Phase Retrieval Method Research Articles

A combined speckle- & propagation-based single shot two-dimensional phase retrieval method

A combined speckle- & propagation-based single shot two-dimensional phase retrieval method

Measurements of microwave transmission mode in HL-3 tokamak relevant ECH corrugated waveguides transmission line

The transmission modes of high-power millimeter wave in corrugated waveguides transmission line (TL) are crucial, especially for the long-pulse operation for long-distance TL. The microwave transmission mode in the TL on HL-3 tokamak relevant the electron cyclotron heating system are studied for the purpose according to the phase retrieval method based on intensity distribution measured by an infrared camera at several different locations away from the outlet of TL. A specific high power test platform with about 40-meter TL is established and the mode contents in the middle and the end of the TL are analyzed. In the middle of the TL, the proportion of main transmission mode LP01 mode is about 97% and other high-order modes contents are less than 3%. In the end of the TL, the main mode purity is about 94%, and the high-order mode, LP11 even mode is excited about 4.6%. These mode analysis results indicate that the high-power and long-pulse millimeter wave corrugated waveguides TL are designed and machined well, and the alignment method for long distance transmission line installation is highly useful for high-purity wave mode transmission.

Connection between weak measurement in quantum physics and analytic phase retrieval in classical wave optics

Recently, various precision optical experiments have been proposed that utilize the concept of weak measurement in quantum physics. Since it is known that the results appearing in weak measurements are related to the phase of the quantum system, it is important to investigate the phase in order to understand the weak measurements. We present that one of phase-retrieval methods in classical wave optics, the analytic phase retrieval, has a close connection with quantum weak measurement. We explain such a connection for two emblematic optical weak measurements that have the same mathematical formalism as quantum systems: one is a system for the anomalous probe displacement of polarized light in a birefringent crystal, and the other is a system for the direct measurement of a wave function by polarization. We reveal that the same physical operation as the analytic phase retrieval is behind these two systems, namely the use of filtering effects.

High-resolution lensless holographic microscopy using a physics-aware deep network.

Lensless digital inline holographic microscopy (LDIHM) is an emerging quantitative phase imaging modality that uses advanced computational methods for phase retrieval from the interference pattern. The existing end-to-end deep networks require a large training dataset with sufficient diversity to achieve high-fidelity hologram reconstruction. To mitigate this data requirement problem, physics-aware deep networks integrate the physics of holography in the loss function to reconstruct complex objects without needing prior training. However, the data fidelity term measures the data consistency with a single low-resolution hologram without any external regularization, which results in a low performance on complex biological data. We aim to mitigate the challenges with trained and physics-aware untrained deep networks separately and combine the benefits of both methods for high-resolution phase recovery from a single low-resolution hologram in LDIHM. We propose a hybrid deep framework (HDPhysNet) using a plug-and-play method that blends the benefits of trained and untrained deep models for phase recovery in LDIHM. The high-resolution phase is generated by a pre-trained high-definition generative adversarial network (HDGAN) from a single low-resolution hologram. The generated phase is then plugged into the loss function of a physics-aware untrained deep network to regulate the complex object reconstruction process. Simulation results show that the SSIM of the proposed method is increased by 0.07 over the trained and 0.04 over the untrained deep networks. The average phase-SNR is elevated by 8.2dB over trained deep models and 9.8dB over untrained deep networks on the experimental biological cells (cervical cells and red blood cells). We showed improved performance of the HDPhysNet against the unknown perturbation in the imaging parameters such as the propagation distance, the wavelength of the illuminating source, and the imaging sample compared with the trained network (HDGAN). LDIHM, combined with HDPhysNet, is a portable and technology-driven microscopy best suited for point-of-care cytology applications.

Fourier ptychographic microscopy with multi-height illumination based on energy threshold pre-search

Fourier ptychographic microscopy (FPM) technology combines the concepts of synthetic aperture imaging, ptychography, and phase retrieval to address the contradiction between the large field of view and high resolution in traditional microscopy and can achieve high-resolution amplitude and phase images with a large field of view. However, for most samples, the primary information is concentrated in the low-frequency region, and traditional single-height FPM may suffer from insufficient sampling, leading to low reconstruction accuracy. In addition, the reconstruction process typically requires a large number of low-resolution images, which also significantly reduces the reconstruction efficiency. To overcome these issues, this paper proposes a form of FPM with multi-height illumination based on an energy threshold pre-search. This method simply involves moving the LED array to three planes for multi-height sample illumination on the traditional FPM hardware, thus improving the sampling conditions and enhancing the reconstruction accuracy. The low-resolution images acquired in this way are then screened using an energy threshold method to select images with higher energy, and a phase retrieval method is employed to reconstruct high-resolution complex amplitude images. The results of simulations and experiments demonstrate that compared to traditional methods, our approach not only improves the reconstruction accuracy but also reduces the number of low-resolution images by at least approximately 60%, thereby significantly enhancing the reconstruction efficiency.

