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Optical real-time data processing is advancing fields like tensor algebra acceleration, cryptography, and digital holography. This technology offers advantages such as reduced complexity through optical fast Fourier transform and passive dot-product multiplication. In this study, the proposed Reconfigurable Complex Convolution Module (RCCM) is capable of independently modulating both phase and amplitude over two million pixels. This research is relevant for applications in optical computing, hardware acceleration, encryption, and machine learning, where precise signal modulation is crucial. We demonstrate simultaneous amplitude and phase modulation of an optical two-dimensional signal in a thin lens's Fourier plane. Utilizing two spatial light modulators (SLMs) in a Michelson interferometer placed in the focal plane of two Fourier lenses, our system enables full modulation in a 4F system's Fourier domain. This setup addresses challenges like SLMs' non-linear inter-pixel crosstalk and variable modulation efficiency. The integration of these technologies in the RCCM contributes to the advancement of optical computing and related fields. [ABSTRACT FROM AUTHOR]

Fourier Ptychographic Microscopy (FPM) is a microscopy imaging technique based on optical principles. It employs Fourier optics to separate and combine different optical information from a sample. However, noise introduced during the imaging process often results in poor resolution of the reconstructed image. This article has designed an approach based on a residual local mixture network to improve the quality of Fourier ptychographic reconstruction images. By incorporating channel attention and spatial attention into the FPM reconstruction process, the network enhances the efficiency of the network reconstruction and reduces the reconstruction time. Additionally, the introduction of the Gaussian diffusion model further reduces coherent artifacts and improves image reconstruction quality. Comparative experimental results indicate that this network achieves better reconstruction quality, and outperforming existing methods in both subjective observation and objective quantitative evaluation. [ABSTRACT FROM AUTHOR]

The numerical calculation of partially coherent imaging involves a fourfold integral, which is numerically complex and impracticable to be calculated directly. The use of coherent-mode decomposition (CMD) can make this problem more manageable but finding the coherent-modes for complicated partial coherent fields (without already-known coherent-mode expansion) are rather computationally intensive. In this letter, a modified modal expansion method is proposed, which significantly reduces the requirement of computational resources. The propagation of partial coherence in imaging systems with extremely large sampling number could be handled by an ordinary computer. A comparison between the new method and the traditional method in terms of memory resource requirements and computational time consumption is also detailed in this article. We will also show that this method could deal with the anisoplanatic imaging cases while maintaining the same computational efficiency. [ABSTRACT FROM AUTHOR]

This article is an interview with optical scientist and engineer Joseph Braat, who discusses his career and contributions to the field of optics. He talks about his experiences at the Institut d'Optique in Paris and his work on holography using spatially incoherent light. Braat also discusses his role in designing the light path for recording and reading optical discs, including CD, DVD, and Blu-ray technology. The article explores the development of optical data storage and lithography technology, noting the challenges faced and advancements made. It concludes with Braat's reflections on his career and advice for students and researchers in the field of optics and photonics. [Extracted from the article]

Advancements in optical communications have increasingly focused on leveraging spatial-structured beams such as orbital angular momentum (OAM) beams for high-capacity data transmission. Conventional electronic convolutional neural networks exhibit constraints in efficiently demultiplexing OAM signals. Here, we introduce a hybrid optical-electronic convolutional neural network that is capable of completing Fourier optics convolution and realizing intensity-recognition-based demultiplexing of multiplexed OAM beams under variable simulated atmospheric turbulent conditions. The core part of our demultiplexing system includes a 4F optics system employing a Fourier optics convolution layer. This optical spatial-filtering-based convolutional neural network is utilized to realize the training and demultiplexing of the 4-bit OAM-coded signals under simulated atmospheric turbulent conditions. The current system shows a demultiplexing accuracy of 72.84% under strong turbulence scenarios with 3.2 times faster training time than all electronic convolutional neural networks. Optical beams carrying orbital angular momentum (OAM) are promising candidates for free-space optical communication. The authors devise a hybrid optical-electronic convolutional neural network approach reaching a 4-bit OAM-coded signal demultiplexing accuracy of 72.84% under strong atmospheric turbulence conditions with 3.2 times faster training time than all electronic convolutional neural network. [ABSTRACT FROM AUTHOR]

Optical microscopy techniques are among the most used methods in biomedical sample characterization. In their more advanced realization, optical microscopes demonstrate resolution down to the nanometric scale. These methods rely on the use of fluorescent sample labeling in order to break the diffraction limit. However, fluorescent molecules' phototoxicity or photobleaching is not always compatible with the investigated samples. To overcome this limitation, quantitative phase imaging techniques have been proposed. Among these, holographic imaging has demonstrated its ability to image living microscopic samples without staining. However, for a 3D assessment of samples, tomographic acquisitions are needed. Tomographic Diffraction Microscopy (TDM) combines holographic acquisitions with tomographic reconstructions. Relying on a 3D synthetic aperture process, TDM allows for 3D quantitative measurements of the complex refractive index of the investigated sample. Since its initial proposition by Emil Wolf in 1969, the concept of TDM has found a lot of applications and has become one of the hot topics in biomedical imaging. This review focuses on recent achievements in TDM development. Current trends and perspectives of the technique are also discussed. [ABSTRACT FROM AUTHOR]

