Radial Index Research Articles

Hacking the topographic ruggedness index

The topographic ruggedness index (TRI) is widely adopted for the analysis of digital elevation models, providing information on local surface spatial variability. In this work, the TRI is interpreted according to a geostatistical perspective, highlighting its main characteristics and drawbacks. TRI can be interpreted as an omnidirectional short-range spatial variability index, computed according to a pixel centered perspective. The simplicity and interpretability of the index, free from user-dependent selections, promoted its implementation in several software environments and its application in a wide set of case studies. However, the index has several drawbacks for its application in earth sciences, such as a strong dependency on local slope (it is basically an average adjacent neighbor slope algorithm) and the selection of different lag distances in the computation of spatial variability along the main directions and the diagonal ones. We propose a new metric radial roughness index (RRI) in order to solve the main drawbacks of TRI but maintaining its main philosophy (i.e., pixel centered perspective and simplicity of the algorithm). The new index corrects for the differences in lag distances and resolves the dependency on trend using increments of order 2. The code of the index, implemented in R statistical language, and test data are provided with the paper (https://doi.org/10.5281/zenodo.7132160) to promote its implementation in other software environments.

Mode Selection Method in Spherical Optical Cavities with Thin Metal Film

A new method for the selection of the radial modes of a spherical microresonator by the quality factor, based on the effect of absorption in a thin metal film deposited on a sphere together with a dielectric layer, is proposed. The method was proved by numerical simulation on the example of the second and third radial modes TEl,l,q, l = 455, q = 2, 3 selection in 80 μm radius quartz microsphere with 5 nm thick nickel film. The structure of the metal-dielectric coating was determined using analytical formulas in such a way that the metal film was placed at the node of the selected mode E-field distribution. The finite element method was used to refine the calculation, optimizing the position of the film in terms of obtaining the maximum quality factor. As a result, it was shown that the selected mode could have a relatively high quality factor (Q~107), while the other radial modes are significantly suppressed (Q~103). In addition, it is shown that selection is carried out by the mode index number (l) simultaneously with selection by the radial index.

Set of mathematical models for Bessel-Gauss beams coupling into the parabolic-index fiber under the influence of atmospheric turbulence and random jitter.

The expression of efficiency for Bessel-Gauss (BG) beams coupling into the parabolic fibers (PF) after passing through the Cassegrain antenna system is first derived. The effects of atmospheric turbulence and random jitter of the coupling lens on the efficiency are also taken into account to improve the practical applicability of our model. This article use a BG beam with a wavelength of 1550 mm and fiber with a core radius RF of 50 μm and a relative refractive index difference ζ of 0.01 for simulation testing. The optimal parameters of the antenna system are determined: the radius of the primary mirror and the secondary mirror is 8.33 cm and 1.25 cm, respectively. The coupling efficiency of BG beams of different orders reaches above 94% simultaneously when the lens's focal length is 7.8 cm. After taking into account the transmission efficiency of the antenna system, the system's total efficiency for BG beams of different orders averages 76.33%, when the transmission distance is 1 km. The results show that the same degree of turbulence and random jitter have different influences on the coupling efficiency of BG beams of different orders, and lower-order BG beams have better resistance to turbulence and jitter during propagation and coupling. Moreover, the effect of the guided mode field on the coupling efficiency and the resistance to turbulence varies for different values of mode radial index in the fiber p. The guided mode with p = 0 not only enables the BG beams of different orders to achieve the highest transmission efficiency in the coupling system almost simultaneously but also the random jitter and turbulence have less influence on the coupling efficiency of this mode. It means that the BG beams can have higher efficiency when coupled to the mode with p = 0 after long-distance transmission. This property of the fiber mode at p = 0 provides conditions for the simultaneous propagation of multiple BG beams in a parabolic fiber, which provides a theoretical basis for higher transmission capacity. This research work provides a theoretical model for the theoretical study of vortex beams and optical communication, which is beneficial for the design and application of vortex beams and has instructive meaning for practical engineering design.

Extending orbital angular momentum multiplexing to radially high orders for massive mode channels in fiber transmission.

