NeuPh:scalable and generalizable neural phase retrieval with local conditional neural fields

Deep learning has transformed computational imaging,but traditional pixel-based representations limit their ability to capture continuous multiscale object features.Addressing this gap,we introduce a local conditional neural field(LCNF)framework,which leverages a continuous neural representation to provide flexible object representations.LCNF’s unique capabilities are demonstrated in solving the highly ill-posed phase retrieval problem of multiplexed Fourier ptychographic microscopy.Our network,termed neural phase retrieval(NeuPh),enables continuous-domain resolution-enhanced phase reconstruction,offering scalability,robustness,accuracy,and generalizability that outperform existing methods.NeuPh integrates a local conditional neural representation and a coordinate-based training strategy.We show that NeuPh can accurately reconstruct high-resolution phase images from low-resolution intensity measurements.Furthermore,NeuPh consistently applies continuous object priors and effectively eliminates various phase artifacts,demonstrating robustness even when trained on imperfect datasets.Moreover,NeuPh improves accuracy and generalization compared with existing deep learning models.We further investigate a hybrid training strategy combining both experimental and simulated datasets,elucidating the impact of domain shift between experiment and simulation.Our work underscores the potential of the LCNF framework in solving complex large-scale inverse problems,opening up new possibilities for deep-learning-based imaging techniques.

A new method of detecting interferogram in differential phase-contrast imaging system based on special structured x-ray scintillator screen

An x-ray scintillator screen with a special structure, functioning as detector and analyser grating, was proposed for collecting the interferogram of differential phase contrast imaging without absorption grating and difficulty of fabrication by a state of the art technique. On the basis of phase grating diffraction, a detecting model of the scintillator screen was built for analysing the phase and absorption information of objects. According to the analysis, a new method of phase retrievals based on two-images and the optimal structure of screen were presented.

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.

Time-reversed optical focusing through scattering mediaby dligital fullphase and amplitude recovery usinga single phase-only SLM

Focusing light though scattering media beyond the ballistic regime is a challenging task in biomedical optical imaging.This challenge can be overcome by wavefront shaping technique,in which a time reversed(TR)wavefront of scattered light is generated to suppress the scattering.In previous TR optical focusing experiments,a phase only spatial light modulator(SLM)has.been typically used to control the wavefront of incident light.Unfortunately,although the phase information is reconstructed by the phase-only SLM,the amplitude information is lost,resulting in decreased peak to-background ratio(PBR)of optical focusing in the TR wavefront recon-struction.A new method of TR optical focusing through scattering media is proposed here,which numerically reonstructs the full phase and amplitude of a simulated scattered light field by using a single phase only SLM.Simulation results and the proposed optical setup show that the time-reversal of a fully developed speckle field can be digially implemented with both phase and ampltude recovery,affording a way to improve the performance of light focusing through scattering media.

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.

Phase-only stereoscopic hologram calculation based on Gerchberg–Saxton iterative algorithm

A phase-only computer-generated holography（CGH） calculation method for stereoscopic holography is proposed in this paper.The two-dimensional（2D） perspective projection views of the three-dimensional（3D） object are generated by the computer graphics rendering techniques.Based on these views,a phase-only hologram is calculated by using the Gerchberg–Saxton（GS） iterative algorithm.Comparing with the non-iterative algorithm in the conventional stereoscopic holography,the proposed method improves the holographic image quality,especially for the phase-only hologram encoded from the complex distribution.Both simulation and optical experiment results demonstrate that our proposed method can give higher quality reconstruction comparing with the traditional method.

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.

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)>|.

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.

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.

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.

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.

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.

Physics-informed deep learning for fringe pattern analysis

Recently,deep learning has yielded transformative success across optics and photonics,especially in optical metrology.Deep neural networks (DNNs) with a fully convolutional architecture (e.g.,U-Net and its derivatives) have been widely implemented in an end-to-end manner to accomplish various optical metrology tasks,such as fringe denoising,phase unwrapping,and fringe analysis.However,the task of training a DNN to accurately identify an image-to-image transform from massive input and output data pairs seems at best naive,as the physical laws governing the image formation or other domain expertise pertaining to the measurement have not yet been fully exploited in current deep learning practice.To this end,we introduce a physics-informed deep learning method for fringe pattern analysis (PI-FPA) to overcome this limit by integrating a lightweight DNN with a learning-enhanced Fourier transform profilometry (Le FTP) module.By parameterizing conventional phase retrieval methods,the Le FTP module embeds the prior knowledge in the network structure and the loss function to directly provide reliable phase results for new types of samples,while circumventing the requirement of collecting a large amount of high-quality data in supervised learning methods.Guided by the initial phase from Le FTP,the phase recovery ability of the lightweight DNN is enhanced to further improve the phase accuracy at a low computational cost compared with existing end-to-end networks.Experimental results demonstrate that PI-FPA enables more accurate and computationally efficient single-shot phase retrieval,exhibiting its excellent generalization to various unseen objects during training.The proposed PI-FPA presents that challenging issues in optical metrology can be potentially overcome through the synergy of physics-priors-based traditional tools and data-driven learning approaches,opening new avenues to achieve fast and accurate single-shot 3D imaging.