The direction of particle accelerator development is ever-increasing beam quality, currents and repetition rates. This poses a challenge to traditional diagnostics that directly intercept the beam due to the mutual destruction of both the beam and the diagnostic. An alternative approach is to infer beam parameters non-invasively from the synchrotron radiation emitted in bending magnets. However, inferring the beam distribution from a measured radiation pattern is a complex and computationally expensive task. To address this challenge we present SYRIPY (SYnchrotron Radiation In PYthon), a software package intended as a tool for performing inference of synchrotron-radiationbased diagnostics. SYRIPY has been developed using PyTorch, which makes it both differentiable and able to leverage the high performance of GPUs, two vital characteristics for performing statistical inference. The package consists of three modules: a particle tracker, Lienard-Wiechert solver and Fourier optics propagator, allowing start-to-end simulation of synchrotron radiation detection to be carried out. SYRIPY has been benchmarked against SRW, the prevalent numerical package in the field, showing good agreement and up to a 50x speed improvement. Finally, we have demonstrated how SYRIPY can be used to perform Bayesian inference of beam parameters using stochastic variational inference. [ABSTRACT FROM AUTHOR]

Standard optical characterization and spectroscopy techniques rely on the measurement of specular reflection, transmission, or emission at normal incidence. Although the usefulness of these methods is without question, they do not provide information on the angular dependence of the scattered light and, therefore, miss crucial insights on the physical processes governing light emission and scattering. In this Review, we explain the basics of Fourier imaging and show how it can be used to measure the angular distribution of scattered light in single-shot measurements. We then give a comprehensive panorama on recent research exploiting this technique to analyze nanostructures and detail how it unlocks fundamental understandings on the underlying physics of nanophotonic structures. We finally describe how simple additions to a Fourier imaging setup enable measuring not only the radiation pattern of an object but also the energy, polarization, and phase toward resolving all aspects of light in real time. [ABSTRACT FROM AUTHOR]

The hierarchical structure of the biological visual system enables multilevel features of sensory stimuli to be pre-extracted before being transmitted to the nerve center, rendering the remarkable ability to perceive, filter, categorize, and identify targets in complex environments. However, it is a challenge to resemble such extraction capability with respect to spatial features in a neuromorphic visual system. In this Letter, we propose an indium-gallium-zinc-oxide synaptic transistor-based Fourier neuromorphic visual system for image style classifying. The images are transformed into the frequency domain through an optic Fourier system, greatly reducing energy and time dissipation in comparison with numerical computation. Then, the transformed information is coded into spike trains, which are nonlinearly filtered by synaptic transistors. The energy consumption for this filtering process is estimated to be ∼1.28 nJ/pixel. The features of drawing style could be enhanced through the filtering process, which facilitates the followed pattern recognition. The recognition accuracy in classifying stylized images is significantly improved to 92% through such Fourier transform and filtering process. This work would be of profound implications for advancing neuromorphic visual system with Fourier optics enhanced feature extraction capabilities. [ABSTRACT FROM AUTHOR]

The influence of three factors on the formation of a Bessel light beam (BLB) in the scheme of transforming a Gaussian beam by an axicon were investigated using Fourier optics via numerical simulation. The factors were the ellipticity of the incident light beam, the ellipticity of the axicon, and the presence of a round tip on the axicon. The results of the influence of each factor on the structure and quality parameters kc, kr, and ⟨R2⟩. of the formed BLB and its Fourier spectrum (FSBLB) are shown. The quality parameters of the FSBLB kIs, kws, and krs, which characterized the spread of the amplitude, half-width, and average frequency of the conical component of the FSBLB, and the parameter η, which determined the ratio of the energy in the conical component to the total energy of the beam, were introduced to analyze the quality of the FSBLB. The ellipticity of the Gaussian beam incident on the axicon led to a reduction in the length of the BLB region of existence. However, all quality parameters decreased, with the coefficient of constancy kc dropping most quickly, as the longitudinal coordinate increased. FSBLB quality parameters kIs and kws, which characterized the spread of the intensity and half-width of the conical component of the beam, decreased with increasing eccentricity of the Gaussian beam half-width εb. The ellipticity of the axicon affected all BLB quality parameters, most clearly the coefficient of constancy kc and the average value of R2, which decreased with an increase in the axicon eccentricity εa. This happened because of oscillations in the ring closest to the BLB axis. The shape of the FSBLB also changed with increasing εa, transitioning from circular to elliptical and causing the coefficient of constancy of the conical component spectral frequency to decrease. Regularities in the transverse intensity distributions of BLBs formed by azimuthal modulation of the cone angle were considered for the case where the number N of complete oscillation periods of the cone angle were >2. The number of intensity minima in the paraxial ring for a small axicon base angle modulation amplitude B (≤ 0.05) was equal to N for odd N and equal to 2N for even N. The number of minima in the paraxial ring of the beam was equal to 2N for large B values (>0.05) for both even and odd N. A spherical tip of an otherwise conical axicon led to the formation of a separate non-conical component in the spectrum. A hyperbolic axicon broadened the conical component of the spectrum in the direction of low spatial frequencies. The results could be used to form special light fields and to assess the quality of manufactured axicons and the ellipticity of a beam incident on an axicon. [ABSTRACT FROM AUTHOR]

Current ghost imaging phase reconstruction schemes require either complex optical systems, iterative algorithms, Fourier transform steps, or entangled photon pairs. These factors may increase the difficulty of system design, lead to phase retrieval errors, or result in excessive time consumption. To tackle this challenge, we propose a five-step phase-shifting method that eliminates the need for complex optical systems, Fourier transform steps, entangled photon pairs, or iterative algorithms. Using five specifically designed incoherent sources, we can generate five distinct ghost imaging patterns. Subsequently, the phase information of the object can be calculated from these five speckle patterns. Additionally, we offer a detailed theoretical explanation for choosing the five-step phase-shifting method over the more commonly used three-step or four-step phase-shifting methods. We demonstrate the applicability of this theoretical proposal through numerical simulations involving two types of complicated objects. The results illustrate that the phase information of the complex object can be successfully and quantitatively reconstructed. [ABSTRACT FROM AUTHOR]

