Spectral Plane Research Articles

A spectral analysis of the nonlinear Schrödinger equation in the co-exploding frame

The nonlinear Schrödinger model is a prototypical dispersive wave equation that features finite time blowup, either for supercritical exponents (for fixed dimension) or for supercritical dimensions (for fixed nonlinearity exponent). Upon identifying the self-similar solutions in the so-called “co-exploding frame”, a dynamical systems analysis of their stability is natural, yet is complicated by the mixed Hamiltonian-dissipative character of the relevant frame. In the present work, we study the spectral picture of the relevant linearized problem. We examine the point spectrum of 3 eigenvalue pairs associated with translation, U(1) and conformal invariances, as well as the continuous spectrum. We find that two eigenvalues become positive, yet are attributed to symmetries and are thus not associated with instabilities. In addition to a vanishing eigenvalue, 3 more are found to be negative and real, while the continuous spectrum is nearly vertical and on the left-half (spectral) plane. The eigenfunctions and eigenvalues are approximated both asymptotically and numerically, with good agreement between the two approaches. The non-Hamiltonian nature of the co-exploding system results in the 3 eigenvalue pairs failing to be equal-and-opposite by an exponentially small amount. A projection method is used to evaluate this small correction, and at the same time explains the subtle effects of finite boundaries and their role in the observed weak eigenvalue oscillations.

Recognition of the Bare Soil Using Deep Machine Learning Methods to Create Maps of Arable Soil Degradation Based on the Analysis of Multi-Temporal Remote Sensing Data

The detection of degraded soil distribution areas is an urgent task. It is difficult and very time consuming to solve this problem using ground methods. The modeling of degradation processes based on digital elevation models makes it possible to construct maps of potential degradation, which may differ from the actual spatial distribution of degradation. The use of remote sensing data (RSD) for soil degradation detection is very widespread. Most often, vegetation indices (indicative botany) have been used for this purpose. In this paper, we propose a method for constructing soil maps based on a multi-temporal analysis of the bare soil surface (BSS). It is an alternative method to the use of vegetation indices. The detection of the bare soil surface was carried out using the spectral neighborhood of the soil line (SNSL) technology. For the automatic recognition of BSS on each RSD image, computer vision based on deep machine learning (neural networks) was used. A dataset of 244 BSS distribution masks on 244 Landsat 4, 5, 7, and 8 scenes over 37 years was developed. Half of the dataset was used as a training sample (Landsat path/row 173/028). The other half was used as a test sample (Landsat path/row 174/027). Binary masks were sufficient for recognition. For each RSD pixel, value “1” was set when determining the BSS. In the absence of BSS, value “0” was set. The accuracy of the machine prediction of the presence of BSS was 75%. The detection of degradation was based on the average long-term spectral characteristics of the RED and NIR bands. The coefficient Cmean, which is the distance of the point with the average long-term values of RED and NIR from the origin of the spectral plane RED/NIR, was calculated as an integral characteristic of the mean long-term values. Higher long-term average values of spectral brightness served as indicators of the spread of soil degradation. To test the method of constructing soil degradation maps based on deep machine learning, an acceptance sample of 133 Landsat scenes of path/row 173/026 was used. On the territory of the acceptance sample, ground verifications of the maps of the coefficient Cmean were carried out. Ground verification showed that the values of this coefficient make it possible to estimate the content of organic matter in the plow horizon (R2 = 0.841) and the thickness of the humus horizon (R2 = 0.8599). In total, 80 soil pits were analyzed on an area of 649 ha on eight agricultural fields. Type I error (false positive) of degradation detection was 17.5%, and type II error (false negative) was 2.5%. During the determination of the presence of degradation by ground methods, 90% of the ground data coincided with the detection of degradation from RSD. Thus, the quality of machine learning for BSS recognition is sufficient for the construction of soil degradation maps. The SNSL technology allows us to create maps of soil degradation based on the long-term average spectral characteristics of the BSS.

