No full-text available
To read the full-text of this research,
you can request a copy directly from the authors.
A practical algorithm for the determination of phase from image and diffraction plane pictures
Abstract
An algorithm is presented for the rapid solution of the phase of the complete wave function whose intensity in the diffraction and imaging planes of an imaging system are known. A proof is given showing that a defined error between the Thimated function and thecorrect function must decrease as the algorithm iterates. The problem of uniqueness is discussed and results are presented demonstrating the power of the method.
... The reconstruction process utilized error reduction (ER) and hybrid input-output (HIO) algorithms over a total of 620 iterations 69,70 . The phase-retrieval algorithm initiated with 20 ER iterations, followed by 180 iterations of the HIO algorithm with guided analysis. ...
... In the phase-retrieval algorithm, the obtained phase φ(r) provides the lattice displacement projected along scattering vector q throughout the entire crystal volume, by the following equation φ(r) = q·u(r), where u(r) represents the lattice displacement field. We calculated the corresponding strain field ε 111 using the definition ∂u 111 /∂r 111 , where r 111 represents the spatial coordinate in the direction of q 111 69,70 . ...
Photocatalysis is a promising technique due to its capacity to efficiently harvest solar energy and its potential to address the global energy crisis. However, the structure–activity relationships of photocatalyst during wavelength-dependent photocatalytic reactions remains largely unexplored because it is difficult to measure under operating conditions. Here we show the photocatalytic strain evolution of a single Au nanoparticle (AuNP) supported on a TiO2 film by combining three-dimensional (3D) Bragg coherent X-ray diffraction imaging with an external light source. The wavelength-dependent generation of reactive oxygen species (ROS) has significant effects on the structural deformation of the AuNP, leading to its strain evolution. Density functional theory (DFT) calculations are employed to rationalize the induced strain caused by the adsorption of ROS on the AuNP surface. These observations provide insights of how the photocatalytic activity impacts on the structural deformation of AuNP, contributing to the general understanding of the atomic-level catalytic adsorption process.
... Early FPWFS methods relied on iterative projection-based algorithms that find the aberrations most compatible with known constraints in the pupil and focal plane [2][3][4]. Conventional "phase retrieval" algorithms suffer from a sign ambiguity in the estimation, corresponding to a non-unique response in the focal plane for some aberrations when using a single image. To address this limitation, a method known as Phase Diversity was developed [1,5] which introduces an additional image with a known phase variation alongside the scientific data. ...
... Indeed, because the phase appears in a complex exponential in Eq. (1), a variation of 2 at a given point in the pupil plane phase has no effect on the focal plane images. Therefore, the agent's observations only contain information on the wrapped phase [2 ]. The nominal value of the RMS wavefront deviation (125 nm, i.e. /4) considered in this study results in an average peak-to-valley amplitude of the entrance phase maps exceeding 2 . ...
Optical aberrations prevent telescopes from reaching their theoretical diffraction limit. Once estimated, these aberrations can be compensated for using deformable mirrors in a closed loop. Focal plane wavefront sensing enables the estimation of the aberrations on the complete optical path, directly from the images taken by the scientific sensor. However, current focal plane wavefront sensing methods rely on physical models whose inaccuracies may limit the overall performance of the correction. The aim of this study is to develop a data-driven method using model-free reinforcement learning to automatically perform the estimation and correction of the aberrations, using only phase diversity images acquired around the focal plane as inputs. We formulate the correction problem within the framework of reinforcement learning and train an agent on simulated data. We show that the method is able to reliably learn an efficient control strategy for various realistic conditions. Our method also demonstrates robustness to a wide range of noise levels.
... given measurements of the intensity I. Since typically the phase is harder to measure than the intensity but the phase describes the specimen more appropriately, the phase retrieval problem has several applications in the fields of microscopy [19], holography and crystallography (see for instance [9]). There exist experimental setups, such as interferometers [8,4,9] and computational algorithms for phase retrieval, examples for the latter being the Gerchberg-Saxton algorithm [10] and the Hybrid Input-Out method proposed by Fienup [7]. ...
... Acknowledgements. This research was funded in whole, or in part, by the Austrian Science Fund (FWF) 10.55776/P34981 -New Inverse Problems of Super-Resolved Microscopy (NIPSUM) and SFB 10.55776/F68 "Tomography Across the Scales", project F6807-N36 (Tomography with Uncertainties). ...
We investigate the transport of intensity equation (TIE) and the transport of phase equation (TPE) for solving the phase retrieval problem. Both the TIE and the TPE are derived from the paraxial Helmholtz equation and relate phase information to the intensity. The TIE is usually favored since the TPE is nonlinear. The main contribution of this paper is that we discuss situations in which it is possible to use the two equations in a hybrid manner: We show that 2-dimensional phase information retrieved by the TIE can be used as initial data for the TPE, enabling the acquisition of 3-dimensional phase information. The latter is solved using the method of characteristic and viscosity methods. Both the TIE and the viscosity method are numerically implemented with finite element methods.
... These errors impair post-process analysis of phase and amplitude maps, especially for complicated biological specimens (leading to, e.g., erroneous cell count). Across the variety of hardware and software solutions [10][11][12][13][14][15][16][17][18][19] implemented to minimize the twin-image effects, in this study, we investigate single-shot AS method, that is easy to perform in any setup, and robust iterative multi-height Gerchberg-Saxton (GS) 14 twin-imagecorrection approach employing data multiplexing. 17,18 The multi-height GS method requires capturing multiple hologram frames with different z distances (in our case, achieved by moving the camera along the optical axis). ...