In classical Fourier optics, an optical imaging system is regarded as a linear space-invariant system, which is only an approximation. Especially in digital holography, the space-variance effect has a great impact on the image quality and cannot be ignored. Therefore, it is comprehensively investigated in this article. Theoretical analyses indicate that the space-variance effect is caused by linear frequency modulation and ideal low-pass filtering, and it can be divided into three states: the approximate space-invariance state, the high-frequency distortion state, and the boundary-diffraction state. Classical Fourier optics analysis of optical imaging systems only considers the first. Regarding the high-frequency distortion state, the closer the image field is to the edge, the more severe the distortion of high-frequency information is. As for the boundary-diffraction state, in addition to the distortion of high-frequency information in the margin, a prominent boundary-diffraction phenomenon is observed. If the space-variance effect of the imaging lens is ignored, we predict that no space-variance effect in image holography will occur when the hologram is recorded at the back focal plane of the imaging lens. Simulation and experimental results are presented to validate our theoretical prediction. [ABSTRACT FROM AUTHOR]

This study presents the image quality estimates of a hypothetical earth observation satellite (EOS) equipped with metaxel-based image sensors for the oblique viewing angle of the pitch manoeuvre scenario. Oblique-view image estimation methods are proposed and demonstrated for the optical and detector images. Owing to the small detector period (p) of the metaxel supercells ( $ p=1.32\, \mu {}{\rm m} $ p = 1.32 μ m ), the optical system image is optics limited. For oblique angle of $ \theta _{p}=15^{\circ },30^{\circ },45^{\circ },60^{\circ } $ θ p = 15 ∘ , 30 ∘ , 45 ∘ , 60 ∘ , image quality degradation owing to the aberration remained minor and average signal to noise ratio (SNR) for nadir view was SNR = 64 because of the local field enhancement of the metaxels. However, changes in the viewing angle reduced the image quality. Correlation coefficient between synthetic ground truth and oblique viewing cases was corr = 0.833, 0.818, 0.793 and 0.745 for the viewing angles of interest listed above. [ABSTRACT FROM AUTHOR]

Image processing is of fundamental importance for numerous modern technologies. In recent years, due to increasing demand for real-time and continuous data processing, metamaterial and metasurface based all-optical computation techniques emerged as a promising alternative to digital computation. Most of the pioneer research focused on all-optical edge detection as a fundamental step of image processing. Metasurfaces have been shown to enable real time edge detection with low to no power consumption. However, the previous demonstrations were subjected to the several limitations such as need for oblique-incidence, polarization dependence, need for additional polarizers, narrow operation bandwidth, being limited with processing in 1D, operation with coherent light only, and requiring digital post-processing. Here, we propose and experimentally demonstrate 2D isotropic, polarization-independent, broadband edge detection with high transmission efficiency under both coherent and incoherent illumination along the visible frequency range using a metasurface based on Fourier optics principles. Here, the Authors demonstrate a 2D isotropic, polarization-independent, broadband edge detection with high transmission efficiency under both coherent and incoherent illumination along the visible range using a metasurface based on Fourier optics principles. [ABSTRACT FROM AUTHOR]

We introduce an imaging system that can simultaneously record complete Mueller polarization responses for a set of wavelength channels in a single image capture. The division-of-focal-plane concept combines a multiplexed illumination scheme based on Fourier optics together with an integrated telescopic light-field imaging system. Polarization-resolved imaging is achieved using broadband nanostructured plasmonic polarizers as functional pinhole apertures. The recording of polarization and wavelength information on the image sensor is highly interpretable. We also develop a calibration approach based on a customized neural network architecture that can produce calibrated measurements in real-time. As a proof-of-concept demonstration, we use our calibrated system to accurately reconstruct a thin film thickness map from a four-inch wafer. We anticipate that our concept will have utility in metrology, machine vision, computational imaging, and optical computing platforms. [ABSTRACT FROM AUTHOR]

The article discusses quantum imaging, a field in quantum technologies with advantages over classical protocols, and how quantum correlations can be used to differentiate quantum images from classical ones. It introduces a quantum imaging distillation technique that uses the detection of single photons, specifically in the context of quantum imaging with undetected light (QIUL).

Conventional microscopy systems have limited depth of field, which often necessitates depth scanning techniques hindered by light scattering. Various techniques have been developed to address this challenge, but they have limited extended depth of field (EDOF) capabilities. To overcome this challenge, this study proposes an end-to-end optimization framework for building a computational EDOF microscope that combines a 4f microscopy optical setup incorporating learned optics at the Fourier plane and a post-processing deblurring neural network. Utilizing the end-to-end differentiable model, we present a systematic design methodology for computational EDOF microscopy based on the specific visualization requirements of the sample under examination. In particular, we demonstrate that the metasurface optics provides key advantages for extreme EDOF imaging conditions, where the extended DOF range is well beyond what is demonstrated in state of the art, achieving superior EDOF performance. [ABSTRACT FROM AUTHOR]