A higher-order numerical analysis to study the flow physics and to optimize the design of a short-dwell blade coaters for higher efficiency

Blade coaters are most commonly used for coating of paper and paperboard with higher efficiency. The efficiency of short-dwell blades coaters depends on many factors such as the properties of the coating material, design of the coating reservoir, the types of flow behaviour taking place inside the reservoir, etc. In this work, we have proposed an optimal design of the reservoir to improve the efficiency of short-dwell coaters. The reservoir has been modeled as flow inside a two-dimensional rectangular cavity. Incompressible Navier-Stokes equations in primitive variable formulation have been solved to obtain the flow fields inside the cavity. Spatial derivatives present in the momentum, and continuity equations are evaluated using a sixth-order accurate compact scheme whereas the temporal derivatives are calculated using the fourth-order Runge-Kutta method. The actual rate of convergence of the numerical scheme has been discussed in detail. In addition, the accuracy and stability of the used numerical method are also analysed in the spectral plane with the help of amplification factor and group velocity contour plot. The obtained numerical solutions have been validated with the existing literature. Four different aspect ratio cases (L/H = 3/4,4/3,4/5 and 5/4) have been considered for the simulations including the case of square cavity. It has been observed that L/H = 5/4 case provides best results among all others.

Improving physical parameters estimation in the single-beam multiple-intensity reconstruction

The iterative phase retrieval based on phase diversity technologies can solve the stagnation problem of Gerchberg–Saxton algorithm which performs Fourier transform to iterate back and forth between the object and spectral planes with known constraints. However, the application of phase diversity technologies in iterative phase retrieval methods will bring in multiple physical parameters such as distances or wavelengths. The measured accuracy of these physical parameters will ultimately affect the accuracy of the iterative phase retrieval methods. In this paper, a physical parameters estimation method which has the advantages of high global convergence and local convergence is proposed to improve the accuracy of iterative phase retrieval methods. Meanwhile, this method is introduced in the single-beam multiple-intensity reconstruction (SBMIR), termed PE-SBMIR, and its performance is verified by simulations and experiments. By simulating multiple sets of distance parameters with errors, the retrieved accuracy using PE-SBMIR can be improved by 2–4 orders of magnitude compared with SBMIR. Experimental results show that whether it is an amplitude-type object or phase-type object, the accuracy using PE-SBMIR is significantly higher than using SBMIR. The physical parameters estimation method proposed in this paper may be adopted in other iterative phase retrieval methods using phase diversity technologies.

Quantized classical response from spectral winding topology

Topologically quantized response is one of the focal points of contemporary condensed matter physics. While it directly results in quantized response coefficients in quantum systems, there has been no notion of quantized response in classical systems thus far. This is because quantized response has always been connected to topology via linear response theory that assumes a quantum mechanical ground state. Yet, classical systems can carry arbitrarily amounts of energy in each mode, even while possessing the same number of measurable edge states as their topological winding. In this work, we discover the totally new paradigm of quantized classical response, which is based on the spectral winding number in the complex spectral plane, rather than the winding of eigenstates in momentum space. Such quantized response is classical insofar as it applies to phenomenological non-Hermitian setting, arises from fundamental mathematical properties of the Green’s function, and shows up in steady-state response, without invoking a conventional linear response theory. Specifically, the ratio of the change in one quantity depicting signal amplification to the variation in one imaginary flux-like parameter is found to display fascinating plateaus, with their quantized values given by the spectral winding numbers as the topological invariants.

Optical Aberration Calibration and Correction of Photographic System Based on Wavefront Coding.

The image deconvolution technique can recover potential sharp images from blurred images affected by aberrations. Obtaining the point spread function (PSF) of the imaging system accurately is a prerequisite for robust deconvolution. In this paper, a computational imaging method based on wavefront coding is proposed to reconstruct the wavefront aberration of a photographic system. Firstly, a group of images affected by local aberration is obtained by applying wavefront coding on the optical system’s spectral plane. Then, the PSF is recovered accurately by pupil function synthesis, and finally, the aberration-affected images are recovered by image deconvolution. After aberration correction, the image’s coefficient of variation and mean relative deviation are improved by 60% and 30%, respectively, and the image can reach the limit of resolution of the sensor, as proved by the resolution test board. Meanwhile, the method’s robust anti-noise capability is confirmed through simulation experiments. Through the conversion of the complexity of optical design to a post-processing algorithm, this method offers an economical and efficient strategy for obtaining high-resolution and high-quality images using a simple large-field lens.