Orbital angular momentum (OAM) beams with different angular indices l have the potential to greatly increase communication capacity. However, the finite aperture of optical systems limits the value of the angular index. In order to fully use the orthogonal mode channels supported in the fiber for high-capacity communications, we propose extending the radial indices p of OAM modes as an additional multiplexing dimension. In this paper, we introduce spatially discrete multiple phase planes to multiplex the angular and radial OAM modes simultaneously. Due to the orthogonal property of the central symmetric OAM modes, a two-dimensional (2D) input Gaussian beams array can be converted to coaxial OAM modes through Cartesian to log-polar coordinate transformation by inverse design. For a proof-of-concept demonstration, a 10-mode multiplexer for high-order radial OAM modes was designed using five phase planes. The fabricated multiplexer generated high-quality multiplexed OAM modes with a loss of less than 5.4 dB. The multiplexed OAM modes were coupled into a specially designed ring-core fiber by mode-field matching, achieving stable mode transmission in 2 km fiber. The approach provides a scalable technology to increase the number of transmission channels and could lead to the practical applications of OAM multiplexing in communication.

Transformation of Laguerre-Gaussian beams into 1D array of Hermite-Gaussian modes under the Talbot effect.

This work explains diffraction of Laguerre-Gaussian (LG) beams having non-zero radial indices from one dimensional (1D) periodic structures and their transformation into Hermite-Gaussian (HG) modes, theoretically, verifies using simulations and demonstrates the phenomenon experimentally. We first report a general theoretical formulation for such diffraction schemes, and then use it to investigate the near-field diffraction patterns from a binary grating having a small opening ratio (OR) by providing numerous examples. Results show that for OR≲ 0.1, at the Talbot planes, mainly at the first Talbot image, the images of individual lines of the grating obtain HG modes' intensity patterns. Therefore, the topological charge (TC) of the incident beam and its radial index can be determined from the observed HG mode. In this study, the effects of the OR of the grating and the number of Talbot plane on the quality of the generated 1D array of HG modes are also investigated. The optimum beam radius for a given grating is also determined. The theoretical predictions, are well confirmed by a number of simulations based on the free space transfer function and fast Fourier transform approach, and by experiments. The observed phenomenon, the transformation of LG beams into 1D array of HG modes under the Talbot effect, in addition of providing a way for characterization of LG beams with non-zero radial indices, itself is interesting and may be used in other fields of wave physics, especially for long-wavelength waves.

Factors Affecting Radial Artery Occlusion After Right Transradial Artery Catheterization for Coronary Intervention and Procedures.

To determine the factors influencing proximal radial artery occlusion (PRAO) right radial artery after coronary intervention. This is a single-center prospective observational study. A total of 460 patients were selected to undergo coronary angiography (CAG) or percutaneous coronary intervention (PCI) via the proximal transradial approach (PTRA) or distal transradial approach (DTRA). The 6F sheath tube were received by all patients. Radial artery ultrasound was performed 1 day before procedure and 1-4 days after procedure. Patients were divided into the PRAO group (42 cases) and the non-PRAO group (418 cases). General clinical data and preoperative radial artery ultrasound indexes of the two groups were compared to analyze related factors leading to PRAO. The total incidence of PRAO was 9.1%, including 3.8% for DTAR and 12.7% for PTRA. The PRAO rate of DTRA was significantly lower than that of PTRA (p < 0.05). Female, low body weight, low body mass index (BMI) and CAG patients were more likely to develop PRAO after procedure (p < 0.05). The internal diameter and cross-sectional area of the distal radial artery and proximal radial artery were smaller in the PRAO group than in the non-PRAO group, and the differences were statistically significant (p < 0.05). Multifactorial model analysis showed that the puncture approach, radial artery diameter and procedure type were predictive factors of PRAO, and the receiver operating characteristic curve showed a good predictive value. A larger radial artery diameter and DTRA may reduce the incidence of PRAO. Preoperative radial artery ultrasound can guide the clinical selection of appropriate arterial sheath and puncture approach.

Generation of optical vortex lattices by in-line phase modulation with partially coherent light.

Of late, generation of different kinds of optical vortex lattices has been gaining much attention due to various applications. Several methods have been reported for the generation of optical vortex lattices using a coherent light source involving interferometric, diffractive, and pinhole phase plate methods. Owing to cost effectiveness and ease in optical implementation, these days use of incoherent or partially coherent light beams is becoming popular. In this study, we demonstrate generation of different kinds of optical vortex lattices through in-line modulation of phase distributions employing the phase concatenation approach and a light-emitting diode as a light source. It is a non-interferometric and flexible technique for the selection of the parameters that characterize the optical vortices and their arrays. The proposed method allows generation of an array of optical vortices of different topological charges with zero and non-zero radial indices having different symmetries.

