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Abstract A high efficiency simulation method for propagation-based phase-contrast imaging, called directional macro-wavefront (DMWF), is developed with the aim of simulating high-energy phase-contrast imaging. This method takes both Monte Carlo and wave optical propagation into consideration. Traditional wave-optics-based simulation methods for phase-contrast imaging encounter unacceptable computational complexity when high-energy radiation is used. In contrast, this method effectively addresses this issue by using macro-wavefront integration. Several simulation examples using typical parameters of inverse Compton scattering sources are presented to illustrate the excellent energy adaptability and efficiency of the DMWF method. This method provides a more efficient approach for phase-contrast imaging simulations, which will drive the advancement of high-energy phase-contrast imaging.

A high efficiency simulation method for propagation-based phase-contrast imaging, called directional macro-wavefront (DMWF), is developed with the aim of simulating high-energy phase-contrast imaging. This method takes both Monte Carlo and wave optical propagation into consideration. Traditional wave-optics-based simulation methods for phase-contrast imaging encounter unacceptable computational complexity when high-energy radiation is used. In contrast, this method effectively addresses this issue by using macro-wavefront integration. Several simulation examples using typical parameters of inverse Compton scattering sources are presented to illustrate the excellent energy adaptability and efficiency of the DMWF method. This method provides a more efficient approach for phase-contrast imaging simulations, which will drive the advancement of high-energy phase-contrast imaging. [ABSTRACT FROM AUTHOR]

Laser dazzling on complementary metal oxide semiconductor (CMOS) image sensors is an effective method in optoelectronic countermeasures. However, previous research mainly focused on the laser dazzling under far fields, with limited studies on situations that the far-field conditions were not satisfied. In this paper, we established a Fresnel diffraction model of laser dazzling on a CMOS by combining experiments and simulations. We calculated that the laser power density and the area of saturated pixels on the detector exhibit a linear relationship with a slope of 0.64 in a log-log plot. In the experiment, we found that the back side illumination (BSI-CMOS) matched the simulations, with an error margin of 3%, while the front side illumination (FSI-CMOS) slightly mismatched the simulations, with an error margin of 14%. We also found that the full-screen saturation threshold for the BSI-CMOS was 25% higher than the FSI-CMOS. Our work demonstrates the applicability of the Fresnel diffraction model for BSI-CMOS, which provides a valuable reference for studying laser dazzling. [ABSTRACT FROM AUTHOR]

Traditional methods of hologram generation, such as point-, polygon-, and layer-based physical simulation approaches, suffer from substantial computational overhead and generate low-fidelity holograms. Deep learning-based computer-generated holography demonstrates effective performance in terms of speed and hologram fidelity. There is potential to enhance the network's capacity for fitting and modeling in the context of computer-generated holography utilizing deep learning methods. Specifically, the ability of the proposed network to simulate Fresnel diffraction based on the provided hologram dataset requires further improvement to meet expectations for high-fidelity holograms. We propose a neural architecture called Holo-U2Net to address the challenge of generating a high-fidelity hologram within an acceptable time frame. Holo-U2Net shows notable performance in hologram evaluation metrics, including an average structural similarity of 0.9988, an average peak signal-to-noise ratio of 46.75 dB, an enhanced correlation coefficient of 0.9996, and a learned perceptual image patch similarity of 0.0008 on the MIT-CGH-4K large-scale hologram dataset. [ABSTRACT FROM AUTHOR]

In this paper, a comparative analysis and numerical simulation of operation of two types of amplitude binary gratings (conventional and fork), both in the focal plane and near-field diffraction under illumination by mode beams with different polarization states, were performed. The simulation of the field formation in the focal plane was performed using the Richards–Wolf formalism. The diffraction calculation in the near-field diffraction was performed based on the FDTD method, considering the 3D structure of optical elements. The possibility of multiplying the incident beam in different diffraction orders of binary gratings and the polarization transformation associated with spin–orbit interaction at tight focusing were shown. In this case, various polarization transformations were formed in ±1 diffraction orders of the fork grating due to different signs of the introduced vortex-like phase singularity. The obtained results can be useful for the laser processing of materials and surface structuring. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the dynamic collaborative charging scheduling problem with multiple Mobile Chargers (MCs) in the Wireless Rechargeable Sensor Networks (WRSNs) with obstacles. Firstly, we use the Fresnel Diffraction Model (FDM) to describe the influences of obstacles on the charging process. Secondly, we propose a new charging group division algorithm, which can select the sets of the sensor nodes that can be charged simultaneously and determine the selection ranges of the charging spots. Thirdly, we propose a charging spots selection algorithm based on the FDM, which can not only reduce the number of sensor failures, but also guarantee the high-level charging utility. Fourthly, we propose a dynamic zonal collaborative charging scheduling scheme. It divides the charging zones to achieve balanced distribution of the charging loads. When a zone is not schedulable, our scheme will redistribute its high energy-cost charging tasks to the zone with less load for dynamic adjustment. When some charging tasks can not be adjusted, our scheme will discard the ones with less contribution, minimizing the losses of the network. Finally, we conduct a large number of simulations to verify the performances of our work. The simulation results show that our scheme has obviously better performances compared with the other arts. [ABSTRACT FROM AUTHOR]