Multi frame holograms batched optimization for binary phase spatial light modulators

Phase retrieval methods used in computer generated holograms such as Gerchberg-Saxton and gradient descent give results which are prone to noise and other defects. This work builds up on the idea of time-averaging multiple hologram frames, first introduced in methods like One-Step Phase-Retrieval and Adaptive One-Step Phase-Retrieval. The proposed technique called Multi-Frame Holograms Batched Optimization uses the L-BFGS optimization algorithm to simultaneously generate a batch of binary phase holograms which result in an average reconstructed image of improved fidelity and fast algorithmic convergence, both in the Fraunhoffer and the Fresnel regimes. The results are compared to One-Step Phase-Retrieval and Adaptive One-Step Phase-Retrieval in simulation and experimentally, proving the superiority of the proposed approach. This technique can be easily extended to other spatial modulation methods.

Atomic resolution coherent x-ray imaging with physics-based phase retrieval

Coherent x-ray imaging and scattering from accelerator based sources such as synchrotrons continue to impact biology, medicine, technology, and materials science. Many synchrotrons around the world are currently undergoing major upgrades to increase their available coherent x-ray flux by approximately two orders of magnitude. The improvement of synchrotrons may enable imaging of materials in operando at the atomic scale which may revolutionize battery and catalysis technologies. Current algorithms used for phase retrieval in coherent x-ray imaging are based on the projection onto sets method. These traditional iterative phase retrieval methods will become more computationally expensive as they push towards atomic resolution and may struggle to converge. Additionally, these methods do not incorporate physical information that may additionally constrain the solution. In this work, we present an algorithm which incorporates molecular dynamics into Bragg coherent diffraction imaging (BCDI). This algorithm, which we call PRAMMol (Phase Retrieval with Atomic Modeling and Molecular Dynamics) combines statistical techniques with molecular dynamics to solve the phase retrieval problem. We present several examples where our algorithm is applied to simulated coherent diffraction from 3D crystals and show convergence to the correct solution at the atomic scale.

Proposed experiment to measure nonlinear optical susceptibilities in the saturated regime.

When an optical beam passes through a thin slice of a homogeneous material, the change of its phase and amplitude is characterized by the material's linear and nonlinear susceptibility, the latter also known as the hyperpolarizability. The standard method for measuring the nonlinear susceptibility is the scan. This widely used method is sometimes applied outside of its range of validity, leading to systematic errors. These errors are illustrated for a two-level system with parameters taken from atomic rubidium. The present paper proposes a method called the phase retrieval of modes to determine the nonlinear susceptibility without an assumption about its functional form, in contrast to both the -scan method and variants intended to apply in cases of saturation. In brief, a Gaussian beam passes through a thin sample and is detected on three planes in a focal scan. Phase retrieval methods are used to find coefficients of the modes which in turn determine the optical nonlinear susceptibility. Nearly exact recovery of the nonlinear susceptibility is shown numerically in the no-noise case. Additionally, two types of noise are considered: shot noise on the detector and intensity fluctuations of the input.

Fringe pattern normalization using conditional Generative Adversarial Networks

Fringe pattern normalization is an important pre-processing operation in optical fringe analysis, and is usually required as the initial step for several phase retrieval methods. However, noise and rapid amplitude fluctuations in the fringe pattern pose significant challenges for fringe pattern normalization. In this paper, we propose a robust approach for fringe normalization using conditional Generative Adversarial Network, which works on the principle of image-to-image translation with conditioning on input images. The performance of the proposed method under different noise conditions and amplitude variations is demonstrated using numerical simulations. Further, the practical applicability of the proposed method is also tested with experimental data obtained in digital holographic interferometry.

Phase retrieval via conjugate gradient minimization in double-plane lensless holographic microscopy.

