Laser interferometry with higher resolution,faster update rate,and larger dynamic range is highly anticipated in the exploration of physics frontiers,advanced manufacturing,and precision sensing.Real-time dispersive s...Laser interferometry with higher resolution,faster update rate,and larger dynamic range is highly anticipated in the exploration of physics frontiers,advanced manufacturing,and precision sensing.Real-time dispersive spectral interferometry(DSI)shows promise for high-speed precision measurements,whereas the resolution of subnanometers has not yet been achieved.We present a comprehensive theoretical framework to analyze the limitations of real-time DSI based on the signal-to-noise ratio and data volume.A real-time orthogonal polarization spectral interferometry technique is proposed,which utilizes a pair of interferograms with the pi-phase shift to effectively mitigate the phase noise embedded in real-time spectral envelopes,thereby enabling the precise measurements with subnanometer resolution at megahertz frame rates.The recorded time series data are processed through interpolation,segmentation,time–frequency mapping,and de-enveloping to regain the typical cosine-shaped spectral evolution,followed by a fitting-based phase retrieval method to extract the interference phase.The phase resolution of 1.1 mrad(0.91 as for time delay and 0.3 nm for distance)is obtained at the update rate of 22.2 MHz even under the detection bandwidth of 500 MHz,and can be further enhanced to 0.29 mrad(0.24 as for time delay)after 500 times averaging(∼0.5 MHz).Our approach is validated through periodic phase modulations and applied to measure the rapid damped oscillations of a piezo stage,yielding results consistent with those obtained from a commercial picometer interferometer.展开更多
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 ...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.展开更多
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 retr...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.展开更多
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...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.展开更多
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)wavefron...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.展开更多
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 a...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.展开更多
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)i...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)>|.展开更多
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 ...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.展开更多
Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number m so that one can recover d-...Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number m so that one can recover d-dimensional signals from m phaseless measurements. This problem attracts much attention of experts from different areas. In this paper, we review the recent development on the minimal measurement number and also raise many interesting open questions.展开更多
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 ...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.展开更多
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 p...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.展开更多
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 iterativ...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.展开更多
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...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.展开更多
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 metho...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 L<sub>1/2</sub>-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.展开更多
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...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.展开更多
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 ba...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].展开更多
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 endstation...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.展开更多
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 un...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.展开更多
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 ge...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.展开更多
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 fro...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.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.61705193)the Natural Science Foundation of Zhejiang Province(Grant No.LGG20F050002)the Jinhua Science and Technology Plan(Project No.2024-1-064).
文摘Laser interferometry with higher resolution,faster update rate,and larger dynamic range is highly anticipated in the exploration of physics frontiers,advanced manufacturing,and precision sensing.Real-time dispersive spectral interferometry(DSI)shows promise for high-speed precision measurements,whereas the resolution of subnanometers has not yet been achieved.We present a comprehensive theoretical framework to analyze the limitations of real-time DSI based on the signal-to-noise ratio and data volume.A real-time orthogonal polarization spectral interferometry technique is proposed,which utilizes a pair of interferograms with the pi-phase shift to effectively mitigate the phase noise embedded in real-time spectral envelopes,thereby enabling the precise measurements with subnanometer resolution at megahertz frame rates.The recorded time series data are processed through interpolation,segmentation,time–frequency mapping,and de-enveloping to regain the typical cosine-shaped spectral evolution,followed by a fitting-based phase retrieval method to extract the interference phase.The phase resolution of 1.1 mrad(0.91 as for time delay and 0.3 nm for distance)is obtained at the update rate of 22.2 MHz even under the detection bandwidth of 500 MHz,and can be further enhanced to 0.29 mrad(0.24 as for time delay)after 500 times averaging(∼0.5 MHz).Our approach is validated through periodic phase modulations and applied to measure the rapid damped oscillations of a piezo stage,yielding results consistent with those obtained from a commercial picometer interferometer.