... These errors impair post-process analysis of phase and amplitude maps, especially for complicated biological specimens (leading to, e.g., erroneous cell count). Across the variety of hardware and software solutions [10][11][12][13][14][15][16][17][18][19] implemented to minimize the twin-image effects, in this study, we investigate single-shot AS method, that is easy to perform in any setup, and robust iterative multi-height Gerchberg-Saxton (GS) 14 twin-imagecorrection approach employing data multiplexing. 17,18 The multi-height GS method requires capturing multiple hologram frames with different z distances (in our case, achieved by moving the camera along the optical axis). ...
Large field-of-view (FOV) microscopic imaging with high lateral resolution (1-2 microns for high space-bandwidth product) plays a pivotal role in biomedicine and biophotonics, especially within the label-free regime, e.g., for whole slide tissue quantitative analysis and live cell culture imaging. In this context, lensless digital holographic microscopy (LDHM) holds substantial promise. However, one intriguing challenge has been the fidelity of computational quantitative phase imaging (QPI) with LDHM in large FOV. While photonic phantoms, 3D printed by two-photon polymerization (TPP), have facilitated calibration and verification in small FOV lens-based QPI systems, an equivalent evaluation for lensless techniques remains elusive, compounded by issues such as twin-image and beam distortions, particularly towards the detector edges. To tackle this problem, we propose an application of TPP over large area to examine phase consistency in LDHM. In our research, we crafted widefield calibration phase test targets, fabricated them with galvo and piezo scanning, and scrutinized them under single-shot twin-image corrupted conditions and multi-frame iterative twin-image minimization scenarios. By displacing the structures toward the edges of the sensing area, we verified LDHM phase imaging errors across the entire field-of-view, showing less than 12 percent of phase value difference between investigated areas. Interestingly, our research revealed that the TPP technique, following LDHM and Linnik interferometry cross-verification, requires novel design considerations for successful large-area precise photonic manufacturing. Our work thus unveils important avenues toward the quantitative benchmarking of large FOV lensless phase imaging, advancing our mechanistic understanding of LDHM techniques and contributing to their further development and optimization of both phase imaging and fabrication.
... The optical component of this network is implemented using inverse-designed meta-optics. We used the Gerchberg-Saxton (GS) phase retrieval method [6] to design phase masks that correspond to the optimized convolutional kernels. Specifically, each sub-optic is designed to have a PSF which resembles the convolutional kernel. ...
... Furthermore, the Gerchberg-Saxon (GS) algorithm [6] used to design the optics is a well-established technique. The GS algorithm is an iterative phase retrieval algorithm to determine the phase (in the optic plane) that produces an intensity pattern in another desired plane (the focal plane). ...
Optical and hybrid convolutional neural networks (CNNs) recently have become of increasing interest to achieve low-latency, low-power image classification and computer vision tasks. However, implementing optical nonlinearity is challenging, and omitting the nonlinear layers in a standard CNN comes at a significant reduction in accuracy. In this work, we use knowledge distillation to compress modified AlexNet to a single linear convolutional layer and an electronic backend (two fully connected layers). We obtain comparable performance to a purely electronic CNN with five convolutional layers and three fully connected layers. We implement the convolution optically via engineering the point spread function of an inverse-designed meta-optic. Using this hybrid approach, we estimate a reduction in multiply-accumulate operations from 688M in a conventional electronic modified AlexNet to only 86K in the hybrid compressed network enabled by the optical frontend. This constitutes a four orders of magnitude reduction in latency and power consumption. Furthermore, we experimentally demonstrate that the classification accuracy of the system exceeds 93\% on the MNIST dataset.
... To develop our theory, we begin with a brief overview of previous methods for holographic phase retrieval. In the Gerchberg-Saxton (GS) method [7], a phase-only hologram is obtained through iterative projections between the image and hologram constraints. Variants of the GS method have been proposed by many researchers, e.g., Fienup [8] and Netrapalli et al. [9]. ...
... The initial hologram c n [0] was drawn from a zero-mean complex Gaussian distribution with the variance 0.01. We compared our method with three previous methods [7,10,12], which we call the GS method, Kaczmarz method, and WFPF, respectively. These previous methods are known as the de facto standard for holographic phase retrieval, i.e., computation of phase-only holograms. ...
We propose a new gradient method for holography, where a phase-only hologram is parameterized by not only the phase but also amplitude. The key idea of our approach is the formulation of a phase-only hologram using an auxiliary amplitude. We optimize the parameters using the so-called Wirtinger flow algorithm in the Cartesian domain, which is a gradient method defined on the basis of the Wirtinger calculus. At the early stage of optimization, each element of the hologram exists inside a complex circle, and it can take a large gradient while diverging from the origin. This characteristic contributes to accelerating the gradient descent. Meanwhile, at the final stage of optimization, each element evolves along a complex circle, similar to previous state-of-the-art gradient methods. The experimental results demonstrate that our method outperforms previous methods, primarily due to the optimization of the amplitude.
... Specifically, SLM1 must be used in conjunction with a phase retrieval algorithm to accurately produce the desired amplitude distribution of the optical field. The Gerchberg-Saxton (GS) algorithm stands as a widely utilized method for phase retrieval [26]. Through iterative optimization employing the GS algorithm, the phase distribution function, often referred to as the hologram, can be determined at SLM1. ...
