Angular Index Research Articles

Airborne discrete-return LIDAR data in the estimation of vertical canopy cover, angular canopy closure and leaf area index

Remote sensing of forest canopy cover has been widely studied recently, but little attention has been paid to the quality of field validation data. Ecological literature has two different coverage metrics. Vertical canopy cover (VCC) is the vertical projection of tree crowns ignoring within-crown gaps. Angular canopy closure (ACC) is the proportion of covered sky at some angular range around the zenith, and can be measured with a field-of-view instrument, such as a camera. We compared field-measured VCC and ACC at 15° and 75° from the zenith to different LiDAR (Light Detection and Ranging) metrics, using several LiDAR data sets and comprehensive field data. The VCC was estimated to a high precision using a simple proportion of canopy points in first-return data. Confining to a maximum 15° scan zenith angle, the absolute root mean squared error (RMSE) was 3.7–7.0%, with an overestimation of 3.1–4.6%. We showed that grid-based methods are capable of reducing the inherent overestimation of VCC. The low scan angles and low power settings that are typically applied in topographic LiDARs are not suitable for ACC estimation as they measure in wrong geometry and cannot easily detect small within-crown gaps. However, ACC at 0–15° zenith angles could be estimated from LiDAR data with sufficient precision, using also the last returns (RMSE 8.1–11.3%, bias –6.1–+4.6%). The dependency of LiDAR metrics and ACC at 0–75° zenith angles was nonlinear and was modeled from laser pulse proportions with nonlinear regression with a best-case standard error of 4.1%. We also estimated leaf area index from the LiDAR metrics with linear regression with a standard error of 0.38. The results show that correlations between airborne laser metrics and different canopy field characteristics are very high if the field measurements are done with equivalent accuracy.

NUMERICAL TREATMENT OF THIN ACCRETION DISK DYNAMICS AROUND ROTATING BLACK HOLES

In the present study, we perform the numerical simulation of a relativistic thin accretion disk around the nonrotating and rapidly rotating black holes using the general relativistic hydrodynamic code with Kerr in Kerr–Schild coordinate that describes the central rotating black hole. Since the high energy X-rays are produced close to the event horizon resulting the black hole–disk interaction, this interaction should be modeled in the relativistic region. We have set up two different initial conditions depending on the values of thermodynamical variables around the black hole. In the first setup, the computational domain is filled with constant parameters without injecting gas from the outer boundary. In the second, the computational domain is filled with the matter which is then injected from the outer boundary. The matter is assumed to be at rest far from the black hole. Both cases are modeled over a wide range of initial parameters such as the black hole angular momentum, adiabatic index, Mach number and asymptotic velocity of the fluid. It has been found that initial values and setups play an important role in determining the types of the shock cone and in designating the events on the accretion disk. The continuing injection from the outer boundary presents a tail shock to the steady state accretion disk. The opening angle of shock cone grows as long as the rotation parameter becomes larger. A more compressible fluid (bigger adiabatic index) also presents a bigger opening angle, a spherical shock around the rotating black hole, and less accumulated gas in the computational domain. While results from [J. A. Font, J. M. A. Ibanez and P. Papadopoulos, Mon. Not. R. Astron. Soc.305 (1999) 920] indicate that the tail shock is warped around for the rotating hole, our study shows that it is the case not only for the warped tail shock but also for the spherical and elliptical shocks around the rotating black hole. The warping around the rotating black hole in our case is much smaller than the one by [J. A. Font, J. M. A. Ibanez and P. Papadopoulos, Mon. Not. R. Astron. Soc.305 (1999) 920], due to the representation of results at the different coordinates. Contrary to the nonrotating black hole, the tail shock is slightly warped around the rotating black hole. The filled computational domain without any injection leads to an unstable accretion disk. However much of it reaches a steady state for a short period of time and presents quasi-periodic oscillation (QPO). Furthermore, the disk tends to loose mass during the whole dynamical evolution. The time-variability of these types of accretion flowing close to the black hole may clarify the light curves in Sgr A*.

