRs)from 50 dB to 10 dB of the interferogram are simulated,and the RMS of the residual wavefront is from 0.040λto 0.066λ.In terms of experiments,an experimental verification device based on a phase-only spatial light modulator is built,and the known phase on the modulator is retrieved from the actual interferogram.The RMS of the residual wavefront retrieved through FFT is 0.112λ,and it decreases to 0.035λthrough CZT.The experimental results verify the effectiveness of the method proposed in this paper.Furthermore,the method can be used in other types of spatial carrier frequency interference,such as lateral shearing interference,rotational shearing interference,flipping shearing interference,and four-wave shearing interference.

Effect of One/Two-dimensional Bonding Phases on Strength and Toughness of Carbon-containing Refractories

Gaseous phases of carbon-containing and metastable oxides will be resulted from the carbonization of phenolic resin binders and the reduced reactions between C and oxides at high temperatures in carbon-containing refractories. With the in-situ catalysis technique, these gaseous phases can be transformed to one-or two-dimensional bonding phases by deposition,which is favorable for the improvement on strength and toughness of carboncontaining refractories,especially low carbon refractories. The research results reveal that：（ 1） the amorphous carbon resulted from phenolic resin can be transformed to carbon nanotubes,thus,the oxidation peak temperature is raised from 506 to 664. 6 ℃;（ 2） onedimensional whiskers of MgO or Mg Al2 O4 can be in-situ formed in MgO-C refractories, and their CMOR,CCS,rupture displacement and residual CCS（ two water quenching cycles,1 100 ℃） are increased by 66%,47%,13% and 26%,respectively;（ 3） two-dimensional array structure of flake β-SiAlON can be in-situ formed in Al2 O3-C refractories,which improves the material strength by 60% and decreases the residual strength after thermal shock by only 4. 5 MPa. It is believed that the in-situ formation of one-or two-dimensional bonding phases at high temperatures can improvethe comprehensive thermal physical properties of carboncontaining refractories,and will be the developing trend of the strengthening and toughening of low carbon-containing refractories.

ANALYTIC PHASE RETRIEVAL BASED ON INTENSITY MEASUREMENTS

This paper concerns the reconstruction of a function f in the Hardy space of the unit disc D by using a sample value f(a)and certain n-intensity measurements|<f,E_(a1…an)>|,where a_(1)…a_(n)∈D,and E_(a1…an)is the n-th term of the Gram-Schmidt orthogonalization of the Szego kernels k_(a1),k_(an),or their multiple forms.Three schemes are presented.The first two schemes each directly obtain all the function values f(z).In the first one we use Nevanlinna’s inner and outer function factorization which merely requires the 1-intensity measurements equivalent to know the modulus|f(z)|.In the second scheme we do not use deep complex analysis,but require some 2-and 3-intensity measurements.The third scheme,as an application of AFD,gives sparse representation of f(z)converging quickly in the energy sense,depending on consecutively selected maximal n-intensity measurements|<f,E_(a1…an)>|.

L1/2 -Regularized Quantile Method for Sparse Phase Retrieval

The sparse phase retrieval aims to recover the sparse signal from quadratic measurements. However, the measurements are often affected by outliers and asymmetric distribution noise. This paper introduces a novel method that combines the quantile regression and the L1/2-regularizer. It is a non-convex, non-smooth, non-Lipschitz optimization problem. We propose an efficient algorithm based on the Alternating Direction Methods of Multiplier (ADMM) to solve the corresponding optimization problem. Numerous numerical experiments show that this method can recover sparse signals with fewer measurements and is robust to dense bounded noise and Laplace noise.

Temporally Modulated Phase Retrieval Method for Weak Temporal Phase Measurement of Laser Pulses

We propose a simple iterative algorithm based on a temporally movable phase modulation process to retrieve the weak temporal phase of laser pulses. This unambiguous method can be used to achieve a high accuracy and to simultaneously measure the weak temporal phase and temporal profile of pulses, which are almost transform- limited. A detailed analysis shows that this iterative method has valuable potential applications in the charac- terization of pulses with weak temporal phase.

