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
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
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
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
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
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
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
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
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
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....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.展开更多
Accurate depiction of waves in temporal and spatial is essential to the investigation of interactions between physical objects and waves.Digital holography(DH)can perform quantitative analysis of wave-matter interacti...Accurate depiction of waves in temporal and spatial is essential to the investigation of interactions between physical objects and waves.Digital holography(DH)can perform quantitative analysis of wave-matter interactions.Full detector-bandwidth reconstruc-tion can be realized based on in-line DH.But the overlapping of twin images strongly prevents quantitative analysis.For off-axis DH,the object wave and the detector bandwidth need to satisfy certain conditions to perform reconstruction accurately.Here,we present a reliable approach involving a coupled configuration for combining two in-line holograms and one off-axis hologram,using a rapidly converging iterative procedure based on two-plane coupled phase retrieval(TwPCPR)method.It realizes a fast-convergence holographic calculation method.High-resolution and full-field recon-struction by exploiting the full bandwidth are demonstrated for complex-amplitude reconstruction.Off-axis optimization phase provides an effective initial guess to avoid stagnation and minimize the required measurements of multi-plane phase retrieval.The proposed strategy works well for more extended samples without any prior assumptions of the objects including support,non-negative,sparse constraints,etc.It helps to enhance and empower applications in wavefront sensing,computational microscopy and biological tissue analysis.展开更多
High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information.In computational phase imaging,phase retrieval(PR)is required to reconstruct bot...High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information.In computational phase imaging,phase retrieval(PR)is required to reconstruct both amplitude and phase in complex space from intensity-only measurements.The existing PR algorithms suffer from the tradeoff among low computational complexity,robustness to measurement noise and strong generalization on different modalities.In this work,we report an efficient large-scale phase retrieval technique termed as LPR.It extends the plug-and-play generalized-alternating-projection framework from real space to nonlinear complex space.The alternating projection solver and enhancing neural network are respectively derived to tackle the measurement formation and statistical prior regularization.This framework compensates the shortcomings of each operator,so as to realize high-fidelity phase retrieval with low computational complexity and strong generalization.We applied the technique for a series of computational phase imaging modalities including coherent diffraction imaging,coded diffraction pattern imaging,and Fourier ptychographic microscopy.Extensive simulations and experiments validate that the technique outperforms the existing PR algorithms with as much as 17dB enhancement on signal-to-noise ratio,and more than one order-of-magnitude increased running efficiency.Besides,we for the first time demonstrate ultralarge-scale phase retrieval at the 8K level(7680×4320 pixels)in minute-level time.展开更多
Baseline algorithm, as a tool in wavefront sensing （WFS）, incorporates the phase-diverse phase retrieval （PDPR） method with hybrid-unwrapping approach to ensure a unique pupil phase estimate with high WFS accuracy...Baseline algorithm, as a tool in wavefront sensing （WFS）, incorporates the phase-diverse phase retrieval （PDPR） method with hybrid-unwrapping approach to ensure a unique pupil phase estimate with high WFS accuracy even in the case of high dynamic range aberration, as long as the pupil shape is of a convex set. However, for a complicated pupil, such as that in obstructed pupil optics, the said unwrapping approach would fail owing to the fake values at points located in obstructed areas of the pupil. Thus a modified unwrapping approach that can minimize the negative effects of the obstructed areas is proposed. Simulations have shown the validity of this unwrapping approach when it is embedded in Baseline algorithm.展开更多
We propose a novel on-line beam diagnostic method based on single-shot beam splitting phase retrieval. The incident beam to be measured is diffracted into many replicas by a Dammann grating and then propagates through...We propose a novel on-line beam diagnostic method based on single-shot beam splitting phase retrieval. The incident beam to be measured is diffracted into many replicas by a Dammann grating and then propagates through a weakly scattering phase plate with a known structure; the exiting beams propagate along their original direction and form an array of diffraction patterns on the detector plane. By applying the intensity of diffraction patterns into an iterative algorithm and calculating between the grating plane, weakly scattering plane, and detector plane, the complex field of the incident beam can be reconstructed rapidly; the feasibility of this method is verified experimentally with wavelengths of 1053 and 632.8 nm.展开更多
A fundamental task in phase retrieval is to recover an unknown signal x∈R^(n) from a set of magnitude-only measurements y_(i)=|〈a_(i),x〉|,i=1,…,m.In this paper,we propose two novel perturbed amplitude models(PAMs)...A fundamental task in phase retrieval is to recover an unknown signal x∈R^(n) from a set of magnitude-only measurements y_(i)=|〈a_(i),x〉|,i=1,…,m.In this paper,we propose two novel perturbed amplitude models(PAMs)which have a non-convex and quadratic-type loss function.When the measurements a_(i)∈R^(n) are Gaussian random vectors and the number of measurements m≥Cn,we rigorously prove that the PAMs admit no spurious local minimizers with high probability,i.e.,the target solution x is the unique local minimizer(up to a global phase)and the loss function has a negative directional curvature around each saddle point.Thanks to the well-tamed benign geometric landscape,one can employ the vanilla gradient descent method to locate the global minimizer x(up to a global phase)without spectral initialization.We carry out extensive numerical experiments to show that the gradient descent algorithm with random initialization outperforms state-of-the-art algorithms with spectral initialization in empirical success rate and convergence speed.展开更多