The ever‐growing demand for ultracompact micro‐ and nano‐optics is guided by efficient applications in augmented/virtual reality, displays, and Fourier optics. The current technologies, mainly based on meta‐solutions, suffer in terms of efficiency and tunability, as well as complex and multi‐step fabrication methods that may limit their full‐scale potential. Herein, a broadband laser composed of close and highly correlated lines allows, via interference patterning, for simultaneous encoding of multiplexed, independent, and cross‐talk free holograms with nanometric separation. The reported findings show that such light, unusual for holographic recording, unlocks new features of organized collective phenomena, overcoming the usual spatial resolution limitations of the optical techniques. This approach gives promising perspectives for in situ design of reconfigurable structured optics, besides the obvious advantages of full‐scalability, easiness, cost effectiveness, and time and energy consumption. [ABSTRACT FROM AUTHOR]

The nonlinear optical (NLO) response of photonic materials plays an important role in the understanding of light–matter interaction as well as pointing out a diversity of photonic and optoelectronic applications. Among the recently studied materials, 2D-LTMDs (bi-dimensional layered transition metal dichalcogenides) have appeared as a beyond-graphene nanomaterial with semiconducting and metallic optical properties. In this article, we review most of our work in studies of the NLO response of a series of 2D-LTMDs nanomaterials in suspension, using six different NLO techniques, namely hyper Rayleigh scattering, Z-scan, photoacoustic Z-scan, optical Kerr gate, and spatial self-phase modulation, besides the Fourier transform nonlinear optics technique, to infer the nonlinear optical response of semiconducting MoS2, MoSe2, MoTe2, WS2, semimetallic WTe2, ZrTe2, and metallic NbS2 and NbSe2. The nonlinear optical response from a thermal to non-thermal origin was studied, and the nonlinear refraction index and nonlinear absorption coefficient, where present, were measured. Theoretical support was given to explain the origin of the nonlinear responses, which is very dependent on the spectro-temporal regime of the optical source employed in the studies. [ABSTRACT FROM AUTHOR]

The disturbance flow field arises naturally with hypersonic target flying in near space. In situations where traditional infrared and radar systems lose effectiveness, space-based optical detection of this surrounding flow can serve as an alternative method for detecting high-speed targets. This paper presents a remote sensing imaging analysis of the disturbance flow field surrounding a hypersnoic target at different flight altitudes and Mach numbers. Utilizing Fourier Optics and Background-Oriented Schlieren, in conjunction with the fourth-order Runge-Kutta ray tracing algorithm, the imaging blurring and imaging deviation of three typical backgrounds under the influence of the disturbance flow field are obtained. Additionally, the study analyzes the influence of flight conditions and parameters of the imaging system on the imaging characteristics, and provides optical design recommendations. The results indicate that the presence of disturbance flow fields leads to varying degrees of visually apparent blurring effects and indiscernible deviation effects on the background images. Furthermore, the profiles of the disturbance flow field are extracted, in agreement with current experimental research. This study verifies the feasibility of space-based optical detection of hypersonic targets through disturbance flow field remote sensing imaging and contributes to the advancement of imaging research in this field. [ABSTRACT FROM AUTHOR]

A light ray in space is characterized by two vectors: (i) a transverse spatial vector associated with the point where the ray intersects a given spherical cap; (ii) an angular-frequency vector which defines the ray direction of propagation. Given a light ray propagating from a spherical emitter to a spherical receiver, a linear equation is established that links its representative vectors on the emitter and on the receiver. The link is expressed by means of a matrix which is not homogeneous, since it involves both spatial and angular variables (having distinct physical dimensions). Indeed, the matrix becomes a homogeneous rotation matrix after scaling the previous variables with appropriate dimensional coefficients. When applied to diffraction, in the framework of a scalar theory, the scaling operation results directly in introducing fractional-order Fourier transformations as mathematical expressions of Fresnel diffraction phenomena. Linking angular-frequency vectors and spatial frequencies results in an interpretation of the notion of a spherical angular spectrum. Accordance of both homogeneous and non-homogeneous ray matrices with the Huygens–Fresnel principle is examined. The proposed ray-matrix representation of diffraction is also applied to coherent imaging through a lens. [ABSTRACT FROM AUTHOR]

It is one of the basic principles of Fourier Optics that the field distribution in far-field or Fraunhofer diffraction pattern due to a planar diffracting aperture is proportional to the Fourier transform (FT) of field distribution in the aperture plane. The computational technique of discrete convolution is used to simulate planar diffracting apertures of varied geometry. Subsequently, the discrete Fourier transform technique is used to generate Fraunhofer diffraction patterns due to the simulated planar apertures. The basic apertures like single slits, double slits, multiple slits, rectangular and circular are generally treated in theory as a part of any wave optics undergraduate course. Some apertures with geometrical shapes, such as triangles, trapeziums, hexagons and pentagons, have been analysed in the past [1–3]. The results presented in this article1 agree fairly well with theoretical predictions and with those reported in the literature [1–3]. The article aims to highlight the importance and ease of using computational methods in problem-solving. A computational approach has far greater flexibility and scope in exploring different aspects of a given problem compared to a corresponding analytical treatment of the same. The target group are undergraduate students of physics and engineering sciences. [ABSTRACT FROM AUTHOR]

Fourier transform holography overcomes the phase recovery challenge through recording complex field information of the object in an interference pattern recorded at the far field, i.e., Fourier plane. Moreover, this geometry helps to reconstruct the complex field of the object from a single Fourier transform, which is an attractive feature for the numerical reconstruction of the digitally recorded hologram. In this paper, we present a nearly common path experimental design for recording a digital Fourier holographic hologram using a beam displacer, and recover the complex valued objects using the Fourier analysis. The performance of the system is experimentally examined for different objects. [ABSTRACT FROM AUTHOR]