Making the link between ADF and 4D STEM:Resolution,transfer and coherence

Steve Pennycook is a pioneer in the application of high-resolution scanning transmission electron microscopy(STEM)and in particular the use of annular dark-field(ADF)imaging.Here we show how a general framework for 4D STEM allows clear links to be made between ADF imaging and the emerging methods for reconstructing images from 4D STEM data sets.We show that both ADF imaging and ptychographical reconstruction can be thought of in terms of integrating over the overlap regions of diffracted discs in the detector plane.This approach allows the similarities in parts of their transfer functions to be understood,though we note that the transfer functions for ptychographic imaging cannot be used as a measure of information transfer.We also show that conditions of partial spatial and temporal coherence affect ADF imaging and ptychography similarly,showing that achromatic interference can always contribute to the image in both cases,leading to a robustness to partial temporal coherence that has enabled high-resolution imaging.

Image recovery from double amplitudes in fractional Fourier domain

The classical Gerchberg-Saxton algorithm is introduced into the image recovery in fractional Fourier domain after adaptation. When this algorithm is applied directly, its performance is good for smoothed image, but bad for unsmoothed image. Based on the diversity of fractional Fourier transform on its orders, this paper suggests a novel iterative algorithm, which extracts the information of the original image from amplitudes of its fractional Fourier transform at two orders. This new algorithm consists of two independent Gerchberg-Saxton procedures and an averaging operation in each circle. Numerical simulations are carried out to show its validity for both smoothed and unsmoothed images with most pairs of orders in the interval [0, 1].

First commissioning results of the coherent scattering and imaging endstation at the Shanghai soft X-ray free-electron laser facility

The Shanghai soft X-ray free-electron laser(SXFEL)user facility project started in 2016 and is expected to be open to users by 2022.It aims to deliver ultra-intense coherent femtosecond X-ray pulses to five endstations covering a range of 100–620 eV for ultrafast X-ray science.Two undulator lines are designed and constructed,based on different lasing modes:self-amplified spontaneous emission and echo-enabled harmonic generation.The coherent scattering and imaging(CSI)endstation is the first of five endstations to be commissioned online.It focuses on high-resolution single-shot imaging and the study of ultrafast dynamic processes using coherent forward scattering techniques.Both the single-shot holograms and coherent diffraction patterns were recorded and reconstructed for nanoscale imaging,indicating the excellent coherence and high peak power of the SXFEL and the possibility of‘‘diffraction before destruction’’experiments at the CSI endstation.In this study,we report the first commissioning results of the CSI endstation.

Influence of the illumination coherency and illumination aperture on the ptychographic iterative microscopy

While ptychography is an algorithm based on coherent illumination,satisfactory reconstructions can still be generated in most experiments,even though the radiation sources that are used are not ideally coherent.The underlying physics of this phenomenon is that the diffraction patterns of partially coherent illumination can be treated as those of purely coherent illumination by altering the intensities of the diffracted beams relative to their real values.On the other hand,due to the inconsistency in the altering interference among all the diffraction beams,noise/distortion is always involved in the reconstructed images.Furthermore,for a weak object,the noise/distortion in the reconstruction can be mostly reduced by using a highly curved beam for illumination in the data recording and forcing the dark field diffraction to be zero in the reconstruction.

Improvement and error analysis of quantitative information extraction in diffraction-enhanced imaging

Diffraction-enhanced imaging （DEI） is a powerful phase-sensitive technique that provides higher spatial resolution and supercontrast of weakly absorbing objects than conventional radiography. It derives contrast from the X-ray absorption, refraction, and ultra-small-angle X-ray scattering （USAXS） properties of an object. The separation of different-contrast contributions from images is an important issue for the potential application of DEI. In this paper, an improved DEI （IDEI） method is proposed based on the Gaussian curve fitting of the rocking curve （RC）. Utilizing only three input images, the IDEI method can accurately separate the absorption, refraction, and USAXS contrasts produced by the object. The IDEI method can therefore be viewed as an improvement to the extended DEI （EDEI） method. In contrast, the IDEI method can circumvent the limitations of the EDEI method well since it does not impose a Taylor approximation on the RC. Additionally, analysis of the IDEI model errors is performed to further investigate the factors that lead to the image artifacts, and finally validation studies are conducted using computer simulation and synchrotron experimental data.

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.