Metasurface arrays can achieve beam control at low cost and high quality by providing different phase compensations for each unit, effectively focusing microwave energy on target locations. With the development of short‐range communication technology or microwave power transmission technology, the demand for focusing has also increased. Using metasurface arrays to achieve multi‐target focusing has wide application value. However, as the number of focal points increases, the superposition of electromagnetic wave propagation paths leads to significant interference phenomena, which can impact potential applications. Existing solutions are unable to solve such complex problems involving a large number of targets with conflicts between them. Multi‐objective algorithms, by iteratively obtaining a set of optimal solutions, provide decision support for designers in complex multi‐objective problems. This paper alters the phase of cells in a reflective array, calculates the near‐field electric field model using the Fresnel diffraction formula, and employs various solutions using the Non‐dominated Sorting Genetic Algorithm III (NSGA‐III) combined with different constraints. Finally, we select the balanced solution to establish the array. After simulation, three adjacent focal points with normalized central values of 1, 0.86, and 0.88 were obtained, with the maximum electric field value outside the focal points being only 0.58, demonstrating the feasibility of multi‐objective algorithms in solving complex multi‐focal problems. Key Points: Near field multi‐objective focusing is the concentration of microwave energy on multiple target locations within the near‐field rangeMultiple‐objective algorithms is a computational methods for multi‐objective optimization problems and provides a set of optimal solutions [ABSTRACT FROM AUTHOR]

We present a near-field diffraction model for spin waves in perpendicularly magnetized films applicable in any geometries of excitation fields. This model relies on Kalinikos–Slavin formalism to express the dynamic susceptibility tensor in k-space and calculate the diffraction patterns via inverse 2D-Fourier transform of the response functions. We show an excellent quantitative agreement between our model and MuMax3 micro-magnetic simulations on two different geometries of antennas. Our method benchmarks spin wave diffraction in perpendicularly magnetized films and is readily applicable for future designs of magnon beamforming and interferometric devices. [ABSTRACT FROM AUTHOR]

THz radiation has gained great importance due to its potential applications in a wide variety of fields. For this reason, continuous efforts have been made to develop technological tools for use in this versatile band of the electromagnetic spectrum. Here, we propose a reflecting device with long focusing performances in the sub-THz band, using a bimirror device in which the relative angle is mechanically adjusted with the displacement of one of the mirrors. Despite the simplicity of the setup, the performance of this device is satisfactory down to a frequency of 0.1 THz. Theory and experience confirm that the bimirror is capable of focusing 0.1 THz radiation with a 2× magnification of the maximum input intensity while maintaining a longitudinal full width at half maximum (FWHM) of about 6 mm, which is about 12 times the depth of focus of a cylindrical optical element of the same focal length. In the absence of suitable THz equipment, the invariance property of the Fresnel diffraction integral allowed the predicted behavior to be tested in the THz range using conventional equipment operating at visible frequencies. [ABSTRACT FROM AUTHOR]

In recent years, optical systems near the diffraction limit have been widely used in high-end applications. Evidently, an analytical solution of the point spread function (PSF) will help to enhance both understanding and dealing with the imaging process. This paper analyzes the Fresnel diffraction of diffraction-limited optical systems in defocused conditions. For this work, an analytical solution of the defocused PSF was obtained using the series expansion of the confluent hypergeometric functions. The analytical expression of the defocused optical transfer function is also presented herein for comparison with the PSF. Additionally, some characteristic parameters for the PSF are provided, such as the equivalent bandwidth and the Strehl ratio. Comparing the PSF obtained using the fast Fourier transform algorithm of an optical system with known, detailed parameters to the analytical solution derived in this paper using only the typical parameters, the root mean square errors of the two methods were found to be less than 3% in the weak and medium defocus range. The attractive advantages of the universal model, which is independent of design details, objective types, and applications, are discussed. [ABSTRACT FROM AUTHOR]

With the development of digital holography, the accuracy requirements for the reconstruction phase are becoming increasingly high. The transfer function of the double fast transform (D-FFT) algorithm is distorted when the diffraction distance is larger than the criterion distance d t , which reduces the accuracy of solving the phase. In this paper, the Fresnel diffraction integration algorithm is improved by using the low-pass Tukey window to obtain more accurate reconstructed phases. The improved algorithm is called the D-FFT (Tukey) algorithm. The D-FFT (Tukey) algorithm adjusts the degree of edge smoothing of the Tukey window, using the peak signal-to-noise ratio (PSNR) and the structural similarity (SSIM) to remove the ringing effect and obtain a more accurate reconstructed phase. In a simulation of USAF1951, the longitudinal resolution of the reconstructed phase obtained by D-FFT (Tukey) reached 1.5 μ m , which was lower than the 3 μ m obtained by the T-FFT algorithm. The results of Fresnel holography experiments on lung cancer cell slices also demonstrated that the phase quality obtained by the D-FFT (Tukey) algorithm was superior to that of the T-FFT algorithm. D-FFT (Tukey) algorithm has potential applications in phase correction, structured illumination digital holographic microscopy, and microscopic digital holography. [ABSTRACT FROM AUTHOR]

In this paper, diffraction of scalar waves by a screen with a circular aperture is explored, considering the incidence of either a collimated beam or a focused wave, a historical review of the development of the theory is presented, and the introduction of the Fresnel approximation is described. For diffraction by a focused wave, the general case is considered for both high numerical aperture and for finite values of the Fresnel number. One aim is to develop a theory based on the use of dimensionless optical coordinates that can help to determined the general behaviour and trends of different system parameters. An important phenomenon, the focal shift effect, is discussed as well. Explicit expressions are provided for focal shift and the peak intensity for different numerical apertures and Fresnel numbers. This is one application where the Rayleigh–Sommerfeld diffraction integrals provide inaccurate results. [ABSTRACT FROM AUTHOR]