Effects of Seismic Incident Directionality on Ground Motion Characteristics and Responses of a Single-Mass Bi-Degree-of-Freedom System

To investigate the variability of ground motion characteristics (GMC) with the angle of seismic incidence (ASI) and the impact of seismic incident directionality on structural responses, first, a large-scale database of recorded ground motions was used to analyze the causes of GMC variability due to the seismic incident directionality effect (SIDE). Then a single-mass bi-degree-of-freedom system (SM-BDOF-S) with different types of symmetrical sections was selected to explore the influence mechanism of SIDE on the seismic responses. The results illustrated that the GMC has substantial variability with the ASI, which is independent of the earthquake source, propagation distance, and site condition, and exhibits complex random characteristics. Additionally, a classification method for ground motions is proposed based on this GMC variability to establish a criterion for selecting ground motions in seismic analysis considering the SIDE. Moreover, for an SM-BDOF-S, the response spectral plane is proposed to explain the transition behavior of spectral responses that are very similar among different stiffness ratios, but divergent for different types of ground motions. The influence of SIDE on structures is determined by their stiffness and stiffness ratio in the [Formula: see text]- and [Formula: see text]-directions, as well as the type of ground motion.

Spectral dimensional correlation and sparse reconstruction model of hyperspectral images

The high dimensionality and redundancy properties of hyperspectral image (HSI) constitute great challenges for transmission and process. Recently, HSI reconstruction based on compressed sensing has received increasing attention and has become a frontier problem. Effectively exploiting the sparse prior of HSI is crucial to improve the reconstruction quality. In this paper, the spectral dimension plane of the HSI band group is defined, and the structural correlation of HSI spectral dimension is studied. The following conclusions can be obtained. First, the texture distribution of the HSI spectral dimension is simpler and more uniform than that of the HIS spatial domain, and its texture exhibits low contrast and high properties, thus simplifying the sparse representation process. Second, in the HSI spectral dimension plane, the search area adjacent to the reference block has a certain number of spectral curve blocks that are highly similar to the reference block. Based on this observation, the structure correlation of the HIS spectral dimension is defined, and a sparse measurement model is proposed. Finally, the sparse model S-SCoSM is proposed by integrating the sparse representation of spatial dimension nonlocal correlation and the spectral dimension structure correlation. The sparse reconstruction model of HSI is constructed using this sparse constrain prior. Experimental results show that by further exploring the correlation of HSI from the viewpoint of spatial and spectral domains, the proposed sparse model S-SCoSM obtains a more adequate and effective HSI sparse constraint prior; hence, the reconstruction quality of HSI is improved. Consequently, the spatial information quality of the reconstructed band image can be effectively improved as well as the spectral attributes of band groups can be well maintained.

Optical multiple-image encryption in discrete multiple-parameter fractional Fourier transform scheme using complex encoding, theta modulation and spectral fusion

We present a novel encryption method for multiple images in a discrete multiple-parameter fractional Fourier transform scheme, using complex encoding, theta modulation and spectral fusion. All pairs of original images are encoded separately into a complex signal. The spectrum of each complex signal can then be scattered into various positions in the spectral plane and multiplexed into one spectral image with a combination of theta modulation and spectral fusion. After Fourier transforming back to the spatial domain, the multiplexed signal is encrypted in the discrete multiple-parameter fractional Fourier transform domain. Information about the original images can only be successfully decrypted given the possession of all correct keys. The parameters of chaotic pixel scrambling for the proposed method enlarge the key space. Moreover, the proposed method solves the crosstalk problem of multiple images and improves the multiplexing capacity. Numerical simulations demonstrate the effectiveness of the proposed method.

Influence of Vertical Heterogeneity of Atmospheric Temperature on the Propagation of Acoustic-Gravity Waves

A new approach to the study of acoustic-gravity waves in the Earth’s atmosphere in the presence of vertical temperature inhomogeneity is proposed. Using this approach, the local AGW dispersion equation was obtained for the atmosphere with a small vertical temperature gradient. The modification of the acoustic and gravitational regions of freely propagating AGWs on the spectral plane $$\left( {\omega ,{{k}_{x}}} \right)$$ depending on the temperature gradient was investigated. It is shown that the acoustic and gravitational regions approach each other with a positive temperature gradient, while the distance between them increases with a negative gradient. On the spectral plane, the indicators of the location of the acoustic and gravitational regions of freely propagating AGWs are the dispersion curves of the non-divergent and inelastic horizontal wave modes. The possibility of overlapping the acoustic and gravitational regions of AGWs in a nonisothermal atmosphere was investigated.

Influence of vertical heterogeneity of the atmosphere temperature on the propagation of acoustic-gravity waves

A new approach to the study of acoustic-gravity waves (AGW) in the Earth’s atmosphere in the presence of a vertical temperature inhomogeneity is proposed. Using this approach, the local AGW dispersion equation is obtained for an atmosphere with a small vertical temperature gradient. The modification of acoustic and gravitational regions of freely propagating AGWs on the spectral plane is studied depending on the temperature gradient. It is shown that, the acoustic and gravitational regions approach each other with a positive temperature gradient and the distance between them increases with a negative gradient. On the spectral plane, the dispersion curves of non-divergent and anelastic horizontal wave modes are the indicators of location of the acoustic and the gravitational regions of freely propagating AGWs. The possibility of overlapping the acoustic and the gravitational regions of AGWs in non-isothermal atmosphere is investigated.