Optimization-based phase retrieval method for digital lensless holographic microscopy in the double-plane recording configuration is proposed. In our method the phase retrieval is framed as an optimization problem that can be efficiently and rigorously tackled with gradient decent tools. This is done with the conjugate gradient method that possesses excellent theoretical features such as global and fast convergence (compared to steepest descent) and relatively low computational cost (compared to second order optimizers). The proposed method is extensively tested with simulations and experimental measurements that show superiority of our method over the Gerchberg-Saxton algorithm, especially in terms of reconstruction of problematic low frequency components of viable phase information.

Single-frame interferogram phase retrieval using a phase-shifting generative adversarial network with physics-based fine-tuning

Phase retrieval from a single-frame interferogram is a challenge in optical interferometry. This paper proposes an accurate physics-based deep learning method for one-shot phase retrieval. This approach involves both data-driven pre-training of a phase-shifting network and subsequent model-driven fine-tuning. The well-designed pre-training network is capable of simultaneously generating π/2, π, and 3π/2 phase-shifted versions of the input interferogram to facilitate phase extraction. Moreover, integrating the interferometric model into the testing dataset enables self-supervised fine-tuning, optimizing the use of both data and physics-based priors. Simulations and experiments demonstrate the effectiveness of the proposed method in overcoming the common generalization limitation of data-driven models and achieving accurate phase retrieval. The proposed method not only enhances the accuracy of phase retrieval but also improves the generalization capability, making it robust under experimental conditions for interferometric applications.

Speckle tracking phase-contrast computed tomography at an inverse Compton X-ray source.

Speckle-based X-ray imaging (SBI) is a phase-contrast method developed at and for highly coherent X-ray sources, such as synchrotrons, to increase the contrast of weakly absorbing objects. Consequently, it complements the conventional attenuation-based X-ray imaging. Meanwhile, attempts to establish SBI at less coherent laboratory sources have been performed, ranging from liquid metal-jet X-ray sources to microfocus X-ray tubes. However, their lack of coherence results in interference fringes not being resolved. Therefore, algorithms were developed which neglect the interference effects. Here, we demonstrate phase-contrast computed tomography employing SBI in a laboratory-setting with an inverse Compton X-ray source. In this context, we investigate and compare also the performance of the at synchrotron conventionally used phase-retrieval algorithms for SBI, unified modulated pattern analysis (UMPA) with a phase-retrieval method developed for low coherence systems (LCS). We successfully retrieve a full computed tomography in a phantom as well as in biological specimens, such as larvae of the greater wax moth (Galleria mellonella), a model system for studies of pathogens and infections. In this context, we additionally demonstrate quantitative phase-contrast computed tomography using SBI at a low coherent set-up.

Low-Bit-Depth Detection for Phase Retrieval with Higher Efficiency in Holographic Data Storage

In the past, comprehensive information was imperative for image processing, prompting a preference for high-depth cameras. However, in our research, we discovered that the abundance of image details may impede phase retrieval. Consequently, this paper presents an iterative phase retrieval method based on a low bit depth. Through simulations and experiments, this approach has proven effective in evidently enhancing phase retrieval outcomes. Furthermore, the concept of low bit depth holds promise for broader application across diverse domains within the field of image retrieval.

Single-shot lensless masked imaging with enhanced self-calibrated phase retrieval.

Single-shot lensless imaging with a binary amplitude mask enables a low-cost and miniaturized configuration for wave field recovery. However, the mask only allows a part of the wave field to be captured, and thus the inverse decoding process becomes a highly ill-posed problem. Here we propose an enhanced self-calibrated phase retrieval (eSCPR) method to realize single-shot joint recovery of mask distribution and the sample's wavefront. In our method, a sparse regularized phase retrieval (SrPR) algorithm is designed to calibrate the mask distribution. Then, a denoising regularized phase retrieval (DrPR) algorithm is constructed to reconstruct the wavefront of the sample. Compared to conventional single-shot methods, our method shows robust and flexible image recovery. Experimental results of different samples are given to demonstrate the superiority of our method.

Single-beam digital holographic reconstruction: a phase-support enhanced complex wavefront on phase-only function for twin-image elimination.

In in-line digital holographic microscopy (DHM), twin-image artifacts pose a significant challenge, and reduction or complete elimination is essential for object reconstruction. To facilitate object reconstruction using a single hologram, significantly reduce inaccuracies, and avoid iterative processing, a digital holographic reconstruction algorithm called phase-support constraint on phase-only function (PCOF) is presented. In-line DHM simulations and tabletop experiments employing the sliding-window approach are used to compute the arithmetic mean and variance of the phase values in the reconstructed image. A support constraint mask, through variance thresholding, effectively enabled twin-image artifacts. Quantitative evaluations using metrics such as mean squared error, peak signal-to-noise ratio, and mean structural similarity index show PCOF's superior capability in eliminating twin-image artifacts and achieving high-fidelity reconstructions compared with conventional methods such as angular spectrum and iterative phase retrieval methods. PCOF stands as a promising approach to in-line digital holographic reconstruction, offering a robust solution to mitigate twin-image artifacts and enhance the fidelity of reconstructed objects.