Due to its complex spatial distribution, the higher-order Hermite–Gaussian mode possesses significant application in fields such as precision measurement and optical communication. The spatial light modulator, with its capability to modulate the complex amplitude distribution of the incident light field, finds extensive applications in optical information processing and adaptive optics, thus making it an indispensable tool in these fields. Using cascaded spatial light modulators can efficiently and superbly generate a higher-order Hermite–Gaussian mode; however, the experimental system is challenging, and there are many influencing factors, such as the misalignment between the optical field on the plane of the second spatial light modulator and the hologram loaded onto it, as well as the spot size of the optical field on the plane of the second spatial light modulator. In this paper, we analyzed the influence of the above factors on the quality of generating a higher-order Hermite–Gaussian mode, providing a reference for the efficient and high-quality generation of the higher-order Hermite–Gaussian mode.
... This characteristic makes the codeword design problem similar to the phase retrieval problem in the field of digital holography imaging. Gerchberg-Saxton (GS) algorithm is widely used to solve phase retrieval problem [25], [26]. By iteratively imposing the two amplitude measurements in the object plane and diffraction pattern plane, the phase information of the image can be recovered. ...
Reconfigurable intelligent surface (RIS) is considered as one of the key technologies for future 6G communications. To fully unleash the performance of RIS, accurate channel state information (CSI) is crucial. Beam training is widely utilized to acquire the CSI. However, before aligning the beam correctly to establish stable connections, the signal-to-noise ratio (SNR) at UE is inevitably low, which reduces the beam training accuracy. To deal with this problem, we exploit the coded beam training framework for RIS systems, which leverages the error correction capability of channel coding to improve the beam training accuracy under low SNR. Specifically, we first extend the coded beam training framework to RIS systems by decoupling the base station-RIS channel and the RIS-user channel. For this framework, codewords that accurately steer to multiple angles is essential for fully unleashing the error correction capability. In order to realize effective codeword design in RIS systems, we then propose a new codeword design criterion, based on which we propose a relaxed Gerchberg-Saxton (GS) based codeword design scheme by considering the constant modulus constraints of RIS elements. In addition, considering the two dimensional structure of RIS, we further propose a dimension reduced encoder design scheme, which can not only guarentee a better beam shape, but also enable a stronger error correction capability. Simulation results reveal that the proposed scheme can realize effective and accurate beam training in low SNR scenarios.
... In our experiments, 10100 positions were recorded in an area of 10 × 10 µm 2 (step of 100 nm; probe size of (200 × 500) H × V nm 2 , overlap > 50%, including random variations in the probe positions to a perfect square grid) [27] . The scan was performed at the energy of 10 keV in fly-scan mode with a constant velocity of 10 µm/s, giving a total acquisition time of 172 s. ...
Metal halide perovskites (MHP) suffer from photo-structural-chemical instabilities whose intricacy requires state-of-the-art tools to investigate their properties under various conditions. This study addresses the damage caused by focused X-ray beams on MHP through a correlative multi-technique approach. The damage after high-dose irradiation is noticeable in many ways: the loss of iodine and organic components, whose relative amount is reduced; the formation of an excavated area modifying the sample morphology; and an altered optical reflectivity indicating an optically inactive layer. The damage mechanism combines radiolysis and sputtering processes. Interestingly, the bulk underneath the excavated area maintains the initial halide proportion demonstrated by a stable photoluminescence emission energy. We also show that controlling the beam dose and environment is an excellent strategy to mitigate the dose harm. Hence, we combined a controlled X-ray dose with an inert N2 atmosphere to certify the conditions to probe MHP properties while mitigating damage efficiently. Finally, we applied optimized conditions in an X-ray ptychography experiment, reaching a 15-nm spatial resolution, an outcome that has never been attained in this class of materials.
... The holograms displayed on SLM3 were designed to generate multiple 12 μm holographic spots targeted to chosen neurons throughout the field of excitation following the calibration procedure outlined in the Supplementary Information. All holograms were calculated using an iterative Gerchberg-Saxton algorithm 99 . The zeroth diffraction order was removed using a physical beam block positioned in a conjugate image plane. ...
Two-photon voltage imaging has long been heralded as a transformative approach capable of answering many long-standing questions in modern neuroscience. However, exploiting its full potential requires the development of novel imaging approaches well suited to the photophysical properties of genetically encoded voltage indicators. We demonstrate that parallel excitation approaches developed for scanless two-photon photostimulation enable high-SNR two-photon voltage imaging. We use whole-cell patch-clamp electrophysiology to perform a thorough characterization of scanless two-photon voltage imaging using three parallel illumination approaches and lasers with different repetition rates and wavelengths. We demonstrate voltage recordings of high-frequency spike trains and sub-threshold depolarizations from neurons expressing the soma-targeted genetically encoded voltage indicator JEDI-2P-Kv. Using a low repetition-rate laser, we perform multi-cell recordings from up to fifteen targets simultaneously. We co-express JEDI-2P-Kv and the channelrhodopsin ChroME-ST and capitalize on their overlapping two-photon absorption spectra to simultaneously evoke and image action potentials using a single laser source. We also demonstrate in vivo scanless two-photon imaging of multiple cells simultaneously up to 250 µm deep in the barrel cortex of head-fixed, anaesthetised mice.
... Phase retrieval is the problem of inferring these aberrations from data, 13 which is in general ill-posed: 14 because of the Hermitian symmetry of the Fourier transform, and because we measure intensity and not electric field in optical astronomy, there is a large space of aberrations that would generate the same intensity PSF. Fortunately, this space can be restricted to physically-realistic solutions and readily solved by algorithms such as the Gerchberg-Saxton algorithm, 15 using ideas from compressed sensing, 16 or by machine learning. [17][18][19] Phase retrieval was memorably performed to infer and correct the serious aberration on the Hubble Space Telescope mirror at launch. ...