A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements.In this work we introduce three novel quotient intensity models(QIMs) based on a deep modification...A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements.In this work we introduce three novel quotient intensity models(QIMs) based on a deep modification of the traditional intensity-based models.A remarkable feature of the new loss functions is that the corresponding geometric landscape is benign under the optimal sampling complexity.When the measurements ai∈Rn are Gaussian random vectors and the number of measurements m≥Cn,the QIMs admit no spurious local minimizers with high probability,i.e.,the target solution x is the unique local minimizer(up to a global phase) and the loss function has a negative directional curvature around each saddle point.Such benign geometric landscape allows the gradient descent methods to find the global solution x(up to a global phase) without spectral initialization.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
Embedded data are used to retrieve phases quicker with high accuracy in phase-modulated holographic data storage(HDS).We propose a method to design an embedded data distribution using iterations to enhance the intensi...Embedded data are used to retrieve phases quicker with high accuracy in phase-modulated holographic data storage(HDS).We propose a method to design an embedded data distribution using iterations to enhance the intensity of the high-frequency signal in the Fourier spectrum.The proposed method increases the antinoise performance and signal-to-noise ratio(SNR)of the Fourier spectrum distribution,realizing a more efficient phase retrieval.Experiments indicate that the bit error rate(BER)of this method can be reduced by a factor of one after 10 iterations.展开更多
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.
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 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 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 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 Key Research and Development Program of China(Grant Nos.2022YFA1404800,and 2019YFA0705000)the National Natural Science Foundation of China(Grant Nos.12174280,12204340,12192254,11974218,92250304,and 92050202)+1 种基金the China Postdoctoral Science Foundation(Grant No.2022M722325)the Priority Academic Program Development of Jiangsu Higher Education Institutions,Key Lab of Modern Optical Technologies of Jiangsu Province(Grant No.KJS2138)。
文摘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.
基金National Natural Science Foundation of China(NSFC)(61827825).
文摘Accurate depiction of waves in temporal and spatial is essential to the investigation of interactions between physical objects and waves.Digital holography(DH)can perform quantitative analysis of wave-matter interactions.Full detector-bandwidth reconstruc-tion can be realized based on in-line DH.But the overlapping of twin images strongly prevents quantitative analysis.For off-axis DH,the object wave and the detector bandwidth need to satisfy certain conditions to perform reconstruction accurately.Here,we present a reliable approach involving a coupled configuration for combining two in-line holograms and one off-axis hologram,using a rapidly converging iterative procedure based on two-plane coupled phase retrieval(TwPCPR)method.It realizes a fast-convergence holographic calculation method.High-resolution and full-field recon-struction by exploiting the full bandwidth are demonstrated for complex-amplitude reconstruction.Off-axis optimization phase provides an effective initial guess to avoid stagnation and minimize the required measurements of multi-plane phase retrieval.The proposed strategy works well for more extended samples without any prior assumptions of the objects including support,non-negative,sparse constraints,etc.It helps to enhance and empower applications in wavefront sensing,computational microscopy and biological tissue analysis.
基金supported by the National Natural Science Foundation of China(Nos.61971045,61827901,61991451)National Key R&D Program(Grant No.2020YFB0505601)Fundamental Research Funds for the Central Universities(Grant No.3052019024).
文摘High-throughput computational imaging requires efficient processing algorithms to retrieve multi-dimensional and multi-scale information.In computational phase imaging,phase retrieval(PR)is required to reconstruct both amplitude and phase in complex space from intensity-only measurements.The existing PR algorithms suffer from the tradeoff among low computational complexity,robustness to measurement noise and strong generalization on different modalities.In this work,we report an efficient large-scale phase retrieval technique termed as LPR.It extends the plug-and-play generalized-alternating-projection framework from real space to nonlinear complex space.The alternating projection solver and enhancing neural network are respectively derived to tackle the measurement formation and statistical prior regularization.This framework compensates the shortcomings of each operator,so as to realize high-fidelity phase retrieval with low computational complexity and strong generalization.We applied the technique for a series of computational phase imaging modalities including coherent diffraction imaging,coded diffraction pattern imaging,and Fourier ptychographic microscopy.Extensive simulations and experiments validate that the technique outperforms the existing PR algorithms with as much as 17dB enhancement on signal-to-noise ratio,and more than one order-of-magnitude increased running efficiency.Besides,we for the first time demonstrate ultralarge-scale phase retrieval at the 8K level(7680×4320 pixels)in minute-level time.