In shallow-water ocean-bottom cable (OBC) seismic data, the ineffectiveness of conventional surface-related multiple elimination (SRME) methods due to poor seabed records is addressed. This research utilizes the seismic wavefield received by multiple cables from a single shot gather to predict shallow water multiple models for that shot gather. Initially, the seismic data within a finite aperture around a seismic trace in the time domain shot gather is treated as the known seismic wavefield. This seismic wavefield is then extrapolated along the water layer to this seismic trace, following the Fresnel diffraction principle. The extrapolated data becomes the shallow water multiple model for this seismic trace. This process is repeated for each trace in the shot gather to obtain the shallow water multiple model of the entire shot gather. Forward modeling tests have shown that smaller data apertures can effectively avoid the impact of spatial aliasing on multiple model prediction. To address the overlap of primary waves and shallow water multiples in deep seismic data, which have lower dominant frequencies, the multiple model data is used as a known seismic wavefield and extrapolated along the water layer again. This produces second-order and higher-order multiple models. Applying this model to suppress multiple waves can minimize primary waves loss. This entirely data-driven approach necessitates solely water depth information, imposing no additional conditions. Both forward modeling and real seismic data testing validate the efficacy of this method in shallow water. [ABSTRACT FROM AUTHOR]

Neural networks allow solving many ill-posed inverse problems with unprecedented performance. Physics informed approaches already progressively replace carefully hand-crafted reconstruction algorithms in real applications. However, these networks suffer from a major defect: when trained on a given forward operator, they do not generalize well to a different one. The aim of this paper is twofold. First, we show through various applications that training the network with a family of forward operators allows solving the adaptivity problem without compromising the reconstruction quality significantly. Second, we illustrate that this training procedure allows tackling challenging blind inverse problems. Our experiments include partial Fourier sampling problems arising in magnetic resonance imaging with sensitivity estimation and off-resonance effects, computerized tomography with a tilted geometry, and image deblurring with Fresnel diffraction kernels. [ABSTRACT FROM AUTHOR]

This study explores the influence of inter-dot tunneling effects within a quantum dot molecule on the Fresnel diffraction phenomenon. Our findings indicate that the Fresnel diffraction of the output probe Gaussian field can be manipulated by adjusting the inter-dot tunneling parameter's strength and the characteristics of the coupling field. The inter-dot tunneling effect establishes a closed-loop system, setting conditions for the interference of the applied fields. We specifically examine a Laguerre–Gaussian (LG) coupling field, investigating how its properties-such as strength, value, and sign of the orbital angular momentum (OAM)-impact the Fresnel diffraction of the output probe field. Increasing the inter-dot tunneling parameter and the coupling LG field's strength allows for control over the spatial distribution of the Fresnel diffraction pattern. Notably, the inter-dot tunneling parameter can disturb the symmetry of the diffraction patterns. Additionally, considering a negative OAM for the coupling LG field transforms the diffraction pattern into its inverse shape. This suggests that, in the presence of the inter-dot tunneling effect, the Fresnel diffraction pattern is contingent on the direction of rotation of the helical phase front of the coupling LG field. Our results offer insights into quantum control of Fresnel diffraction patterns and the identification of OAM in LG beams, presenting potential applications in quantum technologies. [ABSTRACT FROM AUTHOR]

Most of the current optical information hiding methods are designed for protecting grayscale or color images. However, as an important information communication medium, the security of voice has also received a lot of attention in several application areas. In this paper, we propose an optical voice hiding scheme based on chaotic fingerprint phase masks (CFPMs) and three-step phase-shifting digital holography (PSDH). In this proposed scheme, the CFPMs are generated from the fingerprint using the secure hash algorithm (SHA-256) and chaotic Henon map. And to hide the voice into a host image, the voice signal is first converted into a two-dimensional (2D) matrix form (i.e., the "voice map"). Then, the "voice map" is encoded into three noise-like holograms using two CFPMs located in Fresnel transform (FrT) domain and three-step PSDH. Finally, the three noise-like holograms are hidden into a color host image using a fusion method based on discrete wavelet transform (DWT), thus achieving the hiding of the voice signal. The security of this optical voice hiding scheme can be greatly improved because the fingerprint key shared by the sender and authorized receiver is closely linked to the user and does not need to be transmitted over the open network. In addition, the parameters of chaotic Henon map and Fresnel diffraction distances can also provide additional security to the proposed scheme. We have verified the feasibility, security and robustness of the proposed scheme through extensive experiments. [ABSTRACT FROM AUTHOR]

[Objective] Due to the extensive application of self-imaging effects in different fields such as precise measurements, structured light illumination, high-resolution imaging, image processing, and other fields, studies on self-imaging effects, also known as the Talbot effects, have gradually expanded to various physical systems. In the field of optics, it has been theoretically predicted and experimentally demonstrated that self-imaging effects can be realized by using different types of structural beams. Meanwhile, optical beams carrying orbital angular momentum have significant applications in optical manipulation, optical imaging, quantum key distribution, and quantum entanglement. Propagation dynamics of vortex beams are a hotspot in optics research. Focusing on the formation of well-ordered spatial arrays of optical vortices, the effect of different optical vortices on the dynamic behavior of periodic beam evolution would offer novel ideas and ways to systematically understand the evolution dynamic behaviors of vortex beams and the realization of novel structural beams. [Methods] Herein, theoretical and numerical investigations on the propagation dynamics of three different types of vortex Gaussian beams are performed. Classical optical vortex beams, asymmetric power-law optical vortices, beams and symmetric power-law optical vortices beams are considered. Both the intensity distribution and self-imaging distance of transverse periodic Gaussian beams are determined based on the Fresnel diffraction integral theorem. Afterward, the above three types of vortex phases imposed on the initial transverse periodic Gaussian beams are considered, which are chosen as the input beams to directly solve the two-dimensional paraxial wave equation numerically by using the beam propagation method. The dynamic behavior of beam energy evolution is obtained. In addition, the light field distribution is examined in detail, and its self-imaging distance is determined. Comparison of the theoretical and numerical results is performed. [Results] The focus is on the dynamics of three types of optical vortex Gaussian beams modeled by the two-dimensional paraxial wave equation. The simulation results reveal that: 1) All three types of optical vortex Gaussian beams can produce integer and fractional self-imaging effects, where the optical field is periodically self-imaged along a straight trajectory during propagation, and the field pattern of the fractional self-imaging effects shows a half-period shift along the transverse direction. 2) The self-imaging distance of the three kinds of optical vortex Gaussian beam is measured by the reproducing distance of the self-imaging phenomenon generated by the transverse periodic Gaussian beam. 3) The vortex phases for the three optical vortex Gaussian beams are still basically unchanged during the propagation. [Conclusions] The light field structure on the self-imaging plane is composed of well-ordered two-dimensional annular beamlet arrays with ring-shaped fields for all the Talbot planes. The intensity distribution on the self-imaging planes is closely associated with the topological charge and power exponent order of the vortex phase and suffers from some distortions resulting from the weak intensity at the center of the incident beam. For the three types of optical vortex Gaussian beams, the array beam demonstrates various field strength distributions of circular, spiral, and petal shapes. However, the vortex phases for all optical vortex Gaussian beams can remain constant during long propagation distances. According to this principle and method, further research is warranted on the self-imaging effects produced by other structure beams, such as power exponent fractional order optical vortices beams and non-Gaussian periodic beams. [ABSTRACT FROM AUTHOR]