Tailoring light structures using an off-axis double axicon holographic pattern

We propose a new method for tailoring light structures using a double axicon holographic pattern. The light structure can be tailored using pairs of Bessel modes with different angular momentum indices, and changed into an optical wheel by combining two copropagating Bessel beams. We also demonstrated that the optical wheel obtained from a pair of Bessel beams had rotation feature over the propagation distance by introducing different axial wavenumbers between the two modes.

Improving Clumping and LAI Algorithms Based on Multiangle Airborne Imagery and Ground Measurements

Measurements at more than one angle capture the directional anisotropy of solar radiance reflected from vegetated surfaces. According to our recent research, we propose that the best two view angles for vegetation structural mapping are the following: 1) the hotspot, where the Sun and view directions coincide, and 2) the darkspot, where the sensor sees the maximum amount of vegetation structural shadows. The Normalized Difference between Hotspot and Darkspot (NDHD), an angular index generated from Compact Airborne Spectrographic Imager (CASI) data, is found to be highly correlated with the field-measured foliage clumping index. The foliage clumping index characterizes the nonrandomness in the spatial distribution pattern of leaves. It is of comparable importance as the leaf area index (LAI) for quantifying radiation interception and distribution in plant canopies, and it also affects estimated LAI mapping using remote sensing data. As the clumping index can vary considerably within a cover type, it is highly desirable to map its spatial distribution for various ecological applications. We have generated clumping index maps based on the previous algorithms and empirical relationships between field-measured ? and CASI-derived NDHD. Through intensive validation using field data, we demonstrate that the combination of the hotspot and darkspot reflectances has the strongest response to changes in vegetation structure. Two crown structural characteristics, namely, crown height and within-crown density, are major factors that impact the NDHD and clumping index difference between the mature and young (regrowth) coniferous forests. The study area is located near Sudbury in the northern Ontario, Canada.

Predicting leaf area index in wheat using angular vegetation indices derived from in situ canopy measurements

Canopy structure significantly affects ecosystem function by influencing light attenuation, and thus there is a great need to characterize changes in canopy structural attributes such as leaf area index (LAI). This study presents an evaluation of a set of anisotropic vegetation indices (VIs) used in the estimation of LAI in the growth cycle of wheat. An analytical two-layer canopy reflectance model (ACRM) was used to simulate a range of bidirectional reflectance with different LAI variations and view zenith angles (VZAs). A number of indices, including the normalized difference vegetation index (NDVI), the enhanced vegetation index (EVI), the hot spot - dark spot index (HDS), the hot spot – dark spot NDVI (NDVIHD), and a new proposed hot spot – dark spot difference index (HDDI), were selected and compared for linearity with increasing LAI in the sensitivity study. Simulation results indicated that EVI was a better candidate than NDVI for LAI estimation in linearity. HDS560 and HDS670 showed nonmonotonical patterns with increasing LAI, and better resistance to saturation limits was observed for both HDS750 and HDS870. Indices of NDVIHD (NDVIHD870 and NDVIHD750) were found to have low sensitivity at high LAI values, with a clear saturation for LAI values above 3. For the two new angular indices, HDDI705 was found to have a relatively linear relationship in an LAI range of 1–5. HDDI750 showed the best linear relationship with LAI, and no saturation was observed for LAI values in the range 1–8. A validation study was conducted for the growth cycle of two types of wheat. NDVI and EVI showed reasonable potential in the estimation of LAI, with determination coefficients R2 of 0.68 and 0.78, respectively, and corresponding root mean square errors (RMSE in LAI units) of 0.79 and 0.66. Band selection was demonstrated to have significant effects on HDS indices. HDS560 showed a very low correlation with LAI (R2 = 0.40, RMSE = 0.85), and no correlation was found between HDS670 and LAI. However, both HDS750 and HDS870 can provide moderate estimates of LAI, with R2 values of 0.76 and 0.73, respectively, and corresponding RMSE values of 0.61 and 0.65. For the NDVIHD indices, low determination coefficients R2 of 0.51 and 0.47 were obtained (RMSE = 0.81 and 0.88). For the two new angular indices, significant correlations (R2 = 0.84 and 0.85, respectively, and RMSE = 0.48 and 0.45) were observed for HDDI705 and HDDI750. These preliminary results provide certain insights for the development of future multi-angle remote sensing models for LAI estimation with satellite observations in other ecosystems.

