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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.

The ability to present three-dimensional (3D) scenes with continuous depth sensation has a profound impact on virtual and augmented reality, human–computer interaction, education and training. Computer-generated holography (CGH) enables high-spatio-angular-resolution 3D projection via numerical simulation of diffraction and interference 1 . Yet, existing physically based methods fail to produce holograms with both per-pixel focal control and accurate occlusion 2 , 3 . The computationally taxing Fresnel diffraction simulation further places an explicit trade-off between image quality and runtime, making dynamic holography impractical 4 . Here we demonstrate a deep-learning-based CGH pipeline capable of synthesizing a photorealistic colour 3D hologram from a single RGB-depth image in real time. Our convolutional neural network (CNN) is extremely memory efficient (below 620 kilobytes) and runs at 60 hertz for a resolution of 1,920 × 1,080 pixels on a single consumer-grade graphics processing unit. Leveraging low-power on-device artificial intelligence acceleration chips, our CNN also runs interactively on mobile (iPhone 11 Pro at 1.1 hertz) and edge (Google Edge TPU at 2.0 hertz) devices, promising real-time performance in future-generation virtual and augmented-reality mobile headsets. We enable this pipeline by introducing a large-scale CGH dataset (MIT-CGH-4K) with 4,000 pairs of RGB-depth images and corresponding 3D holograms. Our CNN is trained with differentiable wave-based loss functions 5 and physically approximates Fresnel diffraction. With an anti-aliasing phase-only encoding method, we experimentally demonstrate speckle-free, natural-looking, high-resolution 3D holograms. Our learning-based approach and the Fresnel hologram dataset will help to unlock the full potential of holography and enable applications in metasurface design 6 , 7 , optical and acoustic tweezer-based microscopic manipulation 8 – 10 , holographic microscopy 11 and single-exposure volumetric 3D printing 12 , 13 . A deep-learning-based approach using a convolutional neural network is used to synthesize photorealistic colour three-dimensional holograms from a single RGB-depth image in real time, and termed tensor holography.

We present computer simulations of a two-way ANOVA gage R&R study to determine the effects on the average speckle width of intensity patterns caused by scattered light reflected from random rough surfaces with different statistical characteristics. We illustrate how to obtain reliable computer data that properly simulate experimental measurements by means of the Fresnel diffraction integral, which represents an accurate analytical model for calculating the propagation of spatially-limited coherent beams that have been phase-modulated after being reflected by the vertical profiles of the generated surfaces. For our description we use four differently generated vertical profiles and five different vertical randomly generated roughness values.

Holography is the most promising route to true-to-life three-dimensional (3D) projections, but the incorporation of complex images with full depth control remains elusive. Digitally synthesized holograms1–7, which do not require real objects to create a hologram, offer the possibility of dynamic projection of 3D video8,9. Despite extensive efforts aimed at 3D holographic projection10–17, however, the available methods remain limited to creating images on a few planes10–12, over a narrow depth of field13,14 or with low resolution15–17. Truly 3D holography also requires full depth control and dynamic projection capabilities, which are hampered by high crosstalk9,18. The fundamental difficulty is in storing all the information necessary to depict a complex 3D image in the 2D form of a hologram without letting projections at different depths contaminate each other. Here, we solve this problem by pre-shaping the wavefronts to locally reduce Fresnel diffraction to Fourier holography, which allows the inclusion of random phase for each depth without altering the image projection at that particular depth, but eliminates crosstalk due to the near-orthogonality of large-dimensional random vectors. We demonstrate Fresnel holograms that form on-axis with full depth control without any crosstalk, producing large-volume, high-density, dynamic 3D projections with 1,000 image planes simultaneously, improving the state of the art12,17 for the number of simultaneously created planes by two orders of magnitude. Although our proof-of-principle experiments use spatial light modulators, our solution is applicable to all types of holographic media.Pre-shaping image wavefronts with random phase to locally reduce Fresnel diffraction to Fourier holography results in Fresnel holograms that form on-axis with full depth control without any crosstalk. This produces large-volume, high-density, dynamic 3D projections with 1,000 simultaneous image planes.

Fueled by the rapid advancement of nanofabrication, metasurface has provided unprecedented opportunities for 3D holography. Large depth 3D meta-holography not only greatly increases information storage capacity, but also enables distinguishing of the relative spatial relationship of 3D objects, which has important applications in fields like optical information storage and medical diagnosis. Although the methods based on Fresnel diffraction theory can reconstruct the real depth information of 3D objects, the maximum depth is only 2 mm. Here, we develop a 3D meta-holography based on angular spectrum diffraction theory to break through the depth limit. By developing the angular spectrum diffraction theory into meta-holography, the metasurface structure with independent polarization control is used to create a polarization multiplexing 3D meta-hologram. The fabricated amorphous silicon metasurface increases the depth range by 47.5 times and realizes 0.95 dm depth reconstruction for polarization independent and different color 3D meta-hologram in visible. Such polarization controlled large-depth color meta-holography is expected to open avenue for data storage, display, information security and virtual reality. The authors present an exciting 3D meta-holography based on angular spectrum diffraction theory that significantly improves depth limits. The showcased amorphous silicon metasurface with independent polarization control herein achieves a 47.5x depth increase and 0.95 dm depth reconstructions for polarization-independent and different color 3D meta-hologram.

When studying diffraction and related issues, one often encounters the need to anticipate and estimate the diffraction patterns of variously shaped apertures. Optical experiments demand high environmental standards, and creating diffraction screens is cumbersome. Designing specialized optical experiments for such simple purposes is time-consuming and labor-intensive, and the clarity of the diffraction patterns is hard to guarantee. Therefore, obtaining diffraction patterns quickly and accurately in different situations has become a bottleneck. This article first obtains the integral expression of the Fresnel diffraction light field produced by a monochromatic point light source illuminating a diffraction hole based on Kirchhoff’s diffraction theory. Then, it establishes a mathematical model of the hole to obtain the integral element and uses mathematical software for computational simulation, obtaining diffraction patterns applicable to any shape hole. The paper performs calculations taking uppercase English letters as shaped aperture examples and conducts detailed analysis of their diffraction patterns.

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.

A novel anti-cat-eye effect imaging technique based on wavefront coding is proposed as a solution to the problem of previous anti-cat-eye effect imaging techniques where imaging quality was sacrificed to reduce the retroreflection from the photoelectric imaging equipment. With the application of the Fresnel–Kirchhoff diffraction theory, and the definition of generalized pupil function combining both phase modulation and defocus factors, the cat-eye echo formation of the wavefront coded imaging system is theoretically modeled. Based on the physical model, the diffracted spot profile distribution and the light intensity distribution on the observation plane are further simulated with the changes in the defocus parameter and the phase modulation coefficient. A verification test on the cat-eye laser echo power of the wavefront coded imaging system and that of the conventional imaging system at a 20 m distance are conducted, respectively. Simulations and experiment results show that compared with conventional imaging systems, the wavefront coding imaging system can reduce the retroreflection echo by two orders of magnitude while maintaining better imaging quality through defocusing.

We analyse the evolution of the wavefunction of a quantum particle propagating on several compact manifolds, including the Klein bottle, Möbius strip and projective plane. We find analytically the stationary states and the energy spectrum and show that the wavefunction exhibits perfect revivals. Using the orbifold structure of the discussed manifolds, we establish the relation of wave evolution on the manifolds to Fresnel diffraction and consequently to the Talbot effect. This connection provides a novel method of optical simulation of the quantum motion on compact manifolds. We discuss some novel phenomena as well as the effects of topology on the properties of the waves on the manifolds.

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.