Single-shot phase retrieval for randomly fluctuated and obstructed vortex beams

Vortex beams with orbital angular momentum play a crucial role in increasing the information capacity in optical communications.The magnitude of orbital angular momentum determines the ability of information encoding.In practice,a vortex beam can encounter random objects or turbulence during free-space propagation,resulting in information damage.Therefore,accurately measuring the orbital angular momentum of a randomly fluctuated and obstructed vortex beam is a considerable challenge.Herein,we propose a single-shot method for the phase retrieval of a randomly fluctuated and obstructed vortex beam by combining the phase-shift theorem and self-reference holography.Experimental results reveal that the sign and magnitude of the initial orbital angular momentum can be simultaneously determined based on their quantitative relation with the number of coherence singularities on the observation plane,thus addressing the effects of random occlusion and atmospheric turbulence.The proposed method considerably improved the accurate decoding of orbital angular momentum information in nonideal freespace optical communications.

An improved wind retrieval algorithm for the HY-2A scatterometer

Since January 2012,the National Satellite Ocean Application Service has released operational wind products from the HY-2A scatterometer(HY2-SCAT),using the maximum-likelihood estimation(MLE) method with a median filter. However,the quality of the winds retrieved from HY2-SCAT depends on the sub-satellite cross-track location,and poor azimuth separation in the nadir region causes particularly low-quality wind products in this region. However,an improved scheme,i.e.,a multiple solution scheme(MSS) with a two-dimensional variational analysis method(2DVAR),has been proposed by the Royal Netherlands Meteorological Institute to overcome such problems. The present study used the MSS in combination with a 2DVAR technique to retrieve wind data from HY2-SCAT observations. The parameter of the empirical probability function,used to indicate the probability of each ambiguous solution being the "true" wind,was estimated based on HY2-SCAT data,and the 2DVAR method used to remove ambiguity in the wind direction. A comparison between MSS and ECMWF winds showed larger deviations at both low wind speeds(below 4 m/s) and high wind speeds(above 17 m/s),whereas the wind direction exhibited lower bias and good stability,even at high wind speeds greater than 24 m/s. The two HY2-SCAT wind data sets,retrieved by the standard MLE and the MSS procedures were compared with buoy observations. The RMS error of wind speed and direction were 1.3 m/s and 17.4°,and 1.3 m/s and 24.0° for the MSS and MLE wind data,respectively,indicating that MSS wind data had better agreement with the buoy data. Furthermore,the distributions of wind fields for a case study of typhoon Soulik were compared,which showed that MSS winds were spatially more consistent and meteorologically better balanced than MLE winds.

Convolutional neural network for transient grating frequency-resolved optical gating trace retrieval and its algorithm optimization

A convolutional neural network is employed to retrieve the time-domain envelop and phase of few-cycle femtosecond pulses from transient-grating frequency-resolved optical gating(TG-FROG) traces.We use theoretically generated TGFROG traces to complete supervised trainings of the convolutional neural networks,then use similarly generated traces not included in the training dataset to test how well the networks are trained.Accurate retrieval of such traces by the neural network is realized.In our case,we find that networks with exponential linear unit(ELU) activation function perform better than those with leaky rectified linear unit(LRELU) and scaled exponential linear unit(SELU).Finally,the issues that need to be addressed for the retrieval of experimental data by this method are discussed.

Experimental Investigation of Two-Dimensional Velocity on the 90&deg;Double Bend Pipe Flow Using Ultrasound Technique

An experimental investigation was performed to investigate two-dimensional axial velocity field at downstream of the 90&deg;double bend pipe with and without inlet swirling condition. The main objectives are to find separation region and observe the influence of inlet swirling flow on the velocity fluctuation using ultrasound technique. The experiments were carried out in the pipe at Reynolds number Re = 1 × 104. In case of inlet swirling flow condition, a rotary swirler was used as swirling generator, and the swirl number was setup S = 1. The ultrasonic measurements were taken at four downstream locations of the second bend pipe. Phased Array Ultrasonic Velocity Profiler (Phased Array UVP) technique was applied to obtain the two-dimensional velocity of the fluid and the axial and tangential velocity fluctuation. It was found that the secondary reverse flow became smaller at the downstream from the bend when the inlet condition on the first bend was swirling flow. In addition, inlet swirling condition influenced mainly on the tangential velocity fluctuation, and its maximum turbulence intensity was 40%.