Experimental generation of Laguerre-Gaussian beam using angular diffraction of binary phase plate

A phase plate was fabricated on a quartz crystal using ion beam etching technique with a predesigned angular phase mask, which can modulate the phase of light illuminating the phase plate by 0 and π rad. Analyzed the field distribution of the diffracted light by angular diffraction theory, which shows the resulting beam is a superposition of two Laguerre-Gaussian(LG) beams with opposite topological charges. Illuminating the phase plate using the expanded beam with diameter 4 mm generates the superposition of two LG beams with the same radian index p=0 and opposite angular index l=20 and l=-20 By increasing the aperture of the illuminating beam, LG beam with higher p index can be acquired, while the l index remains opposite.

Refinement of a formula for decay after weak coherent excitation of a sphere

Abstract A new formula has been given recently by A.A. Svidzinsky and M.O. Scully to describe the temporal evolution of the excitation function β t , r → in a large sphere satisfying the Markov condition after excitation by a single photon. This formula is based on a physically reasonable Ansatz from which differential equations are inferred for the undetermined radial functions in the Ansatz. The solution to these differential equations leads to the formula for β. Numerical calculations from this formula yield a value ∼10% for the maximum probability of occupancy of secondary excited states. In this paper, we refine the formula of Svidzinsky and Scully by allowing the radial functions in the Ansatz to depend on the angular index l of the spherical Bessel functions. By using the Debye formula for the asymptotic behavior of j l ( u ) for large l as well as u, we obtain differential equations in each angular sector, similar to theirs but with a dependence on l. The solution to these equations yields our improved formula, from which we calculate 17.1% for the maximum probability of secondary excited states.

Electrostatically Confined Quantum Rings in Bilayer Graphene

We propose a new system where electron and hole states are electrostatically confined into a quantum ring in bilayer graphene. These structures can be created by tuning the gap of the graphene bilayer using nanostructured gates or by position-dependent doping. The energy levels have a magnetic field (B(0)) dependence that is strikingly distinct from that of usual semiconductor quantum rings. In particular, the eigenvalues are not invariant under a B(0) --> -B(0) transformation and, for a fixed total angular momentum index m, their field dependence is not parabolic, but displays two minima separated by a saddle point. The spectra also display several anticrossings, which arise due to the overlap of gate-confined and magnetically confined states.

Continuous monitoring of nearest neighbors on land surface

As geo-realistic rendering of land surfaces is becoming commonplace in geographical information systems (GIS), games and online Earth visualization platforms, a new type of k Nearest Neighbor (kNN) queries, "surface" k Nearest Neighbor (skNN) queries, has emerged and been investigated recently, which extends the traditional kNN queries to a constrained third dimension (i.e., land surface). All existing techniques, however, assume a static environment, limiting their utility in emerging applications (e.g., Location-based Services) where objects move. In this paper, for the first time, we propose two exact methods that can continuously answer skNN queries in a highly dynamic environment which allows for arbitrary movements of data objects. The first method, inspired by the existing techniques in monitoring kNN in road networks [7] maintains an analogous counterpart of the Dijkstra Expansion Tree on land surface, called Surface Expansion Tree (SE-Tree). However, we show the concept of expansion tree for land surface does not work as SE-tree suffers from intrinsic defects: it is fat and short, and hence does not improve the query efficiency. Therefore, we propose a superior approach that partitions SE-Tree into hierarchical chunks of pre-computed surface distances, called Angular Surface Index Tree (ASI-Tree). Unlike SE-tree, ASI-Tree is a well balanced thin and tall tree. With ASI-Tree, we can continuously monitor skNN queries efficiently with low CPU and I/O overheads by both speeding up the surface shortest path computations and localizing the searches. We experimentally verify the applicability and evaluate the efficiency of the proposed methods with both real world and synthetic data sets. ASI-Tree consistently and significantly outperforms SE-Tree in all cases.