基金supported by the National Natural Science Foundation of China (Grant Nos. 60232090 and 10774102)the Science & Technology Project from Shenzhen Government of China (Grant Nos. 2008340 and 200717)
文摘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.
基金supported by the National Natural Science Foundation of China(6157138861601398)the National Natural Science Foundation of Hebei Province(F2016203251)
文摘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.
基金Project supported by the National Natural Science Foundation of China (Grant Nos. 11179009 and 50875013)the Beijing Municipal Natural Science Foundation, China (Grant No. 4102036)the Beijing NOVA Program, China (Grant No. 2009A09)
文摘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.
基金supported by the National Science Foundation of China (61177018)the Program for New Century Excellent Talents in University (NECT-11-0596)Beijing Nova Program (2011066).
文摘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.
基金Project supported by the National Basic Research Program of China(Grant No.2013CB328803)the National High Technology Research and Development Program of China(Grant Nos.2013AA013904 and 2015AA016301)
文摘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.
基金The Science and Technology Development Fund,Macao SAR(File no.0123/2018/A3)supported by the Natural Science Foundation of China(61961003,61561006,11501132)+2 种基金Natural Science Foundation of Guangxi(2016GXNSFAA380049)the talent project of the Education Department of the Guangxi Government for one thousand Young-Middle-Aged backbone teachersthe Natural Science Foundation of China(12071035)。
文摘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)>|.
基金Supported by Foundation of Hubei Educational Committee (Q20091004)NSFC (10771053)+1 种基金the National Research Foundation for the Doctoral Program of Higher Education of China (SRFDP) (20060512001)Natural Science 373 Foundation of Hubei Province (2007ABA139)
文摘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.
基金Supported by the National Natural Science Foundation of China(Grant Nos.1142211311331012+1 种基金91630203)National Basic Research Program of China(973 Program 2015CB856000)
文摘Phase retrieval is to recover the signals from phaseless measurements which is raised in many areas. A fundamental problem in phase retrieval is to determine the minimal measurement number m so that one can recover d-dimensional signals from m phaseless measurements. This problem attracts much attention of experts from different areas. In this paper, we review the recent development on the minimal measurement number and also raise many interesting open questions.
基金Project supported by the National Natural Science Foundation of China(Grant No.61705254)the Key Research and Development Program of Shaanxi Province of China(Grant No.2020GY-114).
文摘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.
基金Supported by the National Natural Science Foundation of China(11531013,U1630116)the fundamental research funds for the central universities.
文摘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.
基金Project supported by the National Basic Research P.rogram of China (No.2003CB716101)the National Natural Science Foundation of China (No.60532080)+1 种基金the Science Foundation of Chinese Ministry of Education(No.306017)the Science Foundation of Engineering Research Institute of Peking University,and the Science Foundation of Microsoft Research of Asia.
文摘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.
基金Supported by the National Natural Science Foundation of China under Grant No 61205103
文摘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.
文摘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 L<sub>1/2</sub>-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.
基金supported by the National Science Foundation(Grant No.1846784).
文摘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.
文摘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].
基金the Shanghai Soft X-ray Free-Electron Laser Facility beamline projectionfunded by the Major State Basic Research Development Program of China(No.2017YFA0504802)+1 种基金Strategic Priority Research Program of the Chinese Academy of Sciences(No.XDB 37040303)National Natural Science Foundation of China(No.21727817).
文摘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.
基金supported by the Funds from the Engineering and Physical Sciences Research Council(Grant No.EP/E034055/1)the One Hundred Talent Project of the Chinese Academy of Sciences and the Financial Support(Grant No.GFZX0205010502.12)
文摘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.
基金Project supported by the National Key R&D Program of China(Grant No.2017YFB0405202)the National Natural Science Foundation of China(Grant Nos.61690221,91850209,and 11774277)。
文摘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.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.30900333 and 81371549)the WBE Liver Fibrosis Foundation,China(Grant No.CFHPC20131033)
文摘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.