Object pre-localization from computer-generated holograms is still an open problem in the current state of the art. In this work, we propose the use of the hologram phase space representation to determine a set of regions of interest where the searched object can be located. The extracted regions can be used to pre-locate the object in 3D space and are further refined to produce a more accurate depth estimate. An iterative refinement method is proposed for 1D holograms and is extended in a parsimonious version for 2D holograms. A series of experiments are conducted to assess the quality of the extracted regions of interest and the sparse depth estimate produced by the iterative refinement method. Experimental results show that it is possible to pre-localize the object in 3D space from the phase space representation and thus to improve the calculation time by reducing the number of operations and numerical reconstructions necessary for the application of s (DFF) methods. Using the proposed methodology, the time for the application of the DFF method is reduced by half, and the accuracy is increased by a factor of three. [ABSTRACT FROM AUTHOR]

Optical Ising machines promise to solve complex optimization problems with an optical hardware acceleration advantage. Here we study the ground state properties of a nonlinear optical Ising machine realized by spatial light modulator, Fourier optics, and second-harmonic generation in a nonlinear crystal. By tuning the ratio of the light intensities at the fundamental and second-harmonic frequencies, we experimentally observe two distinct ferromagnetic-to-paramagnetic phase transitions: a second-order phase transition where the magnetization changes to zero continuously and a first-order phase transition where the magnetization drops to zero abruptly as the effective temperature increases. Our experimental results are corroborated by a numerical simulation based on the Monte Carlo Metropolis-Hastings algorithm, and the physical mechanism for the distinct phase transitions can be understood with a mean-field theory. Our results showcase the flexibility of the nonlinear optical Ising machine, which may find potential applications in solving combinatorial optimization problems. Optical Ising machines provide a promising approach to solve complex optimization problems and hence are of broad interest in physics society. This paper constructs a nonlinear optical Ising machine with spatial light modulators to find distinct phase transitions, which demonstrates a platform for solving optimization problem in more efficient way. [ABSTRACT FROM AUTHOR]

FOCUS (Fast Monte CarlO approach to Coherence of Undulator Sources) is a new GPU-based simulation code to compute the transverse coherence of undulator radiation from ultra-relativistic electrons. The core structure of the code, which is written in the language C++ accelerated with CUDA, combines an analytical description of the emitted electric fields and massively parallel computations on GPUs. The combination is rigorously justified by a statistical description of synchrotron radiation based on a Fourier optics approach. FOCUS is validated by direct comparison with multi-electron Synchrotron Radiation Workshop (SRW) simulations, evidencing a reduction in computation times by up to five orders of magnitude on a consumer laptop. FOCUS is then applied to systematically study the transverse coherence in typical third- and fourth-generation facilities, highlighting peculiar features of undulator sources close to the diffraction limit. FOCUS is aimed at fast evaluation of the transverse coherence of undulator radiation as a function of the electron beam parameters, to support and help prepare more advanced and detailed numerical simulations with traditional codes like SRW. [ABSTRACT FROM AUTHOR]

Conventional stereoscopic displays suffer from vergence-accommodation conflict and cause visual fatigue. Integral-imaging-based displays resolve the problem by directly projecting the sub-aperture views of a light field into the eyes using a microlens array or a similar structure. However, such displays have an inherent trade-off between angular and spatial resolutions. In this paper, we propose a novel coded time-division multiplexing technique that projects encoded sub-aperture views to the eyes of a viewer with correct cues for vergence-accommodation reflex. Given sparse light field sub-aperture views, our pipeline can provide a perception of high-resolution refocused images with minimal aliasing by jointly optimizing the sub-aperture views for display and the coded aperture pattern. This is achieved via deep learning in an end-to-end fashion by simulating light transport and image formation with Fourier optics. To our knowledge, this work is among the first that optimize the light field display pipeline with deep learning. We verify our idea with objective image quality metrics (PSNR, SSIM, and LPIPS) and perform an extensive study on various customizable design variables in our display pipeline. Experimental results show that light fields displayed using the proposed technique indeed have higher quality than that of baseline display designs. [ABSTRACT FROM AUTHOR]

Vinylsulfur pentafluoride (VSPF), a molecule with a four-fold internal rotor, —SF4, has been studied with high resolution Fourier transform microwave spectroscopy. We believe that this is the first report of resolved four-fold internal rotation. As such, we have presented the tools needed to understand and analyze such a problem. These include debugging the ERHAM computer program necessary to fit the spectra and the free rotor to high barrier correlation diagram necessary to understand the torsional states of the four-fold rotor. The A, E, and B torsional state rotational transitions are well resolved and assigned. Spectroscopic transitions of four isotopologues of VSPF, H2C=CH—SF5, the normal isotopologue, and the singly substituted 34S and 13C isotopologues were measured and assigned. Contrary to expectation, the A torsional state could not be fit with only a semi-rigid Hamiltonian. The barrier to internal rotation, V4, is found to be 227 cm−1. Ab initio calculations at the MP2 aug-cc-pVQZ level of theory and basis set were performed and the results of this calculation are compared to our experimental results. [ABSTRACT FROM AUTHOR]

To avoid mixing of the undesired frequencies in a free‐space, the point sources of gratings, defined by a spatially varying refractive index, should be sinusoidally rather than binarily arranged. This long‐lasting but gold standard lesson attainable from a classical Fourier optics, however, is underutilized in the practical materialization of gratings, mainly because most of the fabrication methods, developed thus far, are intrinsically compatible with a binary rather than sinusoidal grating. Recently, such design concept of optical Fourier elements has been implemented into the real surface gratings (referred to as optical Fourier surfaces) by taking advantage of advanced nanofabrication, whereas their volumetric equivalents (optical Fourier volumes, OFVs) have yet to be conceptually and experimentally elucidated. In this work, the key characteristics of OFVs and their structural requirements are systematically exploited with the assistance of analytical and numerical calculations. Especially, the dynamic range and thickness of volume gratings, required for OFVs, are newly defined. Given these theoretical blueprints, both the holographic photopolymers and photoaddressable polymers are then revisited and they are experimentally validated as easy‐to‐craft mediums of OFVs. The landscape of volume gratings is extended by providing an integrative pipeline of OFVs across their theoretical design and practical materialization. [ABSTRACT FROM AUTHOR]

