Spatial Bandwidth Research Articles

Nonseparable modulation strategy for channeled spatiotemporal Stokes polarimeters.

Spatiotemporally modulated polarimeters have shown promising imaging performance by leveraging the tradeoff between spatial bandwidth and temporal bandwidth to outperform polarimeters that use spatial or temporal modulation alone. However, the existing separable modulation strategy, in which the spatial carriers are generated independently from the temporal carriers, makes such devices sensitive to the systematic errors of the rotation element inevitably. In this paper, we propose two novel strategies that have spatiotemporal modulation that is inherently mixed. The method enables different elements of the Mueller matrix to be used to create the carriers, reducing the effects of systematic errors in different ways. We present the indepth comparison of the channel structure and the reconstruction accuracy of each modulation strategy in various bandwidth scenarios under the presence of systematic error. Simulation results show that the nonseparable modulation can provide higher reconstruction accuracy of polarimetric information as compared to the separable strategy.

A numerical method of improved bandwidth adaptability for simulating diffraction integral of a spatial light modulator

In order to improve the adaptability of spatial light modulator diffraction analysis method to the research object, Collins–Huygens integral is introduced into spatial light modulator (SLM) diffraction analysis. This paper takes two kinds of hollow vortex light waves as examples to discuss the practicability of the simulation method. When the spatial light modulator is used to control the light wave front, the method can greatly improve the adaptability of various types of wave front as simulation objects. In particular, the diffraction of two different types of “holograms” is analyzed, one is CGH that produces hypergeometric beams with extremely wide spatial spectrum, and the other is CGH that produces Laguerre—Gaussian beams with limited spatial bandwidth. In this paper, the phase extraction method in numerical simulation calculation is discussed in detail, and the diffraction characteristics of phase mask and amplitude mask, such as missing order phenomenon, are verified by the numerical method in this paper. Through the simulation, we find that the method proposed in this paper is an effective simulation analysis method. Its applications range from generating light beams with angular momentum to microscopes to trapping neutral atoms. The method is also extended to other beam shaping components using SLM.

Telecentric in-line-and-off-axis hybrid digital holographic high-resolution reconstruction method

In-line digital holography usually employs a phase retrieval algorithm to decouple the phase information but fails to eliminate the unwanted DC and twin image terms when the measured sample does not agree with the sparsity. While the off-axis digital holography can efficiently remove the unwanted image terms but can not reserve the high frequencies of the sample to realize high resolution. The in-line-and-off-axis hybrid digital holography was then developed to provide a relatively high resolution digital holographic imaging without considering the effect of the unwanted terms. In other words, the in-line-and-off-axis hybrid digital holography merges all of the best virtues of the mentioned-above methods in an efficient and elegant way. However, this state-of-the-art method requires prior knowledge about the diffraction distance, which results in time-consuming and low accuracy. In other sense, telecentric technology can realize non-diffractive imaging without the knowledge about the diffraction distance or spherical aberration or defocusing aberration. Therefore, in this paper, a novel in-line-and-off-axis hybrid digital holography is proposed by introducing telecentric imaging architecture, and the corresponding reconstruction method is further proposed by utilizing constrained iterative approach. In this method, telecentric in-line-and-off-axis hybrid digital holography is first used to acquire focused off-axis and in-line holograms, respectively. The low resolution phase information is reconstructed from the off-axis hologram by using Fourier transform method with the help of the sample-free off-axis hologram, and then multiplexed with the amplitude information obtained from the in-line hologram to act as the initial complex amplitude in the iterative recovery process. As a result, constrained iterations are carried out in the spatial domain and frequency domain to realize high resolution and high speed reconstruction. After simulations, we build an experimental setup and demonstrate the operation of the method with USAF resolution target, onion cells and bee wings. Both the simulation and experimental results show that the proposed method can require no prior knowledge to suppress the phase disturbance caused by the unwanted image terms and optical aberrations, resulting in high speed and full utilization of spatial bandwidth product of the digital camera to yield high resolution reconstruction. We hope that the proposed method will have most practical applications in the case where large resolution, high speed and good quality are needed.