The sensitivity limits of space telescopes are imposed by uncalibrated errors in the point spread function, photon-noise, background light, and detector sensitivity. These are typically calibrated with specialized wavefront sensor hardware and with flat fields obtained on the ground or with calibration sources, but these leave vulnerabilities to residual time-varying or non-common path aberrations and variations in the detector conditions. It is therefore desirable to infer these from science data alone, facing the prohibitively high dimensional problems of phase retrieval and pixel-level calibration. We introduce a new Python package for physical optics simulation, dLux, which uses the machine learning framework JAX to achieve GPU acceleration and automatic differentiation (autodiff), and apply this to simulating astronomical imaging. In this first of a series of papers, we show that gradient descent enabled by autodiff can be used to simultaneously perform phase retrieval and calibration of detector sensitivity, scaling efficiently to inferring millions of parameters. This new framework enables high dimensional optimization and inference in data analysis and hardware design in astronomy and beyond, which we explore in subsequent papers in this series.
... To demonstrate the accuracy of the TM calibrated by the Measurement Stage, this TM is used for imaging by a GS phase retrieval algorithm [37]. For the hidden target reconstruction process after measuring TM, the number of input channels is the total pixel number of the calibration signal N, and the number of output channels is the total pixel number of the captured speckle pattern M. With a fixed number of speckles per pixel in the output, the larger M is relative to N, the more it helps to obtain accurate reconstruction results in the hidden target reconstruction. ...
Deep learning (DL) has a wide application in imaging through scattering media, however, most DL approaches lack related physical principle priors. Aiming at the limitation of DL methods that require high completeness of training set, a two-stage network is proposed to complete the transmission matrix (TM) measurement and image reconstruction. Thanks to the appropriate structure of the network, the amount of data required in the Measurement Stage is greatly reduced. The self-closed-loop constraint in the Imaging Stage also enables the imaging network to break from the dependence on the completeness of the training set, and achieve a reconstruction with an SSIM of 0.84 using only 10 pairs of training data. Besides, both the Imaging Stage and the Measurement Stage can be used as a stand-alone method in combination with conventional phase retrieval algorithms. This method can drive the development of TM-based imaging and provide an enlightening reference for the practical application in optical imaging scenes.
... Other similar classical non-interferometric phase imaging techniques that involve imaging both the NF and FF includes Ptychography [43] and the Gerchberg-Saxton (GS) algorithm [44]. However, Ptychography requires scanning of the NF and the GS algorithm is not always convergent, our quantum technique does not have either of these two short comings. ...
In this work, we introduce a quantum-based quantitative phase microscopy technique using a phase gradient approach that is inherently background resistant and does not rely on interferometry or scanning. Here, a transparent sample is illuminated by both photons of a position-momentum entangled pair with one photon setup for position measurement in the near-field (NF) of the sample and its partner for momentum measurement in the far-field (FF). By virtue of the spatial correlation property inherent to the entanglement, both the position and momentum information of the photons can thus be obtained simultaneously. The phase profile of the sample is then deduced through a phase gradient measurement obtained by measuring the centroid shift of the photons' in the FF momentum plane for each NF position. We show that the technique, while achieving an imaging resolution of 2.76\,$\mu$m, is phase accurate to at least $\lambda/30$ and phase sensitive to $\lambda/100$ at a wavelength of 810\,nm. In addition, through the temporal correlation between the photon pairs, our technique shows resilience to strong dynamic background lights, which can prove difficult to account for in classical phase imaging techniques. We believe this work marks a significant advancement in the capabilities of quantum phase microscopy and quantum imaging in general, it showcases imaging and phase resolutions approaching those attainable with classical phase microscopes. This advancement brings quantum imaging closer to practical real-world applications, heralding new possibilities in the field.
... The Gerchberg-Saxton (GS) algorithm, developed by R. W. Gerchberg and W. O. Saxton in 1972, is a method used to determine the phase of light from images in the image-plane and focal-plane [7]. The algorithm utilizes the property that a lens performs a Fourier Transform to a light field. ...
... Common CGH algorithms such as the GS algorithm [34] are alternate projection algorithms, which update the distribution of holograms by iterating between the object plane and the hologram plane. With the development of deep learning technology, the deep learning network can establish a physical mapping relationship between the target image and hologram. ...
Three-dimensional (3D) display can provide more information than two-dimensional display, and real-time 3D reconstruction of the real-world environment has broad application prospects as a key technology in the field of meta-universe and Internet of Things. 3D holographic display is considered to be an ideal 3D display scheme, thus enhancing the computational speed and reconstruction quality of 3D holograms can offer substantial support for real-time 3D reconstruction. Here, we proposed a real-time 3D holographic photography for real-world scenarios driven by both physical model and artificial intelligence. The 3D information of the real scene was acquired by a depth camera and then divided into 30 layers using the layer-based method. Convolutional neural networks (CNN) were used to build the mapping of intensity and depth maps to computer-generated holograms (CGH). The differentiability of the angular spectrum algorithm was used to realize the self-supervised training of the network, while the composite loss function was employed to optimize network parameters by calculating the loss between reconstructed and target images. The trained network can generate a CGH with a resolution of 1024×1024 in 14.5 ms. The proposed system operates at 22 frames per second and successfully reconstructs 3D video of dynamic scene. The system exhibits significant potential for application in intelligent manufacturing, remote office work, distance education and other fields.
... Throughout the history of diffractive optical design, a large number of iterative methods have been presented. After the introduction of the Gerchberg-Saxton algorithm for phase retrieval 19 , many related methods followed. At their root, numerical methods are optimization algorithms that also lead to other approaches such as simulated annealing 20 or genetic algorithms 21 . ...