Aggregate Morphology Affecting Strength and Permanent Deformation Behavior of Unbound Aggregate Materials

This paper presents findings of a research study focused on investigating influences of coarse aggregate morphologies on the strength and permanent deformation behavior of unbound aggregate materials. Angularity and surface texture properties of six different types of aggregates were evaluated using two shape indices, angularity index (AI) and surface texture index (ST), based on image analysis. Twenty-one unbound aggregate blends having the same gradation and voids content but different crushed percentages were prepared by mixing the imaging evaluated aggregates and tested using triaxial tests for strength and permanent deformation. The laboratory permanent strain—load application ( ep –N) curves evaluated using a phenomenological power model showed the A and b parameters to be heavily dependent on applied stress levels. Aggregate blends with higher AI and ST indices were consistently associated with lower magnitudes of A and b . The angularity property was found to contribute mainly to the strength and ...

Reply to: “Comment on: ‘Effects of including the counterrotating term and virtual photons on the eigenfunctions and eigenvalues of a scalar photon collective emission theory’ [Phys. Lett. A 372 (2008) 2514]” [Phys. Lett. A 372 (2008) 5732

We compute the emission amplitude for the collective emission from a sphere of identical atoms in the scalar photon theory for both the cases of the complex kernel (i.e. including virtual photons) and real kernel. We explicitly show that the single mode theory based on the real kernel neglects the effects of the different decay rates and frequency shifts associated with the eigenfunctions belonging to the same angular index but with different radial indices. We show that these effects modify, for k 0 R ≫ 1 , both the time dependence of the emission amplitude and its angular distribution, in clear contradiction to the assertions made by the Comment's authors.

Development of Ultra Precision Gear Measuring Instrument/UPGMI

The object of this paper is to describe the process and current status of the development project of an Ultra Precision Gear Measuring Instrument that guarantees a measurement accuracy that falls into a submicron range. The angular indexing mechanism, which is the basis of its measurement accuracy, consists of a purely mechanical system. The system is based on the concept of accuracy feedback where its own deviation estimated from measurement results is fed back into the finishing process. It consists of basic axes with minimum error causing factors in order to seek the optimum accuracy that can be achieved by precision machinery. The measurement accuracy of this measuring instrument has already reached the submicron range in its initial assembly state.

Dinuclear copper complexes with cyanamide derivatives as bridging ligands

Three mixed-valence copper complexes [{Cu(phen) 2} 2(μ-L)](PF 6) 2 (where phen = 1,10-phenanthroline, L = 1,4-dicyanamidobenzene (dicyd)), 1,4-dicyanamido-2,5-dimethylbenzene (Me 2dicyd) and 1,4-dicyanamido-2,5-dichlorobenzene (Cl 2dicyd), and one dinuclear Cu(II) complex [{Cu(phen) 2} 2(μ-apc)](PF 6) 3 (where apc = monoanion of 4-azo(phenylcyanamido)benzene) have been prepared and characterized by elemental analysis, IR and electronic absorption spectroscopies and cyclic voltammetry. [{Cu(phen) 2} 2(μ-apc)](PF 6) 3 · 2CH 3COCH 3 crystallized in the triclinic system and both five-coordinate Cu(II) ions in the dinuclear unit are linked through a bridging 4-azo(phenylcyanamido)benzene (apc) ligand. The cyanamide group (NCN) of the bridging ligand is coordinated to Cu(II) ions through the cyano-nitrogen and amido-nitrogen. The bond length between Cu(1) and cyano-nitrogen is slightly larger than that formed by Cu(2) and amido-nitrogen. The angular structural index parameters, τ, for Cu(1) and Cu(2) are 0.9 and 0.5, respectively. The copper(II) atoms display a different geometry with a N 5 chromophore group. The intra Cu⋯Cu separation is 5.156(1) Å. All of the dicyd dinuclear copper complexes show radical anion absorption.

Tree density estimation in a tropical woodland ecosystem with multiangular MISR and MODIS data