Although the classic radar equation has been widely used to analyze the link budget of an automotive radar, it is valid only when the targets are located in the far-field region of the transmitted field and the receiving antenna is located in the far-field region of the scattered field. This paper confirms this hypothesis using measured and simulated data for short-range radars. Furthermore, a novel radar equation based on the Fresnel diffraction formula is proposed for application in situations where the receiving antenna is located in the radiative near-field region (or Fresnel region) of a target, but the target is situated in the far-field region of the transmitting antenna. In addition, the proposed radar equation is assessed by comparing the measured and simulated data. [ABSTRACT FROM AUTHOR]

Digital holography (DH) is an important method for three-dimensional (3D) imaging since it allows for the recording and reconstruction of an object's amplitude and phase information. However, the field of view (FOV) of a DH system is typically restricted by the finite size of the pixel pitch of the digital image sensor. We proposed a new configuration of the DH system based on Fresnel's bi-mirror to achieve doubling the camera FOV of the existing off-axis DH system which leveraged single-shot acquisition and a common-path optical framework. The dual FOV was obtained by spatial frequency multiplexing corresponding to two different information-carrying beams from an object. Experimental evidence of the proposed dual FOV-DH system's viability was provided by imaging two different areas of the test object and an application to surface profilometry by measuring the step height of the resolution chart which showed excellent agreement with an optical profiler. Due to the simple configuration, the proposed system could find a wide range of applications, including in microscopy and optical metrology. [ABSTRACT FROM AUTHOR]

In this work, we propose to give a new mathematical formulation of the Ince–Gaussian beams (IGBs) in terms of generalized Laguerre–Gaussian beams. This new expression reproduces the well-known Ince–Gaussian modes. Based on this expansion and the Huygens–Fresnel diffraction integral, the analytical expression describing the electric field amplitude and the intensity distribution of the IGBs propagating through paraxial ABCD optical system are derived. Numerical simulation and analysis of the propagation of IGBs in free space, thin lens and Fractional Fourier transform system are computed and discussed in details. The results of this work can be regarded as complementary investigation on elliptical beams such as IGBs. [ABSTRACT FROM AUTHOR]

Computer-generated holography has been anticipated in augmented reality (AR) since it can fully provide multi-depth 3D information to users, but speckle noises are often accompanied as one of the most significant degradation factors. Since complex amplitude encoding can suppress speckle noises, applying double-phase encoding to a lensless holographic projection system using a double-step Fresnel diffraction (DSF) algorithm has been reported to reduce those noises. However, a single filtering focus at a virtual focal plane might significantly reduce the projection region compared to the maximum diffraction bandwidth of the spatial light modulator. In this paper, we applied multiple foci for the focal plane of the DSF method with off-axis phase encoding, which can expand the projection region and is applicable to display multi-depth images with DSF. Numerical analysis conducted for image quality compared with conventional single focus DSF algorithm shows that the speckle performance does not degrade so much as the number of foci increase. We expect the proposed method to be useful for holographic projection optical systems such as AR head-up display.

Laser dazzling on complementary metal oxide semiconductor (CMOS) image sensors is an effective method in optoelectronic countermeasures. However, previous research mainly focused on the laser dazzling under far fields, with limited studies on situations that the far-field conditions were not satisfied. In this paper, we established a Fresnel diffraction model of laser dazzling on a CMOS by combining experiments and simulations. We calculated that the laser power density and the area of saturated pixels on the detector exhibit a linear relationship with a slope of 0.64 in a log-log plot. In the experiment, we found that the back side illumination (BSI-CMOS) matched the simulations, with an error margin of 3%, while the front side illumination (FSI-CMOS) slightly mismatched the simulations, with an error margin of 14%. We also found that the full-screen saturation threshold for the BSI-CMOS was 25% higher than the FSI-CMOS. Our work demonstrates the applicability of the Fresnel diffraction model for BSI-CMOS, which provides a valuable reference for studying laser dazzling.