A spatiotemporal weighted regression model (STWR v1.0) for analyzing local nonstationarity in space and time

Abstract. Local spatiotemporal nonstationarity occurs in various natural and socioeconomic processes. Many studies have attempted to introduce time as a new dimension into a geographically weighted regression (GWR) model, but the actual results are sometimes not satisfying or even worse than the original GWR model. The core issue here is a mechanism for weighting the effects of both temporal variation and spatial variation. In many geographical and temporal weighted regression (GTWR) models, the concept of time distance has been inappropriately treated as a time interval. Consequently, the combined effect of temporal and spatial variation is often inaccurate in the resulting spatiotemporal kernel function. This limitation restricts the configuration and performance of spatiotemporal weights in many existing GTWR models. To address this issue, we propose a new spatiotemporal weighted regression (STWR) model and the calibration method for it. A highlight of STWR is a new temporal kernel function, wherein the method for temporal weighting is based on the degree of impact from each observed point to a regression point. The degree of impact, in turn, is based on the rate of value variation of the nearby observed point during the time interval. The updated spatiotemporal kernel function is based on a weighted combination of the temporal kernel with a commonly used spatial kernel (Gaussian or bi-square) by specifying a linear function of spatial bandwidth versus time. Three simulated datasets of spatiotemporal processes were used to test the performance of GWR, GTWR, and STWR. Results show that STWR significantly improves the quality of fit and accuracy. Similar results were obtained by using real-world data for precipitation hydrogen isotopes (δ2H) in the northeastern United States. The leave-one-out cross-validation (LOOCV) test demonstrates that, compared with GWR, the total prediction error of STWR is reduced by using recent observed points. Prediction surfaces of models in this case study show that STWR is more localized than GWR. Our research validates the ability of STWR to take full advantage of all the value variation of past observed points. We hope STWR can bring fresh ideas and new capabilities for analyzing and interpreting local spatiotemporal nonstationarity in many disciplines.

Accelerating and Decelerating Space-Time Optical Wave Packets in Free Space.

Although a plethora of techniques are now available for controlling the group velocity of an optical wave packet, there are very few options for creating accelerating or decelerating wave packets whose group velocity varies controllably along the propagation axis. Here we show that "space-time" wave packets in which each wavelength is associated with a prescribed spatial bandwidth enable the realization of optical acceleration and deceleration in free space. Endowing the field with precise spatiotemporal structure leads to group-velocity changes as high as ∼c observed over a distance of ∼20 mm in free space, which represents a boost of at least ∼4 orders of magnitude over X waves and Airy pulses. The acceleration implemented is, in principle, independent of the initial group velocity, and we have verified this effect in both the subluminal and superluminal regimes.

Phase matching in two-dimensional coherent Raman imaging

Coherent anti-Stokes Raman scattering (CARS) is a valuable spectroscopic tool for the measurement of temperature and species concentration. In recent years, multi-dimensional CARS has seen focused development and is especially important in reacting flows. An important aspect of multi-dimensional CARS is the phase-matching scheme used. Historically, collinear and BOXCARS phase-matching schemes have been used to achieve phase matching over a broad spectral range. For 1-D and 2-D CARS imaging, two-beam or counter-propagating beam arrangements are necessary. The two-beam arrangement offers many advantages, but introduces a phase mismatch which limits the spectral response of the measurement. This work explores the tradeoffs in spatial resolution, spectral bandwidth, and CARS intensity in 2-D CARS arrangements. Calculations are made for two-beam and counter-propagating beam CARS.

Probing hepatic metabolism of [2-13C]dihydroxyacetone in vivo with 1H-decoupled hyperpolarized 13C-MR

ObjectivesTo enhance detection of the products of hyperpolarized [2-13C]dihydroxyacetone metabolism for assessment of three metabolic pathways in the liver in vivo. Hyperpolarized [2-13C]DHAc emerged as a promising substrate to follow gluconeogenesis, glycolysis and the glycerol pathways. However, the use of [2-13C]DHAc in vivo has not taken off because (i) the chemical shift range of [2-13C]DHAc and its metabolic products span over 144 ppm, and (ii) 1H decoupling is required to increase spectral resolution and sensitivity. While these issues are trivial for high-field vertical-bore NMR spectrometers, horizontal-bore small-animal MR scanners are seldom equipped for such experiments.MethodsReal-time hepatic metabolism of three fed mice was probed by 1H-decoupled 13C-MR following injection of hyperpolarized [2-13C]DHAc. The spectra of [2-13C]DHAc and its metabolic products were acquired in a 7 T small-animal MR scanner using three purpose-designed spectral-spatial radiofrequency pulses that excited a spatial bandwidth of 8 mm with varying spectral bandwidths and central frequencies (chemical shifts).ResultsThe metabolic products detected in vivo include glycerol 3-phosphate, glycerol, phosphoenolpyruvate, lactate, alanine, glyceraldehyde 3-phosphate and glucose 6-phosphate. The metabolite-to-substrate ratios were comparable to those reported previously in perfused liver.DiscussionThree metabolic pathways can be probed simultaneously in the mouse liver in vivo, in real time, using hyperpolarized DHAc.