Analysis of Different Scalar Probe Compensation Methods for an Array of Near-Field EMI Probes

This article proposes and analyzes two possible methods to compensate the raw near-field data obtained with an array of near-field probes. The first method is based on the spatial compensation procedure for a single probe and is modified toward an array of probes. The second method is to use standard spectral (plane wave) single-probe compensation. To use the latter, guidelines on how to design an array and modify the overall measurement procedure such that mutual coupling and edge effects have less influence are given. The different methods are tested in simulation and compared with the performance of compensation on a single probe. It is shown that the standard spectral single-probe compensation, in combination with proper array design, will result in an error as low as the same compensation technique used on a single probe. It is also shown that the spatial compensation improves the results in comparison with regular calibration. However, the error is not low enough to be used for postprocessing due to ill-conditioning. This article shows the path to much needed, fast, and accurate near-field measurements.

5G Mixed Mode: NR Multicast-Broadcast Services

This work presents a potential solution for enabling the use of multicast in the 5G New Radio Release 17, called 5G NR Mixed Mode. The proposed multicast/broadcast mode follows one of the two approaches envisaged in 3GPP, which enables a dynamic and seamless switching between unicast and multicast, both in the downlink and the uplink. This paper also provides a performance evaluation of several IMT-2020 KPIs, including available data rate and spectral efficiency, user and control plane latencies, energy efficiency, and mobility, highlighting the potential advantages of this solution over unicast in relevant scenarios. Finally, other multipoint-based KPIs such as coverage or packet loss rate are also evaluated by means of system level simulations.

A HAUNTOLOGICAL ANALYSIS OF DIGITAL MEMORIALIZATION OF THE DEAD

Facebook now allows pages of the deceased to remain active, controlled by immediate family members of a deceased person, as a sort of memorialization or “electronic wake,” (Stokes, 2011). The overall goal of the author is to examine the evolution of the materiality of memorialization and investigate how our human connection with death has changed as our media tools have become untethered from tangible artefact. To explore the links between media, human relationships, and the spectral plane, and how those links might be revelatory in an age of digital media, a hauntological examination of these questions will be endeavored. The basic premise of hauntology, a clever merge of haunting and ontology derived by Jacques Derrida (1993), is that an idea, once tangibly realized and made real in the cultural zeitgeist, is never truly extinguished. Derrida’s hauntology derives from the ontological quest to articulate the nature of being, yet with the added perspective that everything that exists might not have ever lived, and nothing which is past ever really quite dies. This is no more so true than in our heavily mediated age in which written documents, photographs, film, and the Internet are able to capture, record, store—and, as will be discussed—even replicate beingness in physical form. In an age where simulacra parade as true being, and cultural memory of events as accepted historical provenance, perhaps a new perspective on the relationship between being and death is timely.

Multiband optical flux density and polarization microvariability study of optically bright blazars

ABSTRACT We present the results of flux density, spectral index, and polarization intra-night monitoring studies of a sample of eight optically bright blazars, carried out by employing several small to moderate aperture (0.4 to 1.5 m diameter) telescopes fitted with CCDs and polarimeters located in Europe, India, and Japan. The duty cycle of flux variability for the targets is found to be ∼45 per cent, similar to that reported in earlier studies. The computed two-point spectral indices are found to be between 0.65 to 1.87 for our sample, comprised of low- and intermediate-frequency peaked blazars, with one exception: they are also found to be statistically variable for about half the instances where ‘confirmed’ variability is detected in flux density. In the analysis of the spectral evolution of the targets on hourly time-scale, a counterclockwise loop (soft-lagging) is noted in the flux–spectral index plane on two occasions, and in one case a clear spectral flattening with the decreasing flux is observed. In our data set, we also observe a variety of flux–polarization degree variability patterns, including instances with a relatively straightforward anticorrelation, correlation, or counterclockwise looping. These changes are typically reflected in the flux–polarization angle plane: the anticorrelation between the flux and polarization degree is accompanied by an anticorrelation between the polarization angle and flux, while the counterclockwise flux–PD looping behaviour is accompanied by a clockwise looping in the flux–polarization angle representation. We discuss our findings in the framework of the internal shock scenario for blazar sources.