Computer-generated holography has been anticipated in augmented reality (AR) since it can fully provide multi-depth 3D information to users, but speckle noises are often accompanied as one of the most significant degradation factors. Since complex amplitude encoding can suppress speckle noises, applying double-phase encoding to a lensless holographic projection system using a double-step Fresnel diffraction (DSF) algorithm has been reported to reduce those noises. However, a single filtering focus at a virtual focal plane might significantly reduce the projection region compared to the maximum diffraction bandwidth of the spatial light modulator. In this paper, we applied multiple foci for the focal plane of the DSF method with off-axis phase encoding, which can expand the projection region and is applicable to display multi-depth images with DSF. Numerical analysis conducted for image quality compared with conventional single focus DSF algorithm shows that the speckle performance does not degrade so much as the number of foci increase. We expect the proposed method to be useful for holographic projection optical systems such as AR head-up display. [ABSTRACT FROM AUTHOR]

The recent emerging alternative to classic numerical Fast Fourier transform (FFT) computation, based on GHz ultrasonic waves generated from and detected by piezoelectric transducers for wavefront computing (WFC), is more efficient and energy-saving. In this paper, we present comprehensive studies on the modeling and simulation methods for ultrasonic WFC computation. We validate the design of the WFC system using ray-tracing, Fresnel diffraction (FD), and the full-wave finite element method (FEM). To effectively simulate the WFC system for inputs of 1-D signals and 2-D images, we verified the design parameters and focal length of an ideal plano-concave lens using the ray-tracing method. We also compared the analytical FFT solution with our Fourier transform (FT) results from 3-D and 2-D FD and novel 2-D full wave FEM simulations of a multi-level Fresnel lens with 1-D signals and 2-D images as inputs. Unlike the previously reported WFC system which catered only for 2-D images, our proposed method also can solve the 1-D FFT effectively. We validate our proposed 2-D full wave FEM simulation method by comparing our results with the theoretical FFT and Fresnel diffraction method. The FFT results from FD and FEM agree well with the digitally computed FFT, with computational complexity reduced from O (N 2 l o g N) to O(N) for 2-D FFT, and from O(NlogN) to O(N) for 1-D FFT with a large number of signal sampling points N. [ABSTRACT FROM AUTHOR]

Optical diffractometry (OD) using a phase step is an alternative for interferometry, further, has least sensitivity to environmental vibrations. Therefore, OD has found numerous interesting metrological and technological applications. OD utilizes a phase step to detect the influence of objects under measurement by the changes in the Fresnel diffraction pattern. Recently, we showed that such measurements do not require infinitively sharp phase steps, although fabrication of such sharp elements is also impossible. Here, we address the issue of smoothness of the phase step surfaces. So far, in all of the OD applications the surfaces of the incorporated phase steps are considered to be optically smooth and flat. However, practically, some amount of roughness and unflatness is unavoidable even in precise and careful fabrication process. We show that preserving the OD-diffraction-pattern characteristics of a phase step depends on the level of roughness in the surfaces of the phase step. We define number of detectable fringes and autocorrelation functions of the diffraction patterns as the measures for evaluating the similarity of the rough phase step diffractions to the ideal case. We derive the theoretical description and confirm the results with simulations and experiments. [ABSTRACT FROM AUTHOR]

The knife‐edge diffraction model (KED) and the uniform geometrical theory of diffraction (UTD) have been widely used to predict the shadowing effect at millimetre‐wave (mmWave) bands. This letter proposes a mathematical derivation to rigorously prove that, for an absorbing screen, UTD applying the narrow‐angle Fresnel approximation is equivalent to KED. The simulation scenarios are designed to validate the proposal by comparing KED with UTD in the narrow‐angle (less than 20°) and wide‐angle (over 20°) regions at mmWave bands (20100 GHz). Simulated results agree with the proposal that KED is identical to UTD with a low error of less than 0.1 dB in the narrow‐angle region, while they have a difference with an error of over 1 dB in the wide‐angle region. In addition, the average computational time is measured and results in both UTD and KED taking approximately 8.0 ms for one test. From the proposal, it can be theoretically explained the differences and similarities between KED and UTD for an absorbing screen. [ABSTRACT FROM AUTHOR]

In-line X-ray phase contrast imaging, which is simple to experiment with, provides significantly higher sensitivity, compared to conventional X-ray absorption imaging. The inversion of the relationship between recorded Fresnel diffraction intensity and the phase shift induced by the object is called phase retrieval. The transport of intensity equation (TIE), a simple method of phase retrieval, which is solved by the fast Fourier transform algorithm proposed by Paganin et al., has been widely adopted. However, the existing method suffers from excessive suppression of high-frequency information, resulting in loss of image details after phase retrieval, or insufficient detail contrast, leading to blurry images. Here, we present a straightforward extension of the two-distance FFT-TIE method by modifying the Fourier filter through the use of a five-point approximation to calculate the inverse Laplacian in a discrete manner. Additionally, we utilize a combination of continuous Fourier transform and a four-point approximation to compute the gradient operator. The method is evaluated by simulating samples with a shape similar to the resolution test map and by using a photograph of a dog for further evaluation. The algorithm that incorporates the modified gradient operator and the algorithm that solely utilizes the continuous Fourier transform for gradient computation were compared with the results obtained using the two-distance FFT-TIE method. The comparisons were conducted using the results obtained from two distances from the sample to the detector. The results show that this method improves the contrast of spatial details and reduces the suppression of high spatial frequencies compared to the two-distance FFT-TIE method. Furthermore, in the low-frequency domain, our algorithm does not lose much information compared to the original method, yielding consistent results. Furthermore, we conducted our experiments using carbon rods. The results show that both our method and the FFT-TIE method exhibit low-frequency distortion due to the requirement of close proximity between the absorption maps and the detector. However, upon closer inspection, our proposed method demonstrates superior accuracy in reproducing the finer details of the carbon rod fibers. [ABSTRACT FROM AUTHOR]

The current study examines the diffraction of Humbert beam of type-II by a helical axicon based on the diffraction integral formula. The considered beam is a new donut beam family which generated by converting the Bessel–Gaussian beams passing through a paraxial ABCD optical system with a spiral phase plate. For the diffracted beam produced by the stationary phase approach, we have formulated the intensity distribution. By adjusting the input beam features and the topological charge of the helical axicon, numerical simulations are carried out to examine the behavior of the diffracted beam. [ABSTRACT FROM AUTHOR]