Phase retrieval for radar waveform design

Abstract The ability of a radar to discriminate in both range and Doppler velocity is completely characterized by the ambiguity function (AF) of its transmit waveform. Mathematically, it is obtained by correlating the waveform with its Doppler-shifted and delayed replicas. We consider the inverse problem of designing a radar transmit waveform that satisfies the specified AF magnitude. This process may be viewed as a signal reconstruction with some variation of phase retrieval methods. We provide a trust-region algorithm that minimizes a smoothed non-convex least-squares objective function to iteratively recover the underlying signal-of-interest for either time- or band-limited support. The method first approximates the signal using an iterative spectral algorithm and then refines the attained initialization based on a sequence of gradient iterations. Our theoretical analysis shows that unique signal reconstruction is possible using signal samples no more than thrice the number of signal frequencies or time samples. Numerical experiments demonstrate that our method recovers both time- and band-limited signals from sparsely and randomly sampled, noisy and noiseless AFs.

Improved phase retrieval method with dual-plane holograms for slightly off-axis digital holography

An improved phase retrieval method with dual-plane holograms for slightly off-axis digital holography (DH) is proposed. By applying the Hilbert transform (HT) twice on defocused hologram, the DC term can be effectively eliminated while preserving the original object information. The phase of tested sample can be retrieved from two transformed holograms with only a straightforward algebraic equation. The derivation of algebraic equation and characteristic analysis of HT on hologram are discussed in details. Our method offers a viable solution for quantitative phase imaging in slightly off-axis DH system, eliminating the need for complex spectrum filtering, phase-shifting devices, and iterative operation. Numerical simulation and experiment results of microlens array and phase plate demonstrate the validity of proposed method.

One-shot self-calibrating phase-shifting interferometry by direct normalization of interferograms

Dynamic phase measurement is a valuable technique applied across various scientific and technological domains due to its high accuracy, non-contacting method, and numerous practical applications. In this manuscript, we present a phase retrieval method capable of measuring the object’s phase in real-time. Our proposal is based on a double aperture common-path interferometer adapted for polarization modulation in the input windows, enabling the superposition of two fields with orthogonal circular polarizations. Two interferograms and two intensities are captured in a single shot, showcasing the possibility of obtaining two normalized interferograms directly and straightforwardly. This allows for the derivation of expressions for phase recovery and, additionally, the determination of the arbitrary phase step. We demonstrate that this method is easy to implement, highly accurate, and sufficiently fast for real-time applications. To validate the effectiveness of the method, we conduct numerical error analysis and laboratory experiments.

3D fluorescence imaging through a scattering medium using the transport of intensity equation and Fresnel ping-pong algorithm.

A three-dimensional (3D) fluorescent imaging method through a scattering medium has been presented. The proposed method combines digital phase conjugate reconstruction of the scattered light wave by the transport of intensity equation-based 3D fluorescent imaging to the position of scattering medium and followed phase retrieval method by Fresnel ping-pong algorithm. The effectiveness of the proposed method is experimentally verified by measuring the 3D distribution of fluorescent beads and tobacco-cultured cells through a thin diffuser. Compared to other methods, the reconstructed images show enhancement of the detailed structure of the objects blurred by the diffuser in a wide area. In the simulation, the proposed method is capable of recovering images degraded by scattering in the phase modulation range from 0 to 2π. The capability to identify the depth position is also presented.

Accelerated phase retrieval using adaptive support and statistical fringe processing of phase estimates.

A technique for accelerated multiple-plane phase retrieval is demonstrated by creating adaptive support through the statistical analysis of phase estimates. Its technical advantage arises from, what we believe to be, the first time use of both phase estimates and a statistical metric, enabling the fast generation of noise-robust support masks. This results in a fourfold improvement in convergence speed when compared to the conventional multiple-plane method. Evaluating data fitting performance with fewer intensity recordings showed that using four or more recordings resulted in accurate fitting, three recordings caused overfitting, and two recordings led to underfitting for the test object waves used. In principle, the adaptive support strategy based on the statistical analysis of phase estimates may be applied to other iterative phase retrieval methods.