A Filter Theory Approach to the Synthesis of Capacitive Power Transfer Systems

Resonant-coupled wireless power transfer (WPT) systems are typically modeled as circuits with inductively or capacitively coupled resonators. In a two-resonator system, the transmit and receive resonators are linked by a coupling coefficient, and the coupling can be adjusted for critical coupling, overcoupling, and undercoupling. In this work, we show that the coupled-resonator structure is equivalent to a filter structure and provide a demonstration of how filter theory can be used to design a capacitive WPT system. An advantage of this approach is that it provides access to a wide range of canonical structures and methods of impedance scaling to realize matched links. We show a maximally flat filter has a critically coupled response and an equiripple Chebychev filter has an overcoupled response. There is a relationship between frequency bandwidth in a filter design and spatial bandwidth in a WPT link. Therefore, the filter context can be used to synthesize wideband filters that are more robust to spatial variation than narrowband filters.

3-D Short-Range Imaging With Irregular MIMO Arrays Using NUFFT-Based Range Migration Algorithm

3-D imaging with irregular planar multiple-input-multiple-output (MIMO) arrays is discussed. Due to signal acquisition on irregular spatial sampling grids by using these antenna arrays, the fast Fourier transform (FFT)-based imaging algorithms cannot readily be used for image formation. To avoid the application of computationally intensive coherent summation algorithms such as filtered backprojection or Kirchhoff migration, we propose a nonuniform FFT (NUFFT)-based MIMO Range Migration Algorithm (i.e., NUFFT-based MIMO-RMA) for efficient microwave imaging. The algorithm exploits NUFFT to reconstruct the wavenumber–domain spectra related to each Fourier frequency. It is generic and applicable to 3-D imaging with irregular planar MIMO arrays. The effects of irregular spatial sampling and signal bandwidth on the imaging performance and computational efficiency of the proposed algorithm are analyzed. Finally, some numerical simulations and experimental results are presented to demonstrate the performance of the proposed imaging algorithm.

Can Abbe theory of image formation be improved ?

Abbe theory of image formation can be expanded from two-dimensional to three-dimensional space. It has to consider an optical system that forms an image of a grating in an object space. It is possible to introduce various inclinations of this grating relatively the optical axis round the axis in the object plane that is parallel to its slits. In this case, the minimum resolvable period and the corresponded spatial cut off frequency of the optical system may be calculated as the functions of the angle of grating inclination, the numerical apertures and the wavelength using the idea of Abbe theory. In case of axial symmetry of the optical system, the function for calculation of the spatial cut off frequencies describes a surface in the three-dimensional space of spatial frequencies that covers the three-dimensional spatial bandwidth. The spatial harmonics with spatial frequencies inside this spatial bandwidth can pass through an optical system and they participate in formation of three-dimensional images. The other spatial harmonics cannot pass through it. This approach makes understanding and explanation of formation of three-dimensional images clearer, faster and logically completed.

Polarimetric Semivariogram-Based Spatial Scale Selection for PolSAR Image Segmentation With Mean-Shift Algorithm

Image segmentation has been an important procedure in object-based image analysis (OBIA), which takes image object as a processing unit. The spatial scale in image segmentation has great importance in OBIA. Due to the high heterogeneity and large dynamic range of polarimetric synthetic aperture radar (PolSAR) images, it is often difficult to choose optimal spatial scales. This letter proposes a polarimetric semivariogram-based spatial scale selection method for PolSAR image segmentation. The optimal spatial bandwidth parameter in the mean-shift algorithm is pre-estimated based on the combined polarimetric and statistical analysis of PolSAR images. By implementing a quantitative evaluation of segmentation result, the effectiveness of the proposed method in optimal spatial bandwidth selection for PolSAR image segmentation is verified. Experiments on both the EMISAR and UAVSAR L-band PolSAR data sets testify the validity of the proposed adaptive optimal bandwidth selection strategy for PolSAR images.

