Coherent Wavefront Research Articles

High-security holographic display with content and copyright protection based on complex amplitude modulation

The computer-generated hologram provides an approach to modulate the coherent wavefront and has been widely applied in holographic displays. In the actual application, holograms need to be transmitted through the network, which results in the illegal acquisition and malicious manipulation of holographic images. Therefore, it is necessary to develop a practical method to protect the content and copyright of holographic images. In this paper, we develop a high-security holographic display method based on complex amplitude modulation. In our proposed method, the complex hologram of a holographic image is decomposed into two phase-only holograms, one of which is designed as the ciphertext, and the other is regarded as the key. As a result, the holographic image can be reconstructed only when the ciphertext and the key are paired, which boosts the security of the holographic image. Meanwhile, the copyright of the holographic image is protected via a watermark that is embedded in the ciphertext in the form of a hologram. Due to the simultaneous use of encryption and watermark technology, our proposed method could transmit holographic images at a high security level, and has great potential to be applied in holographic displays in the future.

Adaptive constraints by morphological operations for single-shot digital holography

Digital holography provides access to quantitative measurement of the entire complex field, which is indispensable for the investigation of wave-matter interactions. The emerging iterative phase retrieval approach enables to solve the inverse imaging problem only from the given intensity measurements and physical constraints. However, enforcing imprecise constraints limits the reconstruction accuracy and convergence speed. Here, we propose an advanced iterative phase retrieval framework for single-shot in-line digital holography that incorporates adaptive constraints, which achieves optimized convergence behavior, high-fidelity and twin-image-free reconstruction. In conjunction with morphological operations which can extract the object structure while eliminating the irrelevant part such as artifacts and noise, adaptive constraints allow the support region to be accurately estimated and automatically updated at each iteration. Numerical reconstruction of complex-valued objects and the capability of noise immunity are investigated. The improved reconstruction performance of this approach is experimentally validated. Such flexible and versatile framework has promising applications in biomedicine, X-ray coherent diffractive imaging and wavefront sensing.

Real-time machine-learning-driven control system of a deformable mirror for achieving aberration-free X-ray wavefronts.

A neural-network machine learning model is developed to control a bimorph adaptive mirror to achieve and preserve aberration-free coherent X-ray wavefronts at synchrotron radiation and free electron laser beamlines. The controller is trained on a mirror actuator response directly measured at a beamline with a real-time single-shot wavefront sensor, which uses a coded mask and wavelet-transform analysis. The system has been successfully tested on a bimorph deformable mirror at the 28-ID IDEA beamline of the Advanced Photon Source at Argonne National Laboratory. It achieved a response time of a few seconds and maintained desired wavefront shapes (e.g., a spherical wavefront) with sub-wavelength accuracy at 20 keV of X-ray energy. This result is significantly better than what can be obtained using a linear model of the mirror's response. The developed system has not been tailored to a specific mirror and can be applied, in principle, to different kinds of bending mechanisms and actuators.

Reflectionless programmable signal routers.

We demonstrate experimentally that reflectionless scattering modes (RSMs), a generalized version of coherent perfect absorption, can be functionalized to perform reflectionless programmable signal routing. We achieve versatile programmability both in terms of operating frequencies and routing functionality with negligible reflection upon in-coupling, which avoids unwanted signal power echoes in radio frequency or photonic networks. We report in situ observations of routing functionalities like wavelength demultiplexing, including cases where multichannel excitation requires adapted coherent input wavefronts. All experiments are performed in the microwave domain based on the same irregularly shaped cavity with strong modal overlap that is massively parametrized by a 304-element-programmable metasurface. RSMs in our highly overdamped multiresonance transport problem are fundamentally intriguing because the simple critical coupling picture for reflectionless excitation of isolated resonances fails spectacularly. We show in simulation that the distribution of damping rates of scattering singularities broadens under strong absorption so that weakly damped zeros can be tuned toward functionalized RSMs.

A comprehensive framework for evaluation of high pacing frequency and arrhythmic optical mapping signals.