In this paper we evaluate the potential of spectral, temporal and angular aspect of remotely sensed data for quantitative extraction of forest structure information in tropical woodlands. Moderate resolution imaging spectroradiometer (MODIS) multispectral data at 500-meter spatial resolution from different dates, multiangle imaging spectroradiometer (MISR) bidirectional reflectance factors (BRF) and normalized difference angular index (NDAI) derived from MISR data at 275-meter spatial resolution were used as input data. The number of trees per hectare bigger than 20cm in diameter at breast height was taken as variable of interest. Simple and multiple ordinary least square regressions and artificial neural networks (ANN) were tested to understand the relationships between the various sources of remotely sensed data and the output variable. An experimental design technique, followed by a classification of the input variables and a factor analysis were implemented in order to understand the structure, reduce the dimensionality of the data and avoid the overfitting of the neural network. The results show that there is a significant amount of independent information in the angular dimension, and this information is highly relevant to the estimation of tree densities in the study area. The MISR NDAI indexes improved the performance of the MISR BRF. The non-linear ANN outperformed the linear regressions. The best results were obtained with the ANN after selecting the input variables according to the results of the experimental design, the classification and the factor analysis, with a 0.71 correlation coefficient against the 0.58 of the best linear regression model.

Synthesis, structure, spectroscopic, magnetic and electrochemical studies of a rare syn–anti acetate-bridged copper(II) complex

The structure, spectroscopy and electrochemical properties of a novel dinuclear copper(II) complex, [{Cu(phen) 2} 2(μ-CH 3COO)][PF 6] 3 where phen = 1,10-phenanthroline, is reported. The crystal structure contains two independent Cu(II) ions, with different geometry around each copper center, which are bridged by an acetate anion. The acetate-bridged ligand shows a syn–anti coordination mode with a trigonal bipyramidal geometry for the Cu(1) center and a distorted square-based pyramidal geometry for the Cu(2) center. The angular structural index parameter τ for Cu(1) and Cu(2) is 0.9 and 0.33, respectively. The copper(II) atoms display a different geometry with a N 4O chromophore group and with Cu–O distances of 1.993(5)–1.996(5) Å and Cu–N distances which vary from 1.980(5) to 2.161(6) Å. The intra Cu…Cu separation is 4.9904(5) Å. The effective magnetic moment ( μ eff) of the complex was measured by the Evans method. The cyclic voltammogram of [{Cu(phen) 2} 2(μ-CH 3COO)][PF 6] 3 shows two waves at positive potential which are assigned to the two Cu(II/I) reduction couples.

Advances in Structural Analysis of Fluoroaluminates Using DFT Calculations of 27Al Electric Field Gradients

Based on the analysis of 23 aluminum sites from 16 fluoroaluminates, the present work demonstrates the strong potential of combining accurate NMR quadrupolar parameter measurements, density functional theory (DFT)-based calculations of electric field gradients (EFG), and structure optimizations as implemented in the WIEN2k package for the structural and electronic characterizations of crystalline inorganic materials. Structure optimizations are essential for compounds whose structure was refined from usually less accurate powder diffraction data and provide a reliable assignment of the 27Al quadrupolar parameters to the aluminum sites in the studied compounds. The correlation between experimental and calculated EFG tensor elements leads to the proposition of a new value of the 27Al nuclear quadrupole moment Q(27Al) = 1.616 (+/-0.024) x 10(-29) m2. The DFT calculations provide the orientation of the 27Al EFG tensors in the crystal frame. Electron density maps support that the magnitude and orientation of the 27Al EFG tensors in fluoroaluminates mainly result from the asymmetric distribution of the Al 3p orbital valence electrons. In most cases, the definition of relevant radial and angular distortion indices, relying on EFG orientation, allows correlations between these distortions and magnitude and sign of the Vii.

Influence of woody elements of a Norway spruce canopy on nadir reflectance simulated by the DART model at very high spatial resolution