Structured decomposition of a multi-snapshot nine-reconstructables Mueller matrix polarimeter.

Snapshot channeled polarimeters forgo temporal modulation in favor of modulating polarization information in either space or wavenumber. We have recently introduced methodologies for describing both channeled and partial polarimeters. In this paper, we focus on the nine-reconstructables design, which limits the resolution loss by reducing the number of carriers. The architecture offers a number of favorable trade-offs: a factor of 5.44 increase in spatial bandwidth or a factor of 3.67 increase in spectral bandwidth, for a smaller amount of temporal bandwidth loss as dictated by the number of snapshots taken. The multi-snapshot structured decomposition given here allows one to analytically shape the measured space with optimal noise characteristics and minimum system complexity. A two-snapshot system can measure a premeditated set of 14 reconstructables; we provide the null space for the subset of optimal systems that also achieve better SNR than the baseline single-snapshot system. A three-snapshot system can measure all 16 Mueller elements while offering an overall 26.3% or 50.4% better bandwidth-SNR figure of merit for the spectral and spatial systems, respectively. Finally, four-snapshot systems provide diminishing returns, but may be more implementable.

Optical analog computing of spatial differentiation and edge detection with dielectric metasurfaces.

We propose and demonstrate that optical analog computing of spatial differentiation and edge detection can be realized with a single layer of dielectric metasurface. The optical transfer function for second-order derivation is obtained by engineering the spatial dispersion of electric dipole resonance supported by the silicon nanodisks in the metasurface. Benefiting from this unique mechanism of electric dipole resonance, spatial differentiation can be performed for two dimensions and arbitrary polarization with a large spatial bandwidth and high efficiency at the visible wavelength. Explicitly, we have numerically validated the application with one-dimensional spatial functions as well as an image, and the results show excellent performance. Our study can facilitate the research of optical computing with artificial nanostructures.

A Spatiotemporal Analysis of the Effects of Urbanization’s Socio-Economic Factors on Landscape Patterns Considering Operational Scales

Landscape patterns are significantly affected during the urbanization process. Identifying the spatiotemporal impacts of urbanization’s socio-economic factors on landscape patterns is very important and can provide scientific evidence to support urban ecological management and guide managers to establish appropriate sustainability policies. This article applies multiscale geographically weighted regression (MGWR) to reveal the relationships between landscape patterns and the socio-economic factors of urbanization in Shenzhen, China, from 2000 to 2015, in five-year intervals. MGWR is a powerful extension of geographically weighted regression (GWR) that can not only reveal spatial heterogeneity patterns but also measure the operational scale of covariates. The empirical results indicate that MGWR is superior to GWR. Furthermore, the changes in operational scale represented by the spatial bandwidth of MGWR in different years reflect temporal changes in the spatial relationships of given factors, which is significant information for urban studies. These multiscale relationships between landscape patterns and the socio-economic factors of urbanization, revealed via MGWR, are useful for strategic planning around urban dynamic development and land resource and ecological landscape management. The results can provide additional insight into landscape and urbanization studies from a multiscale perspective, which is important for local, regional, and global urban planning.

The Limits of Effective Degrees of Freedom in UCA based Orbital Angular Momentum Multiplexed Communications

Orbital angular momentum (OAM) multiplexing technique has recently emerged and generated widespread interests since the OAM was discovered as a property of electromagnetic wave and acoustic wave. It was widely acknowledged that OAM multiplexing can achieve very high effective degrees of freedom (EDOF) and improve the spectral efficiency in optical, radio and acoustic communications. However, in the field of free-space optical (FSO) communications, it was demonstrated that OAM multiplexing is not the optimal multiplexing technique and the spatial bandwidth product (SBP) limits the EDOF. Is there any EDOF limits of OAM multiplexing in radio and acoustic communications? Could OAM multiplexing be safely scaled to far field? Here, we discover that the azimuthal resolution of OAM mode generator in OAM multiplexing limits its EDOF. Furthermore, we also verify that the OAM multiplexing in radio and acoustic communication fails to enable a long distance transmission and high EDOF simultaneously incurred by the inherently imperfect OAM mode generator.

Single SH guided wave mode generation method for PPM EMATs**Project supported by the National Natural Science Foundation of China (Grant No. 51977044).