This paper investigates the feasibility of applying the hologram segmentation method for homogeneous illumination. Research focuses on improving the uniformity of the illumination obtained from diffractive optical elements in the THz range. The structures are designed with a modified Ping-Pong algorithm and a neural network-based solution. This method allows for the improvement of uniform illumination distribution with the desired shape. Additionally, the phase modulations of the structures are divided into segments, each responsible for imaging at different distances. Various segment combination methods are investigated, differing in shapes, image plane distances, and illumination types. The obtained image intensity maps allow for the identification of the performance of each combination method. Each of the presented structures shows significant improvements in the uniformity of imaged targets compared to the reference Ping-Pong structure. The presented structures were designed for a narrow band case—260 GHz frequency, which corresponds to 1.15 mm wavelength. The application of diffractive structures for homogenization of illumination shows promise. The created structures perform designed beamforming task with variability of intensity improved up to 23% (standard deviation) or 45% (interquartile range) compared with reference structure.
... A number of algorithms can be used to generate high-quality CGHs, for example, Lenses and Gratings (L&G) [17,18], Gerchberg-Saxton (GS) [19], Weighted GS (WGS) [20], Multiplexed Phase Fresnel Lenses (MPFL) [21], and Mixed-Region Amplitude Freedom (MRAF) [22]. The L&G algorithm is a non-iterative method which can produce single or multiple beams by combing the phase of lenses and gratings, resulting in axial and lateral shifts [17,18]. ...
In this paper, a method for generating multiple rotationally-symmetric power-exponent-phase vortex beams (RSPEPVBs) on a spatial arbitrary distribution was demonstrated. The properties of a single RSPEPVB were studied experimentally and theoretically with good agreement. Then, the flexibilities of user-defined spatial arbitrary distribution of multiple RSPEPVBs were illustrated by applying an appropriated computer-generated hologram (CGH) on a spatial light modulator (SLM). This CGH was generated by superposing the interference pattern of a single RSPEPVB, which derived from a phase mask of Laguerre-Gaussian (LG) beam and PEPVB, and the phase shift calculated by the lenses and gratings (L&G) algorithm. As a result, the user-defined beam number, radial exponent (p), topological charge (TC), and power exponent (n) of the RSPEPVBs can be controlled. Compared with the results of a single RSPEPVB, the properties of individual spatial arbitrary distribution RSPEPVBs were still kept the same as the CGH generated by the L&G algorithm would only bring a phase shift and would not involve additional phase transformations. The propagation properties of the multiple RSPEPVBs were also studied. These results will extend the applications of RSPEPVBs in optical trapping and may provide a new method to generate complex patterns like chiral structures.
... The deterministic phase mask eases the transmission with bandwidth and key distribution. The Gerchberg-Saxton algorithm is the most widely used phase retrieval algorithm [21]. In the literature, Liu et al. proposed an asymmetric cryptosystem based on a cascaded amplitude and phase retrieval process termed as Yang-Gu mixture amplitude-phase retrieval algorithm [22] (Yang-Gu algorithm). ...
... where . T denotes the conjugate-transpose of a matrix/vector, A ' classic' PR problem 31,32 can be seen here. Considering the input matrix E T , each element of the complex-valued column of H T is estimated using each column of P T . ...
Transcranial ultrasound stimulation (TUS) has been clinically applied as a neuromodulation tool. Particularly, the phase array ultrasound can be applied in TUS to non-invasively focus on the cortex or deep brain. However, the vital phase distortion of the ultrasound induced by the skull limits its clinical application. In the current study, we aimed to develop a hybrid method that combines the ultrashort echo time (UTE) magnetic resonance imaging (MRI) sequences with the prDeep technique to achieve focusing ventral intermediate thalamic nucleus (VIM). The time-reversal (TR) approach of the UTE numerical acoustic model of the skull combined with the prDeep algorithm was used to reduce the number of iterations. The skull acoustic model simulation therapy process was establish to valid this method’s prediction and focus performance, and the classical TR method were considered as the gold standard (GS). Our approach could restore 75% of the GS intensity in 25 iteration steps, with a superior the noise immunity. Our findings demonstrate that the phase aberration caused by the skull can be estimated using phase retrieval techniques to achieve a fast and accurate transcranial focus. The method has excellent adaptability and anti-noise capacity for satisfying complex and changeable scenarios.
... Coherent diffraction imaging (CDI) [5,6] is a kind of phase retrieval technique using various iterative algorithms. The G-S algorithm [7,8] is the earliest CDI algorithm that records diffraction intensity at two separated planes. The error reduction (ER) algorithm [9] and Fienup's hybrid-input-output (HIO) algorithm [10] , which recorded only one frame of diffraction intensity, have much faster convergence and much better reconstruction quality than the G-S algorithm. ...
... This camera is mounted on a motorized translation stage, allowing to take images along the propagation direction. Images captured a few millimeters before and after the focal plane can be used to obtain the beam quality factor M 2 as well as to retrieve the wavefront, using a modified version of the Gerchberg-Saxton algorithm 47,48 . With the help of numerical beam propagation, the wavefront can be obtained in any plane of interest and aberrations can be corrected by displaying the inverse of the retrieved wavefront in the plane of the SLM. ...