文摘Baseline algorithm, as a tool in wavefront sensing （WFS）, incorporates the phase-diverse phase retrieval （PDPR） method with hybrid-unwrapping approach to ensure a unique pupil phase estimate with high WFS accuracy even in the case of high dynamic range aberration, as long as the pupil shape is of a convex set. However, for a complicated pupil, such as that in obstructed pupil optics, the said unwrapping approach would fail owing to the fake values at points located in obstructed areas of the pupil. Thus a modified unwrapping approach that can minimize the negative effects of the obstructed areas is proposed. Simulations have shown the validity of this unwrapping approach when it is embedded in Baseline algorithm.
基金supported by the National Natural Science Foundation of China(No.61675215)the Shanghai Sailing Program(No.18YF1426600)
文摘We propose a novel on-line beam diagnostic method based on single-shot beam splitting phase retrieval. The incident beam to be measured is diffracted into many replicas by a Dammann grating and then propagates through a weakly scattering phase plate with a known structure; the exiting beams propagate along their original direction and form an array of diffraction patterns on the detector plane. By applying the intensity of diffraction patterns into an iterative algorithm and calculating between the grating plane, weakly scattering plane, and detector plane, the complex field of the incident beam can be reconstructed rapidly; the feasibility of this method is verified experimentally with wavelengths of 1053 and 632.8 nm.
基金supported in part by Hong Kong Research Grant Council General Research Grant Nos.16309518,16309219,16310620 and 16306821supported in part by the Hong Kong Research Grant Council General Research Grant Nos.16306415 and 16308518.
文摘A fundamental task in phase retrieval is to recover an unknown signal x∈R^(n) from a set of magnitude-only measurements y_(i)=|〈a_(i),x〉|,i=1,…,m.In this paper,we propose two novel perturbed amplitude models(PAMs)which have a non-convex and quadratic-type loss function.When the measurements a_(i)∈R^(n) are Gaussian random vectors and the number of measurements m≥Cn,we rigorously prove that the PAMs admit no spurious local minimizers with high probability,i.e.,the target solution x is the unique local minimizer(up to a global phase)and the loss function has a negative directional curvature around each saddle point.Thanks to the well-tamed benign geometric landscape,one can employ the vanilla gradient descent method to locate the global minimizer x(up to a global phase)without spectral initialization.We carry out extensive numerical experiments to show that the gradient descent algorithm with random initialization outperforms state-of-the-art algorithms with spectral initialization in empirical success rate and convergence speed.
基金supported in part by Hong Kong Research Grant Council General Research Grant Nos.16309518,16309219,16310620,and 16306821supported in part by Hong Kong Research Grant Council General Research Grant Nos.16306415 and 16308518
文摘A fundamental problem in phase retrieval is to reconstruct an unknown signal from a set of magnitude-only measurements.In this work we introduce three novel quotient intensity models(QIMs) based on a deep modification of the traditional intensity-based models.A remarkable feature of the new loss functions is that the corresponding geometric landscape is benign under the optimal sampling complexity.When the measurements ai∈Rn are Gaussian random vectors and the number of measurements m≥Cn,the QIMs admit no spurious local minimizers with high probability,i.e.,the target solution x is the unique local minimizer(up to a global phase) and the loss function has a negative directional curvature around each saddle point.Such benign geometric landscape allows the gradient descent methods to find the global solution x(up to a global phase) without spectral initialization.
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the Open Project Program of Wuhan National Laboratory for Optoelectronics(No.2019WNLOKF007)the National Key R&D Program of China(No.2018YFA0701800).
文摘Embedded data are used to retrieve phases quicker with high accuracy in phase-modulated holographic data storage(HDS).We propose a method to design an embedded data distribution using iterations to enhance the intensity of the high-frequency signal in the Fourier spectrum.The proposed method increases the antinoise performance and signal-to-noise ratio(SNR)of the Fourier spectrum distribution,realizing a more efficient phase retrieval.Experiments indicate that the bit error rate(BER)of this method can be reduced by a factor of one after 10 iterations.