Introduction: High pacing frequency or irregular activity due to arrhythmia produces complex optical mapping signals and challenges for processing. The objective is to establish an automated activation time-based analytical framework applicable to optical mapping images of complex electrical behavior. Methods: Optical mapping signals with varying complexity from sheep (N = 7) ventricular preparations were examined. Windows of activation centered on each action potential upstroke were derived using Hilbert transform phase. Upstroke morphology was evaluated for potential multiple activation components and peaks of upstroke signal derivatives defined activation time. Spatially and temporally clustered activation time points were grouped in to wave fronts for individual processing. Each activation time point was evaluated for corresponding repolarization times. Each wave front was subsequently classified based on repetitive or non-repetitive events. Wave fronts were evaluated for activation time minima defining sites of wave front origin. A visualization tool was further developed to probe dynamically the ensemble activation sequence. Results: Our framework facilitated activation time mapping during complex dynamic events including transitions to rotor-like reentry and ventricular fibrillation. We showed that using fixed AT windows to extract AT maps can impair interpretation of the activation sequence. However, the phase windowing of action potential upstrokes enabled accurate recapitulation of repetitive behavior, providing spatially coherent activation patterns. We further demonstrate that grouping the spatio-temporal distribution of AT points in to coherent wave fronts, facilitated interpretation of isolated conduction events, such as conduction slowing, and to derive dynamic changes in repolarization properties. Focal origins precisely detected sites of stimulation origin and breakthrough for individual wave fronts. Furthermore, a visualization tool to dynamically probe activation time windows during reentry revealed a critical single static line of conduction slowing associated with the rotation core. Conclusion: This comprehensive analytical framework enables detailed quantitative assessment and visualization of complex electrical behavior.

Efficient Coherent Mode Decomposition for Physical Optics Simulations of Beamlines and Experiments

We present simulations of the partially coherent undulator radiation (UR) propagation through several hard X-ray beamlines at NSLS-II, performed with SRW code, adopting two different memory- and CPU-efficient strategies / algorithms for the coherent mode decomposition (CMD). One of these algorithms employs the subtraction of quadratic phase terms from 4D cross spectral density (CSD) at a non-zero radius of the radiation wavefront curvature, whereas the other one applies the CMD at / near a radiation beam waist, where the radiation wavefront is typically “flat”. We show that, when performing the CMD on the 4D CSD of the partially coherent radiation wavefront, the required numbers of grid points of radiation meshes are largely reduced in both cases, compared to standard approaches. This dramatically reduces memory requirements (from TBs typically to several GBs) and improves the time-to-solution of the decomposed modes (from many hours at a parallel execution to several minutes at a sequential execution). Thanks to the implemented algorithms, the propagation simulations of tens or hundreds of thousands coherent wavefronts generated by independent electrons for an undulator-based X-ray beamline at a low- or intermediate- emittance synchrotron light source is reduced to the simulation of over fewer than one thousand major coherent modes obtained from the CMD, which fully recovers the structure of the partially coherent UR before and after the propagation through a beamline. The efficiency and accuracy of the methods is further demonstrated with simulations for two hard X-ray NSLS-II beamlines: HXN and CHX.

Improving plane wave ultrasound imaging through real-time beamformation across multiple arrays

Ultrasound imaging is a widely used diagnostic tool but has limitations in the imaging of deep lesions or obese patients where the large depth to aperture size ratio (f-number) reduces image quality. Reducing the f-number can improve image quality, and in this work, we combined three commercial arrays to create a large imaging aperture of 100 mm and 384 elements. To maintain the frame rate given the large number of elements, plane wave imaging was implemented with all three arrays transmitting a coherent wavefront. On wire targets at a depth of 100 mm, the lateral resolution is significantly improved; the lateral resolution was 1.27 mm with one array (1/3 of the aperture) and 0.37 mm with the full aperture. After creating virtual receiving elements to fill the inter-array gaps, an autoregressive filter reduced the grating lobes originating from the inter-array gaps by − 5.2 dB. On a calibrated commercial phantom, the extended field-of-view and improved spatial resolution were verified. The large aperture facilitates aberration correction using a singular value decomposition-based beamformer. Finally, after approval of the Stanford Institutional Review Board, the three-array configuration was applied in imaging the liver of a volunteer, validating the potential for enhanced resolution.

End-to-end learning of 3D phase-only holograms for holographic display

Computer-generated holography (CGH) provides volumetric control of coherent wavefront and is fundamental to applications such as volumetric 3D displays, lithography, neural photostimulation, and optical/acoustic trapping. Recently, deep learning-based methods emerged as promising computational paradigms for CGH synthesis that overcome the quality-runtime tradeoff in conventional simulation/optimization-based methods. Yet, the quality of the predicted hologram is intrinsically bounded by the dataset’s quality. Here we introduce a new hologram dataset, MIT-CGH-4K-V2, that uses a layered depth image as a data-efficient volumetric 3D input and a two-stage supervised+unsupervised training protocol for direct synthesis of high-quality 3D phase-only holograms. The proposed system also corrects vision aberration, allowing customization for end-users. We experimentally show photorealistic 3D holographic projections and discuss relevant spatial light modulator calibration procedures. Our method runs in real-time on a consumer GPU and 5 FPS on an iPhone 13 Pro, promising drastically enhanced performance for the applications above.