We present a novel, interferometric, two-color, high-order harmonic generation setup, based on a turn-key Ytterbium-doped femtosecond laser source and its second harmonic. Each interferometer arm contains a spatial light modulator, with individual capabilities to manipulate the spatial beam profiles and to stabilize the relative delay between the fundamental and the second harmonic. Additionally, separate control of the relative power and focusing geometries of the two color beams is implemented to conveniently perform automatized scans of multiple parameters. A live diagnostics system gives continuous information during ongoing measurements.
... Therefore, it is crucial to investigate how to obtain flat-top beam from Gaussian beam. A great number of beam-shaping methods have been proposed to achieve flat-top laser beam like diffractive optical element (DOE) [6][7][8][9] , spatial light modulator (SLM) [10][11][12] , spatially variable wave plate (SVWP) [13][14][15] , birefringent lenses [16] , double free-form mirrors [17][18] (somewhat analogous to double aspheric lenses [19][20] ) and microlens array, et al. The shaping methods of DOE and SLM are characterized by energy efficiency up to 80% [9,12] , but cannot obtain collimated flat-top beam after reshaping. ...
Flat-top beam, known for its ability to generate a consistently even irradiation area, holds vast utility in many fields of scientific and industrial applications. In this paper, a reflective laser beam shaping method based on two axisymmetric aspheric mirrors (AAMs), a polarizing beam splitter (PBS) and two quarter wave plates (QWPs) is proposed to transform Gaussian beam into flat-top beam. Compared to alternative beam shaping methods, the method using AAMs demonstrates distinct advantages on notably high energy efficiency and unique capability to generate parallel beams. Thanks to its relative simplicities of design, manufacture and tunability, AAMs-shaping further enhances its appeal in applied research scenarios.
... We employ the Gerchberg-Saxton algorithm to calculate the phase masks required for generating the target light field. Essentially, the algorithm performs an iterative Fourier transform algorithm, given a known incident light beam and the desired array [33,34]. After each iteration, the holographic phase is merged with the incident light amplitude information and subsequently compared with the target pattern. ...
Metasurfaces made of subwavelength silicon nanopillars provide unparalleled capacity to manipulate light, and have emerged as one of the leading platforms for developing integrated photonic devices. In this study, we report on a compact, passive approach based on planar metasurface optics to generate large optical trap arrays. The unique configuration is achieved with a meta-hologram to convert a single incident laser beam into an array of individual beams, followed up with a metalens to form multiple laser foci for single rubidium atom trapping. We experimentally demonstrate two-dimensional arrays of 5 × 5 and 25 × 25 at the wavelength of 830 nm, validating the capability and scalability of our metasurface design. Beam waists ∼1.5 µm, spacings (about 15 µm), and low trap depth variations (8%) of relevance to quantum control for an atomic array are achieved in a robust and efficient fashion. The presented work highlights a compact, stable, and scalable trap array platform well-suitable for Rydberg-state mediated quantum gate operations, which will further facilitate advances in neutral atom quantum computing.
... Phase retrieval, the process of recovering the transverse phase profile of an optical wave from its intensity profile, is an area in which the Gerchberg-Saxton (GS) algorithm is employed as a computational method [45]. Since it was introduced in 1972 by R. W. ...
Scientists are investigating ways of packing more data into several modes of a few-
mode fiber, as single-mode fiber (SMF) is the predominant type used in conventional telecommunication. Unfortunately, this approach is limited by the cross-talk between those modes. OAM presents a feasible substitute for addressing the cross-talk problem.
Such OAM modes are characterized by an azimuthally varying phase with an intensity null at the center corresponding to a phase singularity. Light beams with OAM are also useful in high-resolution microscopy, quantum information systems, and sensing. Several techniques have been explored in the literature for generating these OAM modes, of which spatial light modulators (SLM) are the most common. However, achieving high-purity OAM modes is challenging due to aberrations in the optical system and non-ideal SLM performance. In our work, we demonstrate an idea to quantify the aberration and also determine the optimal configuration for compensating at the same to generate high-purity OAM.
Transverse phase aberrations in the optical system, consisting of lenses, mirrors, and spatial light modulators (SLMs), are degrading the purity of structured light beams. Previous work has investigated several phase compensation strategies, the most well known of which is the Gerchberg–Saxton (GS) phase retrieval algorithm. We have proposed a post-compensation technique based on an aperture-optimized modified GS algorithm. We have compared inline, pre-, and post-phase compensation performance across a wide range of topological charges. The optimal configuration, according to our findings, is the post-compensation setup. With this phase compensation, we can reduce the nearest neighbor cross-talk by 9.37 dB and increase the modal purity of the generated modes by 35%. We discuss free-space to ACF coupling. We have simulated the HE modes for the air-core fiber (ACF) to estimate the MFD, which is necessary to compute the overlap integral and select the ideal focal length. We experimentally achieved a maximum OAM mode coupling efficiency of 27% from free space to ACF.
... Regarding the PR algorithms, one of the most popular approaches is based on the alternating projection method, which was introduced by Gerchberg and Saxton [18], [19] and subsequently extended by Fineup [20]. Nevertheless, this alternative heavily depends on the initial guess and lacks convergence guarantees. ...
Phase retrieval (PR) consists of recovering the phase information from captured intensity measurements, known as coded diffraction patterns (CDPs). Non-convex algorithms for addressing the PR problem require a proper initialization that is refined through a gradient descent approach. These PR algorithms have proven to be robust for different scenarios. Despite deep models showing surprising results in this area, these approaches lack interpretability in their neural architectures. This work proposes unrolling the initialization and iterative reconstruction algorithm for the PR problem using the near-field model based on a non-convex formulation; resulting in an interpretable deep neural network (DNN) that can be trained in an end-to-end (E2E) manner. Furthermore, the proposed method can jointly optimize the phase mask for the CDP acquisition and the DNN parameters. Simulation results demonstrate that the proposed E2E method provides high-quality reconstruction using a learned phase mask from a single projection. Also, the proposed method is tested over an experimental optical setup that incorporates the learned phase mask via an only-phase spatial light modulator.