Spatial modulation of refractive index in a dense atomic ensemble using Laguerre–Gaussian beams

We propose a scheme to investigate the spatial modulation of the refractive index in a dense atomic ensemble under the action of the Laguerre–Gaussian (LG) beams. Theoretical derivations based on a density-matrix approach associated with numerical simulations are utilized to study the behaviors of the index of refraction, showing that the azimuthal and radial mode indices (i.e., l 2 and p 2) of the LG beams significantly affect the real and imaginary parts of the refractive index. To be specific, the number of the dispersive peaks is determined by ( p 2 + 1 ) | l 2 |, and there are 2 | l 2 | lossless petals in conjunction with p 2 concentric absorption rings centered on the vortex center. Furthermore, by tuning the phase values of the electric and magnetic components of the electromagnetic field, the index of refraction can be drastically tuned from negative to zero to positive and accompanied by periodic absorption and amplification. This investigation provides a powerful tool for manipulating the index of refraction through a nonlinear interaction between atoms and the vortex beams and suggests potential applications in optical switching, logic gates, and optical storage with spatially varying refractive indices.

Statistical Properties of Partially Coherent Higher-Order Laguerre-Gaussian Power-Exponent Phase Vortex Beams

In this paper, partially coherent radially polarized (RP) Laguerre-Gaussian (LG) rotationally symmetrical power-exponent phase vortex (RSPEPV) beams with the LG-correlated Schell-model (LGSM) were introduced. The statistical properties of the tightly focused beams, including intensity distribution, degrees of polarization and coherence, and Stokes vector, were studied based on vectorial Richards-Wolf diffraction integral theory. Moreover, when the distance between focal plane and the observation plane z = 0, the relationships between the tight-focusing properties of RP-LG-RSPEPV beams with LGSM and the order of LGSM p’, topological charges l, power exponent n, spatial correlation δ, and radial index p were investigated. The results show that by changing the order of LGSM, topological charge, power exponent, spatial correlation length, and radial index, the focal spot distribution of various shapes can be obtained. This work provides ideas for the application of partially coherent beams in particle capture and optical tweezers.

Sacubitril/Valsartan Improves Left Atrial and Ventricular Strain and Strain Rate in Patients with Heart Failure with Reduced Ejection Fraction.

Data on the impact of sacubitril/valsartan (SV) therapy on phasic left atrial (LA) and left ventricular (LV) strain in heart failure with reduced ejection fraction (HFrEF) are limited. The aim of this study was to evaluate changes in two-dimensional speckle tracking (2D-STE) parameters with SV therapy in HFrEF patients. Prospective evaluation of HFrEF patients receiving optimized medical therapy. Two-dimensional speckle tracking (2D-STE) parameters were assessed at baseline and after 6 months of SV therapy. LA strain and strain rate (SR) in reservoir, conduit, and contraction phases were compared with LV longitudinal, radial, and circumferential strain and SR and stratified according to heart rhythm and HFrEF etiology. A total of 35 patients completed the 6-month follow-up, with a mean age of 59 ± 11 years, 40% in atrial fibrillation, 43% with ischemic etiology, and LVEF of 29 ± 6%. There were significant improvements in LA reservoir, conduit, and contractile strain and SR following SV therapy, particularly among patients in sinus rhythm. There were significant improvements in longitudinal, radial, and circumferential LV function indices. SV therapy in HFrEF was associated with improved longitudinal, radial, and circumferential function, particularly among patients in sinus rhythm. These findings can provide insights into the mechanisms underlying the improvement of cardiac function and help assess subclinical responses to the treatment.

Orbital angular momentum of Laguerre-Gaussian beams with non-zero radial index at limited aperture size

The study of orbital angular momentum (OAM) calculation and measurement of complex radial structure beams with limited receiving aperture size is of practical significance. In this paper, taking the Laguerre-Gaussian beam with non-zero radial index as an example, we give the calculation method of its OAM at limited aperture size and design an experiment. We theoretically and experimentally demonstrate the strong correlation between OAM and radial number and we believe that the calculation method can be extended to all local OAM calculations with complex radial structure beams.