This paper describes how to efficiently solve time‐dependent X‐ray dynamic diffraction problems in distorted crystals with a fast Fourier transform based beam propagation method. Examples are given of using the technique to simulate the propagation of X‐ray beams in deformed crystals in space and time domains relevant to the cavity‐based X‐ray free‐electron lasers and X‐ray free‐electron laser self‐seeding systems. [ABSTRACT FROM AUTHOR]

Manifestations of orbital angular momentum induced effects in the diffraction of a radially polarized vector beam by an off-axis tilted aperture are studied both experimentally and theoretically. Experiments were carried out to extract the degree of circular polarization, which was shown to be proportional to the on-axis component of the spin angular momentum density. We report a clear separation of the regions of dominance of the right and left circular polarizations associated with positive and negative topological charges respectively, which is reminiscent of the standard vortex-induced transverse shift, albeit in the diffraction scenario. The experimental results are supported by model simulations and the agreement is quite satisfactory. The results are useful to appreciate the orbit-orbit related effects due to unavoidable misalignment problems (especially for vortex beams). [ABSTRACT FROM AUTHOR]

Analog optical computing (AOC) has attracted great attention over the past few years, because of its ultra-high speed (potential for real-time processing), ultra-low power consumption, and parallel processing capabilities. In this article, we design an adder and an ordinary differential equation solver (ODE) on chip by Fourier optics and metasurface techniques. The device uses the 4f system consisting of two metalenses on both sides and one middle metasurface (MMS) as the basic structure. The MMS that performs the computing is the core of the device and can be designed for different applications, i.e., the adder and ODE solver in this article. For the adder, through the comparison of the two input and output signals, the effect of the addition can be clearly displayed. For the ODE solver, as a proof-of-concept demonstration, a representative optical signal is well integrated into the desired output distribution. The simulation result fits well with the theoretical expectation, and the similarity coefficient is 98.28%. This solution has the potential to realize more complex and high-speed artificial intelligence computing. Meanwhile, based on the direct-binary-search (DBS) algorithm, we design a signal generator that can achieve power splitting with the phase difference of π between the two output waveguides. The signal generator with the insertion loss of −1.43 dB has an ultra-compact footprint of 3.6 μ m × 3.6 μ m . It can generate a kind of input signal for experimental verification to replace the hundreds of micrometers of signal generator composed of a multi-mode interference (MMI) combination used in the verification of this type of device in the past. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new asymmetric cryptosystem for phase image encryption, using the physically unclonable functions (PUFs) as security keys. For encryption, the original amplitude image is first converted into a phase image and modulated with a PUF to obtain a complex image. This complex image is then illuminated with a plane wave, and the complex wavefront at a distance d is recorded. The real part of the complex wavefront is further processed to obtain the encrypted image and the imaginary part is kept as the private key. The polar decomposition approach is utilized to generate two more private security keys and to enable the multi-user capability in the cryptosystem. Numerical simulations confirm the feasibility of the proposed method. [ABSTRACT FROM AUTHOR]

Photoabsorption cross sections and oscillator strengths for the strong, predissociating vibrational bands, v ≥ 11, in the S 2 B Σ u − 3 − X Σ g − 3 ( v , 0 ) system are reported. Absorption measurements were undertaken on S2 vapor produced by a radio-frequency discharge through H2S seeded in helium, and also in a two-temperature sulfur furnace, at temperatures of 370 K and 823 K, respectively. S2 column densities were determined in each source by combining experimental line strengths in low- v non-predissociating B − X bands ( v < 7) with calculated line f-values based on measured radiative lifetimes and calculated branching ratios. The broad-band capabilities of two vacuum-ultraviolet Fourier-transform spectrometers, used with instrumental resolutions of 0.22 cm−1 and 0.12 cm−1, respectively, allowed for simultaneous recordings of both non-predissociating and predissociating bands, thus placing the predissociating-band cross sections on a common absolute scale. Uncertainties in the final cross section datasets are estimated to be 15% for the 370-K vapor and 10% for the 823-K vapor. The experimental cross sections are used to inform a detailed predissociation model of the B( v ) levels in Paper II [Lewis et al., J. Chem. Phys. 148, 244303 (2018)]. For astrophysical and other applications, this model can be adjusted simply to provide isotopologue-specific cross sections for a range of relevant temperatures. [ABSTRACT FROM AUTHOR]

The multi-slice integration (MSI) method is one of the approachs to extend the depth of view (DOV) of the pulsed laser range-gated imaging (PLRGI) system. When the DOV is large enough and exceeds the depth of focus of the system, it may make some targets in the image clear and others blurred. In addition, forward scatter is also considered to have a blurring effect on the image. There is very little literature to solve the combined effect of forward scatter and defocus. An imaging model is built based on the model from Jaffe–McGlamery and Fourier optics. According to the imaging model, backscattered light is independent from reflected light from the target, and forward scatter has a relationship with the reflected light. Thus, backscattered light should be removed before deblurring. First, rolling ball and intensity transformation are used to remove the backscattered light and enhance the image. Then, a deep learning model based on Transformer is used to deblur the image. To enable the deep learning model to accommodate different degrees of blurred image, 16 different blur kernels are generated according to the imaging model. Sharp images from a DPDD dataset were chosen to train the model. Images of varying degrees of blur were collected from a water tank and a boat tank by the PLRGI system as test sets. Image deblurring results show that the proposed method can remove different levels of blur and can deal with images which have sharp targets and blurred targets together. [ABSTRACT FROM AUTHOR]

The article discusses rapid advances in deep learning have led to paradigm shifts in a number of fields, from medical image analysis to autonomous systems. These advances, however, have resulted in digital neural networks with large computational requirements, resulting in high energy consumption and limitations in real-time decision-making when computation resources are limited.