Avenue for apertometer using spectral plane and Fourier correlation analysis.

This Letter proposes a simple and practical approach for numerical aperture measurement of immersion objectives. The basic concept is to generate a reference on the spectral plane and then apply the Abbe sine condition to evaluate the numerical aperture. An extremely cheap, simple but effective and practical example is to locate a coverslip on the focal plane and then record the resulting back focal plane, on which the total internal reflection ring is applied as the reference. To achieve higher repeatability and impose fewer requirements on both the operation procedure and experiment conditions, we propose an algorithm mainly consisting of two-dimensional Fourier correlation analysis and grayscale statistics to automatically identify the radii of total internal reflection and clear aperture. The proposed approach is further applied in the measurement of an objective lens with adjustable pupils when surface plasmon is employed as reference. Experimental verification is provided.

Multifacet echelle grating for intensity broadening on spectral plane fabricated by rotating ion-beam etching.

This paper describes a new type of multifacet echelle grating (MFEG) for use in an echelle spectrometer. This new type of echelle grating broadens the spectral distribution on the spectral plane. We built a geometric model of MFEG to analyze the influence of the blaze angle and number of facet shapes on the spectral evolution. A dual-facet echelle grating and a four-facet echelle grating with different parameters were fabricated by rotating ion-beam etching with a self-shadowing rotating mask, based on the existing single-facet echelle grating (SFEG) with a line density of 52.7 g/mm and a blaze angle of 63.5°. The distributions of diffraction efficiency for different orders were measured with a He-Ne laser (632.8 nm); furthermore, these echelle gratings were applied in an echelle spectrometer (ICP-OES, Plasma2000), and testing spectra were obtained. The experimental results demonstrate that the MFEG can broaden the intensity distribution on the spectral plane, overcoming the weak spectral margin signal of SFEG spectrometers.

Near zone scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with rough interface

ABSTRACTA solution utilizing the spectral plane wave representation of fields (SPRF) combined with the extended boundary condition method (EBCM) is presented to study the scattering and extinction properties of a left handed material cylinder buried in a semi infinite medium with a rough interface. The EBCM is used to evaluate the field transmitted through the interface, which excites the cylinder. The SPRF is used to study the interaction of scattered field from the cylinder with the rough interface. The effect of the negative permittivity and permeability of the cylinder on the far zone scattered field is observed. Further, the near zone scattered field is investigated, which is very helpful to characterize the scenario in which object detection is a challenging task. It is also observed that the electrical size is an important factor affecting the near zone scattered field since the extinction cross section depends upon size.

Scattered field from a PEMC cylinder buried below rough interface using extended boundary condition method

Use of extended boundary condition method (EBCM) and spectral plane wave representation of fields (SPRF) has been done to evaluate the rough surface scattering and the interactions between the perfect electromagnetic conductor (PEMC) cylinder and the rough surface. Expressions of cylindrical waves in terms of plane waves are written in order to calculate the successive reflections and transmission of initial scattered field. First, results obtained by perturbation method and EBCM are compared. Moreover, far zone, near zone and back scattered fields are reported for size and admittance M of the cylinder. Parameter describing the rough surface is also varied to observe the co as well as cross polarized scattered fields. It is observed that the scattering pattern is quite complicated due to many geometrical and physical parameters involved. The effect of parameters on the scattering pattern cannot be described in terms of increase or decrease of the field. Utilizing the formulation, the special case of flat interface and PEC/PMC cylinder can readily be obtained both for transverse magnetic (TM) and transverse electric (TE) polarization states.

Spectral Zooming and Resolution Limits of Spatial Spectral Compressive Spectral Imagers

The recently introduced Spatial Spectral Compressive Spectral Imager (SSCSI) has been proposed as an alternative to carry out spatial and spectral coding using a binary on-off coded aperture. In SSCSI, the pixel pitch size of the coded aperture, as well as its location with respect to the detector array, play a critical role in the quality of image reconstruction. In this paper, a rigorous discretization model for this architecture is developed, based on a light propagation analysis across the imager. The attainable spatial and spectral resolution, and the various parameters affecting them, is derived through this process. Much like the displacement of zoom lens components leads to higher spatial resolution of a scene, a shift of the coded aperture in the SSCSI in reference to the detector leads to higher spectral resolution. This allows the recovery of spectrally detailed datacubes by physically displacing the mask towards the spectral plane. To prove the underlying concepts, computer simulations and experimental data are presented in this paper.