A wavemeter using the near-field Talbot diffraction is simplified. High accuracy wavelength measurement can be obtained from each spacing between two adjacent maximum intensities of the periodicity along multiples of the Talbot distance. Our experimental results are confirmed by our calculations. In contrast to the previous works, we use a diffraction grating with sufficiently large grating period. Therefore, the setup is practical and the pixel size of camera used to measure the interference pattern can be large. Moreover, the obtained Talbot patterns are sharp without using a post-image processing. According to our recent setup, we use the grating with a period of 12.5 μm. With visible light lasers, the Talbot distances are in the range of a few hundred of micrometers. These distances are much larger than a pixel size of normal camera. An external cavity diode laser with rubidium saturated absorption spectroscopy is used to calibrate our setup. High accuracy at 1 pm can be achieved. [ABSTRACT FROM AUTHOR]

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It is shown that a squared Laguerre-Gaussian (LG) vortex beam is Fourier-invariant and retains its structure at the focus of a spherical lens. In the Fresnel diffraction zone, such a beam is transformed into superposition of conventional LG beams, the number of which is equal to the number of rings in the squared LG beam. If there is only one ring, then the beam is structurally stable. A more general beam, which is a “product” of two LG beams, is also considered. Such a beam will be Fourier-invariant if the number of rings in two LG beams in the “product” is the same. The considered beams complement the well-known family of LG beams, which are intensively studied as they remain stable during their propagation in turbulent media.

In this paper, a design method of diffraction structure based on metasurface is proposed for light splitting and focusing simultaneously. In the method, firstly, the light field calculation model of the proposed structure is established based on Fresnel diffraction and the transmittance function is calculated. Then, the model structural parameter selection mechanism is determined, and the spectrum resolution equation of the structure is derived. Simulation results indicate that the proposed method can offer a broader working bandwidth and enhanced higher resolution compared to off-axis meta-lens. Moreover, this proposed method can be deployed in high-resolution, wide-band ultra-compact spectrometer systems potentially. [ABSTRACT FROM AUTHOR]

Structured light beams have recently attracted enormous research interest for their unique properties and potential applications in optical communications, imaging, sensing, etc. Since most of these applications involve the propagation of structured light beams, which is accompanied by the phenomenon of diffraction, it is very necessary to employ diffraction theories to analyze the obstacle effects on structured light beams during propagation. The aim of this work is to provide a systematic summary and comparison of the scalar diffraction theories for structured light beams. We first present the scalar fields of typical structured light beams in the source plane, including the fundamental Gaussian beams, higher-order Hermite–Gaussian beams, Laguerre–Gaussian vortex beams, non-diffracting Bessel beams, and self-accelerating Airy beams. Then, we summarize and compare the main scalar diffraction theories of structured light beams, including the Fresnel diffraction integral, Collins formula, angular spectrum representation, and Rayleigh–Sommerfeld diffraction integral. Finally, based on these theories, we derive in detail the analytical propagation expressions of typical structured light beams under different conditions. In addition, the propagation of typical structured light beams is simulated. We hope this work can be helpful for the efficient study of the propagation of structured light beams. [ABSTRACT FROM AUTHOR]

In this paper, a beam shaping-based method for design of optical imaging lens is proposed. The optical imaging lens is designed with Fresnel diffraction theory to focus light, and the focusing parameters of the lens, such as the number of the foci, the focal length, the size and the shape of the focal spot, and so on, can be set with great freedom. Therefore, the lens has great flexibility in optical imaging, and the imaging resolution can also be varied with the design. The optical imaging lenses possess advantages such as simple structure, compact size, customized imaging effect, and high performance. The proposed method can be extensively applied to the design of flat optical elements and the customized optical imaging. [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]

A novel optical image encryption is proposed based on multiplexing of the random phase encoding with shift and rotation operations in domains of two transforms, extended fractional Fourier transform (eFrFT) and Fresnel transform. The original image is subjected to eFrFT with the action of the random phase mask. The mask is shifted and rotated to enhance the security of this encryption method. The image obtained from eFrFT is entered into Fresnel diffraction by the use of the phase mask to obtain the final encrypted image. We plan for the phase keys to be multiplexed in order to decrease the amount of keys that need to be stored in an application. Here, the displacement, rotation angle, and wavelength in this system can be used as additional keys to improve the security and reliability of the encryption system. Numerical experiments are conducted to verify the effectiveness and security of the method. The findings demonstrate that the keys are sufficiently sensitive for high security. [ABSTRACT FROM AUTHOR]

In this study, a dual-polarized and dual band reflective Fresnel zone plate with reconfigurable beam is proposed on the basis of fractal frequency selective surface (FSS) unit with nearly 360° phase tunability. Firstly, a new phase distribution calculation strategy based on Fresnel diffraction theory is proposed to improve the performance under certain scenarios like sparse arrays. Then, a novel fractal shape is put forward and applied to the design of the Fresnel zone plate. The introduction of the fractal structure makes the unit cell perform dual band, dual polarization and 309° phase tunability characteristics. Due to the self-symmetry of the unit cell, the proposed fractal Fresnel zone plate (FFZP) is capable of beam steering in ± 45° in both TE and TM incident waves. Besides, the proposed structure shows small performance degradation when it comes to oblique incidence up to 45°, which decreases the focal diameter ratio and profile of the proposed FFZP. The operating bandwidth of the FFZP can reach up to 700 MHz at X and Ku bands. It is applicable in a wide range of RF and microwave settings such as satellite and base station. [ABSTRACT FROM AUTHOR]