Using periodic permanent magnet (PPM) electromagnetic acoustic transducers (EMATs), different shear horizontal (SH) guided wave modes can form simultaneously in some situations, which can interfere with the inspection. The main cause of this phenomenon (typically named multiple modes) is related to the frequency bandwidth of excitation signals and the transducer spatial bandwidth. Simply narrowing the frequency bandwidth cannot effectively limit the number of different SH modes. Previous researches showed that unnecessary SH wave modes can be eliminated by using dual EMATs. However, in practical applications, it is more convenient to change the excitation frequency than to use dual EMATs. In this paper, the stress boundary conditions of the PPM-EMAT are analyzed, the analytical expression of SH guided wave is established, and the magnitude of SH guided wave mode under continuous tone and tone-burst input is obtained. A method to generate a single SH mode by re-selecting an operating point is proposed. Furthermore, the influence of the frequency bandwidth of the tone-burst signal is analyzed. Finally, a single SH mode excitation is achieved with tone-burst input.

Adaptive and efficient Fourier ptychographic microscopy based on information entropy

Fourier ptychographic microscopy is a simple and effective computational imaging method that improves the spatial bandwidth product of the system. Its principle is to realize the aperture expansion by using a phase retrieval algorithm to splice a set of low-resolution images under different illumination angles in the Fourier domain. However, the long periods of time required for the data acquisition limit its application. Therefore, we propose a new adaptive FP algorithm to significantly reduce the volume of data acquired using the information entropy of the image as a judgment function, and a special separation strategy as a judgment method to estimate the information distribution of a high-resolution sample from a specific low-resolution image. Further, the effectiveness and superiority of our method are verified via simulations and experiments. The results show that the volume of data acquired can be reduced by more than 60% without any deterioration in resolution and quality of the recovered image.

400 m rolling-shutter-based optical camera communications link

In this Letter, we develop a novel technique, to the best of our knowledge, to increase the link span ($ {L_s} $Ls) of a rolling shutter (RS)-based optical camera communications (OCC) system by reducing the spatial bandwidth of the camera in the out-of-focus regions. We demonstrate a 400 m line-of-sight RS-based OCC link, which is to date the longest $ {L_s} $Ls reported in these systems, and develop a detection method to extract the information out of the video frames, successfully. The proposed system relaxes the condition of a large surface area for the transmitter light source. Consequently, we show that at 400 m $ {L_s} $Ls and exposure times of 100-80 µs, a data rate of 450 bps is achieved successfully.

Numerical Method for Horizontal and Vertical Spatial Resolutions of Seismic Acquisition Geometries in Complex 3D Media

Spatial sampling, finite bandwidth, and overlying-strata shielding are three key issues to affect the spatial resolution of seismic imaging for deep targets. Some factors have a great impact on the horizontal resolution, whereas others influence the vertical resolution. How to quantify these effects remains controversial for complex media. Most previous studies on seismic acquisition geometries focus on the horizontal resolution for layered media but neglecting to measure the vertical resolution especially in complex media. Conventional criteria for vertical resolution are based on the theory of geometric seismology with the assumption of a simple medium. As a practical alternative for resolution estimation in complex media, numerical methods with wavefield extrapolation for focal-beam analysis can provide comprehensive insight into the combined effect of acquisition geometries, bandlimited frequencies, and complex media on the horizontal and vertical spatial resolutions of acquisition geometries. We incorporate some classic criteria into the focal-beam numerical analysis to measure the spatial resolutions. Four parameters are used to quantify the performance of acquisition geometries. The horizontal (vertical) resolution is defined as the main-lobe width of a focal beam along the horizontal (vertical) direction, whereas the square root of the peak-to-total ratio of energies is referred to as the horizontal (vertical) sharpness. These parameters describe the horizontal and vertical spatial resolution and sharpness to image the target. Numerical examples with typical acquisition geometries demonstrate the performance of numerical resolution analyses in complex media.

Implementation of 10-Bit Phase Modulation for Phase-Only LCOS Devices Using Deep Learning

A deep learning model was built to optimize the phase flicker performance for given pulse width modulation (PWM) driving patterns of a liquid crystal on silicon (LCOS) device. 10-bit phase modulation was physically realized with a phase flicker of 0.055% over 1024 addressed phase levels in respect to the total modulation range of 2 π and a separation probability of 62.63% for the phase to stay within its level without overlapping with the adjacent ones. The spatial information bandwidth of the full high-definition (HD) LCOS device at 100 Hz was improved by 25%, from ~1.6 Gb/sec to ~2 Gb/sec.