Holographic Tailoring of Structured Light Field with Digital Device

Structured light fields have attracted much attention due to rich spatial degrees of freedom. The tailoring of an arbitrary structured light field on demand is the precondition for the application of structured light. Therefore, the computer holography method used to reconstruct a coherent light field wavefront has been naturally applied for generating structured light. In this work, we comprehensively demonstrate the principles and procedures of pure-phase computer-generated holography (PP-CGH) and binary-amplitude computer-generated holography (BA-CGH) methods for tailoring structured light, realized by two digitally programmable devices: liquid-crystal spatial light modulators (Lc-SLM) and digital micromirror devices (DMD), respectively. Moreover, we first compare the two approaches in detail and clarify the recipe to obtain a high tailoring accuracy and efficiency, which will help researchers to better understand and utilize the holographic tailoring of structured optical fields.

Coronal Quasi-periodic Fast-mode Propagating Wave Trains

QFP wave trains in the corona have been studied intensively in the past decade, thanks to the full-disk, high spatiotemporal resolution, and wide-temperature coverage observations taken by the SDO/AIA. In AIA observations, QFP wave trains are seen to consist of multiple coherent and concentric wavefronts emanating successively near the epicenter of the accompanying flares; they propagate outwardly either along or across coronal loops at fast-mode magnetosonic speeds from several hundred to more than 2000 km/s, and their periods are in the range of tens of seconds to several minutes. Based on the distinct different properties of QFP wave trains, they might be divided into two distinct categories including narrow and broad ones. For most QFP wave trains, some of their periods are similar to those of quasi-periodic pulsations (QPPs) in the accompanying flares, indicating that they are probably different manifestations of the same physical process. Currently, candidate generation mechanisms for QFP wave trains include two main categories: pulsed energy excitation mechanism in association with magnetic reconnection and dispersion evolution mechanism related to the dispersive evolution of impulsively generated broadband perturbations. In addition, the generation of some QFP wave trains might be driven by the leakage of three and five minute oscillations from the lower atmosphere. As one of the new discoveries of SDO, QFP wave trains provide a new tool for coronal seismology to probe the corona parameters, and they are also useful for diagnosing the generation of QPPs, flare processes including energy release and particle accelerations. This review aims to summarize the main observational and theoretical results of the spatially-resolved QFP wave trains in extreme ultraviolet observations, and states briefly a number of questions that deserve further investigations.

Three-dimensional shear velocity structure of the Mauléon and Arzacq Basins (Western Pyrenees)

We present a 3-D shear wave velocity model of the Mauléon and Arzacq Basins from the surface down to 10 km depth, inverted from phase velocity maps at periods between 2 and 9 s. These phase velocity maps were obtained by analyzing coherent surface wave fronts extracted from ambient seismic noise recorded by the large-N Maupasacq seismic array with a matched filtering approach. This new model is in good agreement with a local earthquake tomography study performed on the same acquisition dataset. Our passive imaging models reveal the upper crustal architecture of the Mauléon and Arzacq Basins, with new details on the basement and its relationship with the overlying sedimentary cover. Combining these new tomographic images with surface and subsurface geological information allows us to trace major orogenic structures from the surface down to the basement. In the basin, the models image the first-order basin architecture with a kilometric resolution. At depth, high velocity anomalies suggest the presence of dense deep crustal and mantle rocks in the hanging wall of north-vergent Pyrenean Thrusts. These high velocity anomalies spatially coincide with a positive gravity anomaly in the western Mauléon Basin. In addition, our models reveal major changes from the Chaînons Béarnais to the western Mauléon Basin across a set of orogen-perpendicular structures, the Saison and the Barlanès transfer zones. These changes reflect the along-strike variation of the orogenic evolution that led to the preservation of the former rifted domain and its underlying mantle in the orogenic wedge of the Western Pyrenees. We discuss the implications of these results for the 3-D architecture of the Mauléon Basin and its underlying basement.