Laguerre Gaussian mode holography and its application in optical encryption.

Holography provides an approach to reconstructing both intensity and phase information, and has many applications for microscopic imaging, optical security, and data storage. Recently, the azimuthal Laguerre-Gaussian (LG) mode index, orbital angular momentum (OAM), has been implemented in holography technologies as an independent degree of freedom for high-security encryption. The radial index (RI) of LG mode, however, has not been implemented as an information carrier in holography. Here we propose and demonstrate the RI holography by using strong RI selectivity in the spatial-frequency domain. Furthermore, the LG holography is realized theoretically and experimentally with the (RI, OAM) spanning from (1, -15) to (7, 15), which leads to a 26bit LG-multiplexing hologram for high-security optical encryption. Based on LG holography, a high-capacity holographic information system can be constructed. In our experiments, a LG-multiplexing holography with a span of 217 independent LG channels has been realized, which is inaccessible at present for the OAM holography.

The Diastolic Oscillation Amplitude Used as an Arterial Aging Indicator.

The compliance of the distal arteries depends on their vasoconstrictor tone and distensibility and is sensitive to endothelial function and aging.C2, a component of the Windkessel model,is a measure of distal arterial compliance,and establishes the magnitude of the pressure rise during early diastole. It is calculated from the diastolic portion of theradial pulse wave usingsophisticatedanalyses.C2 is used as a cardiovascular risk indicator since it decreases with aging, high blood pressure, and diabetes. Here, we propose an alternative method to assess the distal arteries distensibility by measuring the amplitude of the oscillation that occurs at the beginning of diastole. Peripheral pulse wave was evaluated noninvasively by applanationtonometry in 511 individuals (264 women) aged between 13 and 70 years. Diastolic amplitude (DA) was measured as the peak-to-peak amplitude of the diastolic oscillation. Radial augmentation index (RAIx) and pulse wave velocity (PWV) were also calculated. DA decreased approximately 2% per decade of life between 16 and 70 years from 19% to 7%, and was higher in men than in women (p<0.0001). Linear regression analysis identified RAIx as the strongest predictor of AD (p<0.0001), followed by age and height. Sex modified the age-related decrease in DA (p< 0.001). By applying the method to measure DA frompreviously published data, we found a strong linear correlation with C2. DA decreased linearly with age in a reciprocal manner to the increase in radial augmentation index, was greater in men than women, and was independent of blood pressure and heart rate, as previously reported for C2.We propose that measuring DAcould provide an alternative index to evaluate distal arterial compliance and aging.

First-order statistics of intensity and phase in Laguerre-Gauss speckles.

Laguerre-Gaussian (LG) beams are characterized by an azimuthal index or topological charge (m), associated with the orbital angular momentum, and by a radial index (p), which represents the number of the rings in the intensity distribution. We present a detailed, systematic study of the first-order phase statistics of the speckle fields created when LG beams of different order interact with random phase screens with different optical roughness. The phase properties of the LG speckle fields are studied in both the Fresnel and the Fraunhofer regimes using the equiprobability density ellipse formalism such that analytical expressions can be derived for the phase statistics.

Inner retinal layers' alterations of the microvasculature in early stages of Parkinson's disease: a cross sectional study.

To investigate microcirculation characteristics of the inner retinal layers at the macula and the peripapillary area using Optical Coherence Tomography Angiography (OCT-A) of patients in early stages of Parkinson's disease (PD). 32 PD patients and 46 age- and gender-matched healthy controls were included in this cross sectional study. OCT-A imaging was performed to analyze microcirculation characteristics at each separate macular region (fovea, parafovea, and perifovea) and the peripapillary area of the inner retinal layers. Individuals with PD had significantly lower parafoveal, perifoveal and total vessel density (VD) in the superficial capillary plexus (SCP) than controls (all p < 0.001), while foveal VD was higher in PD eyes than that of controls, though not statistically significant. Similarly, individuals with PD had significantly lower parafoveal, perifoveal and total perfusion in the SCP than control eyes (all p < 0.001), while foveal perfusion was significantly higher in PD eyes than that of controls (p = 0.008). PD eyes had significantly smaller FAZ area and perimeter accompanied by decreased circularity at the SCP as compared to controls (all p < 0.001). Concerning the peripapillary area, individuals with PD had significantly lower radial peripapillary capillary perfusion density and flux index at the SCP than controls (all p < 0.001). All p values remained statistically significant even after using the Bonferroni correction for multiple comparisons, except for that of foveal perfusion. Our study indicates alterations of the inner retinal layers at the macula and the peripapillary area at the preliminary stages of PD. OCT-A parameters could potentially comprise imaging biomarkers for PD screening and improve the diagnostic algorithms.