... The measurement of the complex amplitude (amplitude and phase) of optical fields is widely utilized in various scientific and technological domains [1][2][3][4][5]. Several proposals have emerged to address this crucial task, such as algorithms leveraging the diffraction property of light, known as Gerchberg-Saxton-type algorithms [6][7][8], which were pioneers in this development; models primarily based on the transport-of-intensity equation (TIE) [9,10]; or interferometric methods [11][12][13]. Among the latter, it is noteworthy to highlight the phase-shifting interferometry (PSI) technique [14]. ...
Recently, a novel technique was proposed for recovering the complex amplitude of an optical field from a set of interferograms modulated in both visibility and phase steps for the synchronous case, named amplitude-phase-shifting interferometry (APSI). This requirement leads to errors in the accuracy of phase recovery due to miscalibration or the nonlinear response of the device used to generate the phase steps; in the APSI case, these are polarizers. In this paper, we propose to create a generalized model of the APSI technique where the phase steps can be different from each other. APSI has been successfully implemented in a Mach–Zehnder interferometer, while the present technique has been deployed in a double-aperture common-path interferometer (DACPI). Additionally, it is demonstrated that in a DACPI, the use of experimental elements that may cause aberrations or extra noise in the experimental results is reduced. The aim is to have an even more robust phase and amplitude recovery technique, now named generalized amplitude-phase-shifting interferometry. Experimental results are presented and validated through a numerical noise study.
... Our motivation in adopting these waveforms is the randomness of the kernel, F k , arising due to the stochastic nature of their modulation, and the superposition of the incident fields. While phase retrieval methods were classically studied in the context of optics and Fourier phase retrieval by leveraging prior information and optimization-based methods [55]- [59], the past decade has witnessed a resurgence in the theoretical study of the problem using statistical forward models [30], [51], [60]- [66]. Existing performance guarantees for state-ofthe-art optimization methods in the phase retrieval literature predominantly consider a forward model realized from the i.i.d. ...
Multi-static phaseless synthetic aperture radar (SAR) is a novel imaging modality that offers advantages in reduced hardware complexity, operability at high frequencies, robustness, jamming resistance, and improved accuracy and resolution. Illumination diversity is a key facilitator in designing novel phaseless imaging systems for applications in optics, and with growing interest in radio frequency sensing. In this paper, we present a novel multi-static phaseless SAR imaging method using stochastic waveforms and the non-convex Wirtinger flow (WF) framework that provides performance guarantees under sufficient conditions known to hold for certain random forward models. We present multiple variations of the WF algorithm including different initialization and regularization methods; and study the trade-offs between the performance of our algorithms with respect to the resources needed for phaseless multi-static imaging. Our extensive numerical simulations show that the waveform-diverse random illumination approach coupled with optimization-based reconstruction provide near exact imaging with limited number of transmitters and a single receiver, promoting our method for practical realization of phaseless multi-static SAR.
... Other solutions involve different kinds of cryptosystems that avoid degradation due to speckle noise by using spatially incoherent light sources, though their effectiveness depends on the Fourier spectrum characteristics of the object to be encrypted [15][16][17][18]. On the other hand, phase retrieval algorithms like the Gerchberg-Saxton (GS) algorithm [19] have been utilized to generate optimized random phase masks that increase the quality of the reconstructed object by minimizing the random correlation noise [20]; however, these approaches are limited to a numerical implementation of the encryption setup. ...
We present, to our knowledge, a novel method to achieve experimental encryption using double random phase encoding with full complex modulation and a single phase-only spatial light modulator. Our approach uses double phase encoding to generate phase-only holograms containing complex-valued input planes for a joint transform correlator (JTC) cryptosystem. This approach enables users to independently manipulate both the phase and amplitude of the cryptographic keys and objects, thereby significantly enhancing the versatility of the optical cryptosystem. We validate the capabilities of our proposed scheme by generating optimized random phase masks and using them to experimentally encrypt various grayscale and binary objects. The experimental complex modulation obtained with the system detailed in this work, in conjunction with optimized random phase masks, results in an enhancement in the quality of the decrypted objects during reconstruction. Both numerical simulations and experimental findings corroborate the effectiveness of our proposal.
Widefield microscopy is widely used for non-invasive imaging of biological structures at subcellular resolution. When applied to a complex specimen, its image quality is degraded by sample-induced optical aberration. Adaptive optics can correct wavefront distortion and restore diffraction-limited resolution but require wavefront sensing and corrective devices, increasing system complexity and cost. Here we describe a self-supervised machine learning algorithm, CoCoA, that performs joint wavefront estimation and three-dimensional structural information extraction from a single-input three-dimensional image stack without the need for external training datasets. We implemented CoCoA for widefield imaging of mouse brain tissues and validated its performance with direct-wavefront-sensing-based adaptive optics. Importantly, we systematically explored and quantitatively characterized the limiting factors of CoCoA’s performance. Using CoCoA, we demonstrated in vivo widefield mouse brain imaging using machine learning-based adaptive optics. Incorporating coordinate-based neural representations and a forward physics model, the self-supervised scheme of CoCoA should be applicable to microscopy modalities in general.