The problem of an approximate description of the wave field of many sources is considered. It is shown that, if the problem is considered more comprehensively, the description of the interference and diffraction experiments can be given within the framework of a single scheme. It is shown that the character of wave amplification in these two classical experiments is different. In the case of an interference experiment, the field amplification is fixed at a point, while in the case of a diffraction experiment the field amplification is fixed in the observation direction. The problem of determining the intensity maximum of a diffraction grating in the Fresnel pattern is studied under the condition that the maximum is satisfied in the Fraunhofer pattern. A condition under which a diffraction grating behaves like a lens is obtained. [ABSTRACT FROM AUTHOR]

Terahertz (THz) imaging is a non-invasive and high spatial-resolution technique that uses non-ionizing electromagnetic signals in a frequency range of 0.1–10 THz. Hence, this article focuses on diverse THz imaging techniques, THz antennas and designing methods, image reconstruction algorithms, and its applications. The antennas include planar patch, photoconductive, dielectric-resonator, substrate-integrated waveguide, wire, and wave guide. In this study, it is noted that antennas with high efficient conducting materials having a compact size, high gain, and high directional properties are required for THz imaging. The image reconstruction algorithms cover back-projection algorithm, range migration algorithm, phase-shift migration algorithm, single-band compressed sensing reconstruction and compressed sensing hyper spectral image reconstruction. High-resolution image reconstruction algorithms and challenges are also reported. From this study, it is noted that a multi–input–multi–output-based phase shift migration algorithm is used for THz imaging due to its high-accuracy and low computation time. It is also noted that the image quality can be enhanced by introducing an inverse fresnel diffraction algorithm into THz images retrieved by compressed sensing. Applications of THz imaging focus on cell detection (tissue-detection, cancer-detection, and bacteria-detection), concealed objects detection, food safety and quality inspection, and monitoring the water level of plant leaves. [ABSTRACT FROM AUTHOR]

Fork-shaped gratings are periodic structures containing a spatial dislocation known to be used for the production of optical vortices in a far field. Spatial overlapping of diffraction orders in a near field results in complex spatial evolution of optical vortices. In this paper, we report the results of near-field diffraction on fork-shaped gratings with different topological charges and analyze the evolution of specific optical vortices during propagation. Optical vortices have been shown to form two-dimensional well-ordered spatial configurations in specific transverse planes. The locus of points of optical singularities has been shown to form two helical lines twisted around the ± 1 diffraction order directions. Our results demonstrate that the spatial behaviour of optical vortices is in close connection with the spatial ordering arising from the Talbot effect. The quantity of optical vortices demonstrates complex spatial dynamics, which includes spatial oscillations and decreasing along the propagation direction. These results provide a foundation towards a deeper understanding of near-field singular optics phenomena. [ABSTRACT FROM AUTHOR]

The data transmission validity under conditions of log-normal amplitude fluctuations controlled by the Fresnel diffraction in the spacecraft–ground tracking station transmission line in the case of coherent reception of millimeter-range signals. The optimum signal transmission frequencies in the tropospheric channel are separated by the criterion of minimizing the of error probability and the possibilities of reaching high transmission rates are analyzed. [ABSTRACT FROM AUTHOR]

Interplanetary scintillation (IPS) refers to random fluctuations in radio intensity of distant small-diameter celestial object, over time periods of the order of 1 s. The scattering and scintillation of emergent radio waves are ascribed to turbulent density irregularities transported by the ubiquitous solar wind streams. The spatial correlation length of density irregularities and the Fresnel radius of radio diffraction are two key parameters in determining the scintillation pattern. Such a scintillation pattern can be measured and correlated between multi-station radio telescopes on the Earth. Using the “phase-changing screen” scenario based on the Born approximation, the bulk-flow speed and turbulent spectrum of the solar wind streams can be extracted from the single-station power spectra fitting and the multi-station cross-correlation analysis. Moreover, a numerical computer-assisted tomography (CAT) model, iteratively fit to a large number of IPS measurements over one Carrington rotation, can be used to reconstruct the global velocity and density structures in the inner heliosphere for the purpose of space weather modelling and prediction. In this review, we interpret the underlying physics governing the IPS phenomenon caused by the solar wind turbulence, describe the power spectrum and cross correlation of IPS signals, highlight the space weather application of IPS-CAT models, and emphasize the significant benefits from international cooperation within the Worldwide IPS Stations (WIPSS) network.

Fresnel diffraction on periodic gratings results in a two‐dimensional periodic distribution of light intensity, also known as the Talbot effect. Here this approach is extended to the family of superimposed structures with translational symmetry, which consist of superposed spatial harmonics. The Talbot effect is demonstrated to be valid for superimposed gratings. The considered superimposed gratings provide a wide range of textures of optical super‐lattices. These texture super‐lattices represent a Talbot carpets with a complex motif, which can be varied by choosing structure parameters. These results provide a new functionality for structuring optical lattices and can find potential applications in a wide range of light–matter interactions. [ABSTRACT FROM AUTHOR]

The near‐field effect of diffraction image self‐reproduction or self‐imaging of a periodic grating illuminated by quasi‐monochromatic wave is well‐known as the Talbot effect. Introducing a dislocation to a periodic structure provides a fork‐shaped modulation of the phase/amplitude, which produces discrete diffraction pattern in a far‐field consisting of optical vortices. In this paper, Fresnel diffraction at amplitude fork‐shaped grating is theoretically and experimentally studied. The coexistence of spatial ordering and local violation of translational symmetry of the structure manifests itself in a strict diffraction pattern consisting of optical vortices in the far‐field, which is shown to be accompanied by formation of a spatially ordered intensity distribution in the near‐field, reminiscent the Talbot carpets for periodic structures. These results demonstrate the first evidence of Talbot effect occurred under light diffraction at fork‐shaped gratings, being promising for deep understanding of near‐field singular optics phenomena. [ABSTRACT FROM AUTHOR]