The Celestial Reference Frame at K Band: Imaging. I. The First 28 Epochs

We present K-band (24 GHz) images of 731 compact extragalactic radio sources with submilliarcsecond resolution, based on radio interferometric observations made with the Very Long Baseline Array of 10 telescopes during 29 day long sessions spanning from 2015 to 2018 and recorded at 2048 Mbps. Many of these sources are imaged with submilliarcsecond resolution for the first time at frequencies above X band (8 GHz). From each of the K-band images, we derive the following source properties: peak brightness, core and total flux density, the ratio of peak and core to total flux (compactness measure), radial source extent, structure index, source size, and jet direction. The vast majority of sources are imaged at multiple epochs, providing insights into their temporal behavior. The use of K band was motivated by the fact that the sources are generally intrinsically more compact at higher frequencies, as well as by the factor of 3 improvement in interferometer resolution relative to the historically standard S/X band (2.3/8.4 GHz) used for a large amount of reference frame and calibrator work. Lastly, as most of the sources imaged here are in the K-band component of the third International Celestial Reference Frame, these images serve to characterize the objects used in that International Astronomical Union standard.

The Reliability of Kaplan's Cardinal Line as a Potential Surface Marker for the Superficial Palmar Arch During Carpal Tunnel Release: An Anatomical Study With Surgical Perspective.

Purpose Kaplan's cardinal line (KCL) provides a more accurate reference point to the superficial palmar arch (SPA). The aim was to determine the KCL-SPA distances and their relationship with the other defined superficial landmarks, such as distal wrist crease (DWC) or distal portion of the transverse carpal ligament (TCL) or DWC-TCL distance. The objective was to determine the distal limit of the incision made during carpal tunnel release (CTR). Methods Sixty hands were dissected after KCL was drawn on each hand using standard methods. The distance from KCL to the SPA was measured along the radial and ulnar borders of the ring finger and recorded as radial and ulnar KCL-SPA distance, respectively. The distance between the DWC and the distal portion of the TCL was also measured (DWC-TCL). Correlation analysis was done between the DWC-TCL and KCL-SPA distance. The ratios between the radial and ulnar KCL-SPA distance and DWC-TCL distance were calculated and mentioned as radial and ulnar Kaplan cardinal index, respectively. Results KCL-SPA distance was 6.8±3.7 mm along the radial border and 6.6±3.6 mm along the ulnar border of the ring finger. The DWC-TCL distance was 29.4±1.2 mm. The means of radial and ulnar Kaplan cardinal indices were 0.23 and 0.22, respectively. A significant correlation was found between the DWC-TCL distance and the KCL-SPA distances. Conclusion Clinically, KCL can be appraised as a predictable surface landmark in limiting the distal-most extent of the incision during CTR and protecting SPA from transection. The SPA was found to lie at a variable distance from the KCL, and the minimum distance was found to be 3.3 mm. This should be considered as the maximum permissible extension of CTR incision beyond KCL.

Peripheral Macrovascular Involvement in Systemic Sclerosis: A Cohort Study by Color and Spectral Doppler Ultrasonography.