Amplitude-modulated single-pixel ptychography (SPP) enables non-interferometric complex-field imaging of objects. However, the conventional iterative and nondeterministic reconstruction methods, based on the ptychography algorithm, pose challenges in fully understanding the role of critical optical parameters. In response, this paper introduces an innovative analytical approach that establishes a theoretical foundation for the uniqueness of SPP reconstruction results. The proposed method conceptualizes SPP as a system of linear equations in the frequency domain, involving both object and modulated illumination. Solving this equation system reveals a determined solution for the complex object, providing an alternative to iterative and nondeterministic techniques. Through a series of simulations, this approach not only validates the uniqueness of SPP reconstruction, but also explores key properties influencing accuracy.
We introduce the weighted average of sequential projections, or WASP, an algorithm for ptychography. Using both simulations and real-world experiments, we test this new approach and compare performance against several alternative algorithms. These tests indicate that WASP effectively combines the benefits of its competitors, with a rapid initial convergence rate, robustness to noise and poor initial conditions, a small memory footprint, easy tuning, and the ability to reach a global minimum when provided with noiseless data. We also show how WASP can be parallelised to split operation across several different computation nodes.
In this paper, liquid-crystal spatial light modulators are presented for precise dynamic manipulation of coherent light fields in space, which are used in diffractive optoelectronic and optical data processing systems. In addition, this paper presents the results of the temporal dynamics study of the HoloEye PLUTO‑2 VIS-016 liquid-crystal spatial light modulator for light field rate modulation analysis. Experiments using binary phase computer-generated holograms and binary focusing phase diffractive optical elements are performed. The time characteristics of the modulator response are determined from the experimental data. Displaying the diffraction structure model on the screen of the spatial light modulator results in a rise time of the diffraction efficiency of 146 ms, and switching to a new model leads to a decay time of 97 ms. The obtained results allow implementing the dynamic generation of an alternating diffraction field at 2 Hz update frequency with −16 dB interference level. Increasing the frequency of updating diffraction structure models increases the level of interframe noise in the generated diffraction field, and when updating with the frequency indicated in the specification, separating the generated distributions is virtually impossible. From the presented results, the studied modulator model can be applied for high-precision formation of complex diffraction fields with a frame update rate lower than stated. Determining the actual frame rate from the rise and decay times of diffraction efficiency allows correctly determining the minimum operating time of an information optical system with a liquid-crystal spatial light modulator.
Red blood cells possess a singular mechanobiology, enabling efficient navigation through capillaries smaller than their own size. Their plasma membrane exhibits non-equilibrium shape fluctuation, often reported as enhanced flickering activity. Such active membrane motion is propelled by motor proteins that mediate interactions between the spectrin skeleton and the lipid bilayer. However, modulating the flickering in living red blood cells without permanently altering their mechanical properties represents a significant challenge. In this study, we developed holographic optical tweezers to generate a force field distributed along the equatorial membrane contour of individual red blood cells. In free-standing red blood cells, we observed heterogeneous flickering activity, attributed to localized membrane kickers. By employing holographic optical forces, these active kickers can be selectively halted under minimal invasion. Our findings shed light on the dynamics of membrane flickering and established a manipulation tool that could open new avenues for investigating mechanotransduction processes in living cells.
In studying the interaction of multiple ultrashort pulses with matter, high requirements are put forward for spatiotemporal synchronization accuracy. Limited by the response time and bandwidth of existing devices, the synchronization of multiple ultrashort pulses still faces significant difficulties. By observing the transient phenomena of the optical Kerr effect, high-precision, three-dimensional (x, y, t) synchronization of ultrashort pulses at different angles was achieved. In the optical Kerr effect, the polarization state of the signal pulse changes only when it coincides with the pump pulse, at which point the signal pulse passes through the analyzer. The changes in the intensity and phase of the signal pulse is positively correlated with the degree of spatiotemporal coincidence. In this study, 10-ps pulses were used in the experiments. By observing the intensity and phase distribution of the signal pulses, a time synchronization accuracy between two pulses of less than 1 ps and spatial synchronization accuracy of ±125 µm and ±3 µm in the x and y directions, respectively, were achieved. Moreover, the synchronization of two pulses at an angle of 90 ° was measured, further proving that the method can achieve the spatiotemporal synchronization of pulses with large angles. Therefore, this method has important application prospects in the study of multi-beam interactions with matter and other ultrafast physical phenomena.
The exploration of multiferroic materials and their interaction with light at the nanoscale presents a captivating frontier in materials science. Bismuth Ferrite (BiFeO 3 , BFO), a standout among these materials, exhibits room-temperature ferroelectric and antiferromagnetic behaviour and magnetoelectric coupling. Of particular interest is the phenomenon of photostriction, the light-induced deformation of crystal structures, which enhances the prospect for device functionality based on these materials. Understanding and harnessing multiferroic phenomena holds significant promise in various technological applications, from optoelectronics to energy storage. The orientation of the ferroelectric axis is an important design parameter for devices formed from multiferroic materials. Determining its orientation in the laboratory frame of reference usually requires knowing multiple wavevector transfer (Q-Vector) directions, which can be challenging to establish due to the need for extensive reciprocal-space searches. Our study demonstrates a method to identify the ferroelectric axis orientation using Bragg Coherent X-ray Diffraction Imaging (BCDI) measurements at a single Q-vector direction. This method involves applying photostriction-inducing laser illumination across various laser polarisations. Our findings reveal that photostriction primarily occurs as a surface phenomenon at the nanoscale. Moreover, a photo-induced crystal length change ranging from 30 to 60 nm was observed, consistent with earlier findings on bulk material.
ResearchGate has not been able to resolve any references for this publication.