A detailed sensitivity analysis investigating the effect of woody elements introduced into the Discrete Anisotropic Radiative Transfer (DART) model on the nadir bidirectional reflectance factor (BRF) for a simulated Norway spruce canopy was performed at a very high spatial resolution (modelling resolution 0.2 m, output pixel size 0.4 m). We used such a high resolution to be able to parameterize DART in an appropriate way and subsequently to gain detailed understanding of the influence of woody elements contributing to the radiative transfer within heterogeneous canopies. Three scenarios were studied by modelling the Norway spruce canopy as being composed of i) leaves, ii) leaves, trunks and first order branches, and finally iii) leaves, trunks, first order branches and small woody twigs simulated using mixed cells (i.e. cells approximated as composition of leaves and/or twigs turbid medium, and large woody constituents). The simulation of each scenario was performed for 10 different canopy closures (CC = 50–95%, in steps of 5%), 25 leaf area index (LAI = 3.0–15.0 m 2 m − 2 , in steps of 0.5 m 2 m − 2 ), and in four spectral bands (centred at 559, 671, 727, and 783 nm, with a FWHM of 10 nm). The influence of woody elements was evaluated separately for both, sunlit and shaded parts of the simulated forest canopy, respectively. The DART results were verified by quantifying the simulated nadir BRF of each scenario with measured Airborne Imaging Spectroradiometer (AISA) Eagle data (pixel size of 0.4 m). These imaging spectrometer data were acquired over the same Norway spruce stand that was used to parameterise the DART model. The Norway spruce canopy modelled using the DART model consisted of foliage as well as foliage including robust woody constituents (i.e. trunks and branches). All results showed similar nadir BRF for the simulated wavelengths. The incorporation of small woody parts in DART caused the canopy reflectance to decrease about 4% in the near-infrared (NIR), 2% in the red edge (RE) and less than 1% in the green band. The canopy BRF of the red band increased by about 2%. Subsequently, the sensitivity on accounting for woody elements for two spectral vegetation indices, the normalized difference vegetation index (NDVI) and the angular vegetation index (AVI), was evaluated. Finally, we conclude on the importance of including woody elements in radiative transfer based approaches and discuss the applicability of the vegetation indices as well as the physically based inversion approaches to retrieve the forest canopy LAI at very high spatial resolution.

Inspiral, merger, and ringdown of unequal mass black hole binaries: A multipolar analysis

We study the inspiral, merger, and ringdown of unequal mass black hole binaries by analyzing a catalogue of numerical simulations for seven different values of the mass ratio (from q=M2/M1=1 to q=4). We compare numerical and post-Newtonian results by projecting the waveforms onto spin-weighted spherical harmonics, characterized by angular indices (l,m). We find that the post-Newtonian equations predict remarkably well the relation between the wave amplitude and the orbital frequency for each (l,m), and that the convergence of the post-Newtonian series to the numerical results is nonmonotonic. To leading order, the total energy emitted in the merger phase scales like η2 and the spin of the final black hole scales like η, where η=q/(1+q)2 is the symmetric mass ratio. We study the multipolar distribution of the radiation, finding that odd-l multipoles are suppressed in the equal mass limit. Higher multipoles carry a larger fraction of the total energy as q increases. We introduce and compare three different definitions for the ringdown starting time. Applying linear-estimation methods (the so-called Prony methods) to the ringdown phase, we find resolution-dependent time variations in the fitted parameters of the final black hole. By cross correlating information from different multipoles, we show that ringdown fits can be used to obtain precise estimates of the mass and spin of the final black hole, which are in remarkable agreement with energy and angular momentum balance calculations.

A novel simple and low cost 4 degree of freedom angular indexing calibrating technique for a precision rotary table

For calibrating an angular rotary table, either a high precision standard table or a laser interferometer and related optics are normally employed at high cost. This paper establishes a novel, simple and low cost technique to calibrate the 4-degrees-of-freedom (DOF) errors of a rotary table (three angular position errors and one linear position error) for a 360° full circle by employing one reference rotary table, one 1 dimensional (1D) grating and two 2 dimensional (2D) position-sensing-detectors (PSD). With this technique, no highly accurate reference rotary table, but with good repeatability is needed. After two full circle tests, the 4-DOF errors of both the target rotary table and the reference rotary table could be obtained. The system calibration, stability test, system verification and full circle test were completed. The angular stability of this system was less then 2 arc sec, while the displacement stability was less than 1.2 μm.

Fractionalization of optical beams: II. Elegant Laguerre–Gaussian modes

We apply the tools of fractional calculus to introduce new fractional-order solutions of the paraxial wave equation that smoothly connect the elegant Laguerre-Gaussian beams of integral-order. The solutions are characterized in general by two fractional indices and are obtained by fractionalizing the creation operators used to create elegant Laguerre-Gauss beams from the fundamental Gaussian beam. The physical and mathematical properties of the circular fractional beams are discussed in detail. The orbital angular momentum carried by the fractional beam is a continuous function of the angular mode index and it is not restricted to take only discrete values.