Modeling thermodynamic trends of rotating detonation engines

The formation of a number of co- and counter-rotating coherent combustion wave fronts is the hallmark feature of the Rotating Detonation Engine (RDE). The engineering implications of wave topology are not well understood nor quantified, especially with respect to parametric changes in combustor geometry, propellant chemistry, and injection and mixing schemes. In this article, a modeling framework that relates the time and spatial scales of the RDE to engineering performance metrics is developed and presented. The model is built under assumptions of backpressure-insensitivity and nominally choked gaseous propellant injection. The Euler equations of inviscid, compressible fluid flow in one dimension are adapted to model the combustion wave dynamics along the circumference of an annular-type RDE. These adaptations provide the necessary mass and energy input and output channels to shape the traveling wave fronts and decaying tails. The associated unit processes of injection, mixing, combustion, and exhaust are all assigned representative time scales necessary for successful wave propagation. We find that the separation, or lack, of these time scales is responsible for the behavior of the system, including wave co- and counter-propagation and bifurcations between these regimes and wave counts. Furthermore, as there is no imposition of wave topology, the model output is used to estimate the net available mechanical work output and thermodynamic efficiency from the closed trajectories through pressure–volume and temperature–entropy spaces. These metrics are investigated with respect to variation in the characteristic scales for the RDE unit physical processes.

Optical Hash function based on multiple scattering media

Hash functions, which can extract message digest from input messages as output, play an important role in digital signature and authentication. Meanwhile, Hash functions are essential in many cryptographic protocols and regimes. With the research becoming more and more in depth, a series of Hash functions is proposed, such as MD series and SHA series. At the same time, the security analysis and attacks against Hash functions are carried out. The security of Hash functions is threatened. In this case, how to improve the security of the Hash functions becomes the primary concern. In this paper, an optical Hash function based on the interaction between light and multiple scattering media is proposed. Unlike most of the traditional Hash functions which are based on mathematical transformations or complex logic operations, this method innovatively takes advantage of the natural random scattering effect of multiple scattering media on coherently modulated light, and realizes the “confusion” and “diffusion” of modulated light, which satisfies the core functional requirement of the Hash function: one-way encoding/encryption with strong security. The photoelectric hybrid system designed by this method can effectively simulate the "compression function" in the Hash function. Combined with the Sobel filter with feature extraction function, the input data of arbitrary length can be compressed and encrypted into the output with a fixed length of 256-bit (Hash value). The principle of the proposed optical Hash function can be described as follows. 1) Two 8-bit images with a size of 16×16 pixels are loaded in SLM<sub>1</sub> (amplitude-only spatial modulator) and SLM<sub>2</sub> (phase-only spatial modulator) respectively. 2) The coherent wavefront is modulated by SLM<sub>1</sub> and SLM<sub>2</sub>, and then propagates on multiple scattering media. 3) A speckle pattern is recorded by CCD because of the confusion of multiple scattering media. 4) The features of the speckle pattern, which is extracted by Sobel filter, serve as the input of the next compression function. For the unpredicted and non-duplicated disorder multiple scattering media, it is tremendously difficult to determine the internal state of the multiple scattering media. Therefore, the proposed optical Hash function is considered to have a high security. A series of simulation results shows that the proposed optical Hash function has a good “avalanche effect” and “collision resistance”, and its security performance is comparable to that of the most widely used traditional Hash functions (MD5 and SHA-1).

PyNX: high-performance computing toolkit for coherent X-ray imaging based on operators

The open-source PyNX toolkit has been extended to provide tools for coherent X-ray imaging data analysis and simulation. All calculations can be executed on graphical processing units (GPUs) to achieve high-performance computing speeds. The toolkit can be used for coherent diffraction imaging (CDI), ptychography and wavefront propagation, in the far- or near-field regime. Moreover, all imaging operations (propagation, projections, algorithm cycles…) can be implemented in Python as simple mathematical operators, an approach which can be used to easily combine basic algorithms in a tailored chain. Calculations can also be distributed to multiple GPUs, e.g. for large ptychography data sets. Command-line scripts are available for on-line CDI and ptychography analysis, either from raw beamline data sets or using the coherent X-ray imaging data format.

Eikonal Tomography Using Coherent Surface Waves Extracted From Ambient Noise by Iterative Matched Filtering—Application to the Large‐N Maupasacq Array

AbstractStandard ambient noise tomography relies on cross‐correlation of noise records between pairs of sensors to estimate empirical Green's functions. This approach is challenging if the distribution of noise sources is heterogeneous and can get computationally intensive for large‐N seismic arrays. Here, we propose an iterative matched filtering method to isolate and extract coherent wave fronts that travel across a dense array of seismic sensors. The method can separate interfering wave trains coming from different directions, to provide amplitude and travel time fields for each detected wave front. We use the eikonal equation to derive phase velocity maps from the gradient of these travel time fields. Artifacts originating from scattered waves are removed by azimuthal averaging and spatial smoothing. The method is validated on a synthetic test and then applied to the data of the Maupasacq experiment. Rayleigh wave phase velocity maps are obtained for periods between 2 and 9 s. These maps correlate with surface geology at short period (T<3 s) and reveal the deep architecture of the Arzacq and Mauleon basins at longer periods (T>4 s).