Fourier transforms are an often necessary component in many computational tasks and can be computed efficiently through the fast Fourier transform (FFT) algorithm. However, many applications involve an underlying continuous signal, and a more natural choice would be to work with, e.g., the Fourier series (FS) coefficients in order to avoid the additional overhead of translating between the analog and discrete domains. Unfortunately, there exists very little literature and tools for the manipulation of FS coefficients from discrete samples. This paper introduces a Python library called pyFFS for efficient FS coefficient computation, convolution, and interpolation. While the libraries SciPy and NumPy provide efficient routines for discrete Fourier transform coefficients via the FFT algorithm, pyFFS addresses the computation of FS coefficients through what we call the fast Fourier series (FFS). Moreover, pyFFS includes an FS interpolation method based on the chirp Z-transform that can make it more than an order of magnitude faster than the SciPy equivalent when one wishes to perform distortionless bandlimited interpolation. Graphics processing unit (GPU) support through CuPy is readily available and allows for further acceleration: an order of magnitude faster for computing the 2-D FS coefficients of 1000 × 1000 samples and nearly two orders of magnitude faster for 2-D interpolation. As an application, we discuss the use of pyFFS in Fourier optics. [ABSTRACT FROM AUTHOR]

Temporal focusing-based multiphoton excitation microscopy (TFMPEM) just provides the advantage of widefield optical sectioning ability with axial resolution of several micrometers. However, under the plane excitation, the photons emitted from the molecules in turbid tissues undergo scattering, resulting in complicated background noise and an impaired widefield image quality. Accordingly, this study constructs a general and comprehensive numerical model of TFMPEM utilizing Fourier optics and performs simulations to determine the superior spatial frequency and orientation of the structured pattern which maximize the axial excitation confinement. It is shown experimentally that the optimized pattern minimizes the intensity of the out-of-focus signal, and hence improves the quality of the image reconstructed using the Hilbert transform (HT). However, the square-like reflection components on digital micromirror device leads to pattern residuals in the demodulated image when applying high spatial frequency of structured pattern. Accordingly, the HT is replaced with Hilbert–Huang transform (HHT) in order to sift out the low-frequency background noise and pattern residuals in the demodulation process. The experimental results obtained using a kidney tissue sample show that the HHT yields a significant improvement in the TFMPEM image quality. [ABSTRACT FROM AUTHOR]

For example, in Ref. [[19]] the reported achromatic metalenses have a diameter of HT ht and an NA of HT ht . [Extracted from the article]

The article designs and fabricates a fiber-integrated polarimeter by vertically stacking three photodetection units based on six-layer van der Waals materials. They include one bismuth selenide layer for power calibration, two twisted black phosphorus (BP) layers for polarization detection, and three hexagonal boron nitride layers for encapsulation. Also mentioned are the detection of linearly polarized and circularly polarized light, and photogalvanic effects in the BP units.

Label-free molecular imaging is a promising utility to study tissues in terms of the identification of their compartments as well as chemical features and alterations induced by disease. The aim of this work was to assess if higher magnification of optics in the Fourier transform infrared (FT-IR) microscope coupled with the focal plane detector resulted in better resolution of lung structures and if the histopathological features correlated with clustering of spectral images. FT-IR spectroscopic imaging was performed on paraffinized lung tissue sections from mice with optics providing a total magnification of 61× and 36×. Then, IR images were subjected to unsupervised cluster analysis and, subsequently, cluster maps were compared with hematoxylin and eosin staining of the same tissue section. Based on these results, we observed minute features such as cellular compartments in single alveoli and bronchiole, blood cells and megakaryocytes in a vessel as well as atelectasis of the lung. In the case of the latter, differences in composition were also noted between the tissue from the non-cancerous and cancerous specimen. This study demonstrated the ability of high-definition FT-IR imaging to evaluate the chemical features of well-resolved lung structures that could complement the histological examination widely used in animal models of disease. Graphical Abstract [ABSTRACT FROM AUTHOR]

2 Multifunctionality from the pattern design Polarization [[65]], [[66]], [[67]], [[68]], [[69]], wavelength [[20], [24], [69]], [[70]], [[71]], and angle [[72]], [[73]], [[74]], [[75]] of incidence are part of a non-exhaustive list of parameters of a given light source that are usually taken advantage of as multiplexing channels for the multifunctional metasurfaces [[21]], which realize holography, structural color, and beam steering at the same time. Keywords: multifunctional; optical metasurface; reconfigurable; tunable EN multifunctional optical metasurface reconfigurable tunable 1761 1781 21 05/12/22 20220401 NES 220401 1 Introduction The ability to control the wavefront of light is fundamental to focalization and redistribution of light, enabling many applications from imaging to spectroscopy. Although only the function of holography can be tuned, the vectorial holography that relies on polarization of incident light will bring more information channels, which is vital for optical encryption. Matrix Fourier optics enables polarization multiplexing in holograms [[77]]. [Extracted from the article]