Systemic sclerosis (SSc) is a disease characterized by diffuse sclerosis of skin and organs and small vessel vasculopathy. Despite it, large vessels can also be involved with ulnar artery vasculopathy, revealing as a more frequent feature of SSc. The aim of this paper is to assess the macrovascular involvement of SSc patients through an ultrasound (US) evaluation of radial and ulnar arteries. Radial and ulnar resistance indices (RIs) and peak systolic velocity (PV) (cm/s) together with clinical features of SSc patients were evaluated. Raynaud phenomenon (RP) and healthy control (HC) groups were used for comparison. Forty-three SSc patients were evaluated. Twelve patients (28%) had ulnar artery occlusions (UAOs). In nine cases (75%), UAOs were bilateral. A high UAO prevalence (42%) was found in SSc patients with late nailfold-video-capillaroscopy (NVC) pattern (p = 0.0264). Patients with UAOs had digital ulcers (DUs) in 10 cases (83.3%). Radial and ulnar PVs were lower in SSc and RP patients than the HC group. Radial and ulnar RIs were higher in SSc and RP patients than the HC group. A decision tree analysis led to the classification of 70% of SSc patients with an ulnar RI > 0.82 and ulnar PV > 2.8 cm/s. The most influential variables on UAO development were interstitial lung disease (ILD) (p = 0.002) and NVC pattern (p = 0.002). A positive correlation was shown between modified Rodnan skin score (mRSS) and ILD (p = 0.283; r = 0.033), mRSS and DU (r = 0.344; p = 0.012) and DU and ILD (r = 0.303; p = 0.024). Male sex was associated with increased UAO frequency (p = 0.042). UAO is a peculiar feature of severe SSc present in 28% of the cases, particularly associated with the presence of ILD and late NVC pattern. In 75% of the cases, UAOs are bilateral. DUs are very frequent in patients with UAOs (83%). The RI evaluated by US could be useful to distinguish SSc from HC patients. US could be a useful tool for assessing high-risk DU development in patients.

Longitudinal Associations between Alcohol Intake and Arterial Stiffness, Pressure Wave Reflection, and Inflammation.

This prospective observational study, which utilized repeated annual measurements performed over a 9-year period, applied mixed model analyses to examine age-related differences in longitudinal associations between alcohol intake and arterial stiffness, pressure wave reflection, and inflammation. In 4016 middle-aged (43±9 years) healthy Japanese male employees, alcohol intake, brachial-ankle pulse wave velocity (baPWV), radial augmentation index (rAI), and serum C-reactive protein (CRP) levels were measured annually during a 9-year study period. The estimated marginal mean baPWV (non-drinkers=1306 cm/s, mild-moderate drinkers=1311 cm/s, and heavy drinkers=1337 cm/s, P＜0.01) and that of rAI showed significant stepped increases in an alcohol dose-dependent manner in the entire cohort, but an increase in rAI was not observed in subjects aged ≥ 50 years. The estimated slope of the annual increase in baPWV, but not rAI, was higher for heavy drinkers than for non-drinkers (slope difference, 1.84; P＜0.05), especially for subjects aged ＜50 years (slope difference, 2.84; P＜0.05). In middle-aged male Japanese employees, alcohol intake may attenuate inflammatory activity. While alcohol intake may exacerbate the progression of arterial stiffening in a dose-dependent manner without mediating inflammation, especially in subjects under 50 years of age, it may promote pressure wave reflection abnormalities with aging at earlier ages without further exacerbation at older ages.

Broadband 2D n × n Vortex Arrays Generated from an Efficient Petal‐Like Raman Laser with an Astigmatic Mode Convertor

Broadband vortex arrays distributed in 2D n × n vortices are extremely needed for multiple microparticle manipulation, high‐capacity optical communication, and quantum information. Vortex arrays are usually generated with spatial light modulators, metamaterials; it is a big challenge to improve beam quality and output power. Herein, crisscross 2D n × n vortex arrays are converted from petal‐like Raman lasers with an astigmatic mode convertor. Efficient petal‐like lasers in the form of the Laguerre–Gaussian mode with zero radial index and l azimuthal index (LG0,l ) are irradiated in a Raman microchip laser (RML) by adjusting optimal beam waist and locating the position of focus spot of the annular pump beam. High‐beam‐quality LG0,9 petal‐like Raman laser oscillating at broadband wavelength (bandwidth: 16.2 nm) is generated with power of 773 mW and an efficiency of 10.6%. The conversion efficiency from petal‐like laser to crisscross vortex array is as high as 90%. The vortex array with 5 × 5 vortices operating around 1078 nm is generated with a power of 693 mW and an optical efficiency of 9.5%. Taking advantages of the broad emission spectrum of ytterbium‐doped laser materials and stimulated Raman scattering effect, RMLs are potential sources for generating flexible vortex arrays with desired 2D n × n vortices oscillating in Raman wavelengths.