Fresnel diffraction is a fundamental wave phenomenon happening near the shadow boundary behind a large opaque object. Previously, it was studied for the case of diffraction at large apertures in a black screen. In this paper, we investigate this phenomenon for perfectly conducting cylinders with large cross-sections. First, this theory is developed for the circular cylinders, then extended to the cylinders of arbitrary shape. It is shown that Fresnel diffraction can be interpreted as interference of the shadow radiation with the incident wave. Analytical equations and numerical data are provided and discussed in detail. [ABSTRACT FROM AUTHOR]

Analytical expressions are derived for the spatial coherence function of a speckle field that is generated by the scattering of a Mathieu beam from a random phase mask by following the Fresnel diffraction theory. The general results in the free-space propagation show that the intensity correlation factor is a function of the order of the Mathieu beam, and it evolves spatially as the speckle field propagates. Also, we demonstrate that the intensity correlation factor is non-evolving with the propagation distance in the far-field regime when a lens is placed at the focal distance after the diffuser. The results of this analysis can be used in applications where random fields need to be engineered with structured light beams. [ABSTRACT FROM AUTHOR]

Millimeter-wave (mm-Wave) spectrum is an essential enabler to the fifth generation (5G) wireless technology. Humans are one of the most noticeable blockers that cause temporal variation in indoor radio channels. This paper presents human blockage measurements at 28 GHz, with several humans of different sizes. The effect of the crossing orientations of the human bodies is investigated for three different transmitter heights. A human blockage model based on the Fresnel diffraction scheme is shown to be applicable in estimating the human blockage loss in indoor radio links considering various body sizes, different crossing orientations, and different transmitter heights. The findings reported in this paper could help improve indoor radio channel models at 28 GHz bands for 5G technologies considering the presence of human body blockages. [ABSTRACT FROM AUTHOR]

The compression and encryption of images is essential to securely transmit high quality images over the optical network. In earlier studies, an optical image encryption using Loxodromic cat map with improved double random phase encoding (LCMIDRPE) has been developed. Hilbert huang transform (HHT) used in this encoding model decrease deviations of encrypted images. However, efficient image compression technique is required for compression. An efficient optical image compression and encryption (OICE) technique is developed in this paper by Direction-adaptive discrete wavelet transform (DA-DWT) along with directional lifting and LCMIDRPE. The original image is compressed using the DA-DWT with directional lifting and then encrypted by LCMIDRPE. The inverse version of LCMIDRPE and DA-DWT regain the original image. The missed information's due to lossy compression, decompression, encryption, decryption and transmission of images degrade the quality of regained images. The regained image is enhanced using intensified convolutional neural network (ICNNet). The whole process is termed to be LCMIDRPE-DADWT-ICNNet. Finally, the experimental results exhibits that the LCMIDRPE-DADWT-ICNNet model achieves correlation coefficient (CC) of 0.98, Peak signal-to-noise ratio (PSNR) of 97db, Mean absolute difference (MAD) of 20 and mean square error (MSE) of 0.45 which is higher than OICE methods like Compressive Sensing and Rivest-Shamir-Adleman method (CS-RSA), Fresnel Diffraction and Discrete Wavelet Transform (FD-DWT), 2Dimentional Sparse Representation and Chaotic Map (2DSR-CM), 2Dimensional Compressive Sensing and Hyperchaotic System (2DCS-HS), Diffractive-Imaging-Based Encryption (DIBE) and Content-Adaptive Image Compression and Encryption using Optimized Compressive Sensing with Double Random Phase Encoding (CAIE-OCS-DPRE) methods. [ABSTRACT FROM AUTHOR]

Due to the different features of their various phases and expanding physical understanding, liquid crystals (LCs) play a fundamental and crucial role in contemporary technology. Recently, they have also been utilised in adaptive optics, active switching, and next-generation displays for augmented and virtual reality. In order to determine relevant quantities for thermotropic uniaxial nematic liquid crystals (NLCs), our aim is to assess the applicability of a ground-breaking method. The method being discussed is based on Fresnel diffraction (FD) from phase objects, which has been employed over the past 20 years in several accurate and precise metrological applications. Using a phase step and quantitatively registering the visibility of the diffraction patterns, diffractometry can transform any change in the order of LCs brought on by a change in temperature into a change in the optical phase. Owing to its low sensitivity to environmental vibrations, inherent compactness, and ease of set up, diffractometry can be used much more effectively than interferometry. Additionally, as a special major feature, if the various phases of a LC have the required transparency, it is possible to record the number of phases in the bulk of the LC, the surface ordering, and the approximate temperature of the phase transitions in a single-shot imaging by applying a suitable temperature gradient. The numerical computations and practical data comparisons from our theoretical considerations demonstrate a very high level of agreement with the output from other currently used methodologies. As we shall see, by addressing some of the faults and inadequacies of existing techniques, this strategy has the potential to both complement and strengthen them. [ABSTRACT FROM AUTHOR]

In this paper, we present a theoretical study of the Fresnel diffraction of Hollow–Gaussian laser beams (HGBs) by an opaque disk. Analytical expressions describing the wave amplitude and the intensity distribution of the HGBs diffracted by an opaque disk are derived. In this analysis, important numerical calculations are performed. The effects of some factors, including the radius of the opaque disk and the input beam parameters, on the intensity distribution, are investigated and discussed numerically. Particular case, such as the propagation of the Gaussian beams, is deduced from our main finding. The results of this work have potential applications in optical communications. [ABSTRACT FROM AUTHOR]