Then, the incident light passed through one of three bandpass filters for wavelengths of 633 nm (FL632.8-3, Thorlabs Inc., center wavelength = 632.8 nm, FWHM = 3 nm), 532 nm (FL532-3, Thorlabs Inc., center wavelength = 532 nm, FWHM = 3 nm), and 633 nm (FB440-10, Thorlabs Inc., center wavelength = 440 nm, FWHM = 10 nm), as well as the resolution test target (USAF 1951). Keywords: dielectric metasurface; metalens; silicon; varifocal; waveguide EN dielectric metasurface metalens silicon varifocal waveguide 1941 1948 8 05/12/22 20220401 NES 220401 1 Introduction Metasurfaces are a planar type of metamaterial and are promising as optical components. Rotational varifocal moiré metalens made of single-crystal silicon meta-atoms for visible wavelengths For the negative focal lengths, at the same mutual rotation angle, a shorter wavelength resulted in a larger image and greater focal length. [Extracted from the article]

Optical encryption has received increasing attention recently as information security is playing a crucial role in the modern information society. Particularly, the intensive investigation and rapid development of metasurfaces have significantly facilitated the research of optical encryption with enhanced security and increased capacity for information. Nevertheless, most metasurface encryption schemes still suffer from the challenge of dynamic modulation. Here, we demonstrate a novel dynamic optical encryption scheme in which information can be encrypted in light fields in a reconfigurable manner. Specifically, the spatial frequencies of optical images are utilized as information carriers and dynamically modulated for encrypting information. With the developed reconfigurable Fourier optics technique, various kinds of messages can be directly embedded in the spatial frequency domain of the ciphertext images and maintained with high fidelity. Importantly, information security and capacity can benefit from high-speed dynamic modulation with advanced coding techniques, an example of which has been demonstrated via exploiting the position, profile, and time degrees of freedom of spatial frequency. The proposed novel optical encryption scheme may pave the way for realizing high-performance information encryption systems. • Using the reconfigurable Fourier optics technique can enable dynamic optical encryption to increase efficiency. • The security can be enhanced by encrypting messages at the Fourier domains of optical images. • Information security and capacity can also benefit from high-speed dynamic modulation with advanced coding techniques. [ABSTRACT FROM AUTHOR]

• Frequency-domain feature enhancement and a spatial attention mechanism are employed to enhance the accuracy of misalignment sensing. • The proposed Fourier-attention neural network achieves a two-dimensional misalignment sensing accuracy of 0.23 nm at a frequency of 20 Hz. • The experimental results of the proposed strategy illustrate its robustness to both system errors and noise. A recurring challenge in integrated lithography is subnanoscale misalignment sensing. In widely-used moiré-based misalignment sensing schemes, measurement accuracy is restricted by the performance of the image processing schemes. This is also a fundamental problem in the field of Fourier optics that has received extensive attention in the science and engineering fields. This paper proposes a Fourier-attention neural network that can achieve real time-lapse misalignment sensing with an accuracy of 0.23 nm. This is enabled by the system's robustness to system errors and noise. We hope that this strategy can provide an effective solution for various misalignment sensing applications and that the approach can be applied to future problems. [ABSTRACT FROM AUTHOR]

Coherence scanning interferometry (CSI) is a widely used optical method for surface topography measurement of industrial and biomedical surfaces. The operation of CSI can be modeled using approximate physics-based approaches with minimal computational effort. A critical aspect of CSI modeling is defining the transfer function for the imaging properties of the instrument to predict the interference fringes from which topography information is extracted. Approximate methods, for example, elementary Fourier optics, universal Fourier optics, and foil models, use scalar diffraction theory and the imaging properties of the optical system to model CSI surface topography measurement. In this work, the simulated topographies of different surfaces, including various sinusoids, two posts, and a step height, calculated using the three example methods are compared. The presented results illustrate the agreement between the three example models. [ABSTRACT FROM AUTHOR]

In this work, we show that the near field of leaky-wave resonant antennas (LWAs) radiating into a dense medium can be locally represented as a spherical wave in a certain solid angle around broadside using an accurate definition of the phase center. The near field in this solid angle can be efficiently evaluated through the integration of the spectral Green’s function along the steepest descent path (SDP). Beyond this solid angle, defined as the shadow boundary angle, a residual contribution due to the leaky-wave pole must also be added to fully describe the near field. It is found that this shadow boundary angle can be used to define the phase center and geometry of a truncated lens that couples well to leaky-wave antennas, even in electrically small-to-medium sized lenses and low-contrast cases. To demonstrate the applicability of the proposed study, we combine the SDP field calculation with a Fourier optics (FO) methodology to evaluate the aperture efficiency and radiation patterns of small-to-medium sized lenses in reception. A truncated silicon lens with a diameter of only four free-space wavelengths is presented with almost 80% aperture efficiency. Excellent agreement with full-wave simulations is achieved, which demonstrates the accuracy of the proposed design and analysis methodology. [ABSTRACT FROM AUTHOR]

At relatively small incident and observation angles, the scattered field can be approximated as: HT ht Graph (3)where I r i is the distance from the antenna, I k i is the wave vector, and I i SB I e i sb is the dipole moment of the antenna. (p+|l|)! The corresponding OAM metasurface hologram contains three types of hologram, including OAM conserving hologram, OAM selective hologram, and OAM multiplexing hologram [[102]]. The parameter I z i SB I R i sb is the Rayleigh range of Gaussian envelope, and HT ht corresponds to the Gouy phase. [Extracted from the article]