Optically Inspired Nanomagnonics with Nonreciprocal Spin Waves in Synthetic Antiferromagnets.

Integrated optically inspired wave-based processing is envisioned to outperform digital architectures in specific tasks, such as image processing and speech recognition. In this view, spin waves represent a promising route due to their nanoscale wavelength in the gigahertz frequency range and rich phenomenology. Here, a versatile, optically inspired platform using spin waves is realized, demonstrating the wavefront engineering, focusing, and robust interference of spin waves with nanoscale wavelength. In particular, magnonic nanoantennas based on tailored spin textures are used for launching spatially shaped coherent wavefronts, diffraction-limited spin-wave beams, and generating robust multi-beam interference patterns, which spatially extend for several times the spin-wave wavelength. Furthermore, it is shown that intriguing features, such as resilience to back reflection, naturally arise from the spin-wave nonreciprocity in synthetic antiferromagnets, preserving the high quality of the interference patterns from spurious counterpropagating modes. This work represents a fundamental step toward the realization of nanoscale optically inspired devices based on spin waves.

Mode-locked rotating detonation waves: Experiments and a model equation.

Direct observation of a rotating detonation engine combustion chamber has enabled the extraction of the kinematics of its detonation waves. These records exhibit a rich set of instabilities and bifurcations arising from the interaction of coherent wave fronts and global gain dynamics. We develop a model of the observed dynamics by recasting the Majda detonation analog as an autowave process. The solution fronts become attractors of the engine, i.e., mode-locked rotating detonation waves. We find that denotative energy release competes with dissipation and gain recovery to produce the observed dynamics and a bifurcation structure common to other driven-dissipative systems, such as mode-locked lasers.

Interferometry-free noncontact photoacoustic detection method based on speckle correlation change.

Optical speckle patterns occur when a coherent optical wavefront is randomized but such stochastic yet deterministic information about the medium can be decoded. A simple setup is inspired to monitor the decorrelation of speckle patterns within the memory effect range when the medium is photoacoustically perturbated. Experimentally, a linear relationship is confirmed between the speckle correlation change and the peak-to-peak amplitude of the ultrasonic transducer-detected photoacoustic waves, and the detection sensitivity is comparable. Such a plain specklegram-based method may find special interests when no direct contact is allowed between the sample and the photoacoustic detector.

Inverse Scattering via Transmission Matrices: Broadband Illumination and Fast Phase Retrieval Algorithms

When a narrowband coherent wavefront passes through or reflects off of a scattering medium, the input and output relationship of the incident field is linear and so can be described by a transmission matrix (TM). If the TM for a given scattering medium is known, one can computationally “invert” the scattering process and image through the medium. In this paper, we investigate the effect of broadband illumination, i.e., what happens when the wavefront is only partially coherent? Can one still measure a TM and “invert” the scattering? To accomplish this task, we measure TMs using the double-phase retrieval technique, a method that uses phase retrieval algorithms to avoid difficult-to-capture interferometric measurements. Generally, using the double-phase retrieval method requires performing massive amounts of computation. We alleviate this burden by developing a fast, GPU-accelerated algorithm, prVAMP, which lets us reconstruct 2562 × 642 TMs in under five hours. After reconstructing several TMs using this method, we find that, as expected, reducing the coherence of the illumination significantly restricts our ability to invert the scattering process. Moreover, we find that past a certain bandwidth, an incoherent, intensity-based scattering model better describes the scattering process and is easier to invert.

Shaping coherent x-rays with binary optics.

Diffractive lenses fabricated by lithographic methods are one of the most popular image forming optics in the x-ray regime. Most commonly, binary diffractive optics, such as Fresnel zone plates, are used due to their ability to focus at high resolution and to manipulate the x-ray wavefront. We report here a binary zone plate design strategy to form arbitrary illuminations for coherent multiplexing, structured illumination, and wavefront shaping experiments. Given a desired illumination, we adjust the duty cycle, harmonic order, and zone placement to vary both the amplitude and phase of the wavefront at the lens. This enables the binary lithographic pattern to generate arbitrary structured illumination optimized for a variety of applications such as holography, interferometry, ptychography, imaging, and others.