Inverse Cosine Law Research Articles

Integrated Approach for Cobb Angle Estimation in X-Ray C-Curve Scoliosis Using Image Processing and Inverse Cosine Law

Cobb angle is the angle subtended by the most tilted vertebrae. It represents the degree of the spinal curvature and has been used to diagnose scoliosis. The severity of the scoliosis based on the cobb angle will determine the guide treatment and surgical planning. Manual measurement of Cobb angle using protractor or semi-manual using ONIS software is quite time consuming, and it is subjected to variations in interobserver and intraobserver measurements. This research proposed an algorithm to determine the Cobb angle using image processing and inverse cosine methods. The raw samples of X-ray images were obtained from Pusat Kesihatan Universiti (PKU), UTHM. Several interviews were conducted with radiologist at Pantai Hospital for verification purpose. Gaussian blur and unsharp mask were initially applied for noise removal in the preprocessing step. Three points were marked at the vertebrae image to assist for centroid estimation using Haar Cascade. The Cobb angle was estimated by applying the triangle formula derived from the inverse cosine law. In comparison to semi-manual method (Onis Software), the proposed technique has an error of less than 5 % and computes the Cobb angle 3.28 times quicker. In the future, it is suggested to explore other techniques such as deep learning for alternative data analysis for Cobb angle estimation.

Angular Dependence of SOI Transistor Response to Heavy Ion Irradiation

Experimental results showing angular dependence for charge collection in SOI transistors under heavy ion irradiation are presented. Geant4 and Synopsys Sentaurus simulations are performed to analyze these results in terms of direct ionization effects. The influence of the beam direction in relation to that of the transistor's channel on the transistor's response is underlined. Depending on the considered beam direction, deviation from the inverse-cosine law is shown to vary from 0% to 30%. These differences seem to be independent of the ion energy. However, the use of different ion species may hide this possible effect.

The pinning role of nonferromagnetic β phase in the domain wall motion of ferromagnetic MnAs film on GaAs(001)

We report the pinning role of the nonferromagnetic β phase in the domain wall motion of ferromagnetic MnAs film on GaAs(001) in the temperature range of 20–35°C. The dependence of the coercivity on the applied field direction at all temperatures was found to follow an inverse cosine law, as expected from a theoretical model considering the domain wall motion in ferromagnetic films. From this analysis, it was found that the domain wall pinning energy density increases as the temperature increases. This is ascribed to the increase in the volume fraction of the nonferromagnetic β phase, resulting in an increase of the domain wall pinning effect during the domain wall motion.

Incident-angle dependence of ion-induced electron emission from Al & Co films using swift heavy ion

The interaction of charged particles with solid surfaces leads to ion induced electron emission (IIEE). The study of emission of electrons has been a subject of interest in the field of ion-solid collisions. In the present experiment we have measured electron emission yields for Al and Co targets as a function of angle of incidence in the range 0°–30° using swift heavy ions. We observed that the inverse cosine law is not followed in case of swift heavy ions. The possible reasons for deviation from inverse cosine law are discussed. The aim of this work is to show how the variation of the electron yield with the angle of ion incidence reveals proportionality between the yield and the amount of the energy deposited in the electronic excitation near the target surface.

Simulation Study on Image Contrast and Spatial Resolution in Helium Ion Microscope

We performed Monte Carlo simulation of helium (He) ion induced secondary electron (SE) emission in order to compare the secondary electron image characteristics between He and gallium (Ga) scanning ion microscopes (SIM) and scanning electron microscope (SEM). For 10-50 keV He ion bombardment SE yield increases gradually with increasing the atomic number, Z2, of the target, as well as for the electron bombardment. However, for 30 keV Ga ion bombardment, SE yield shows an opposite Z2 dependence. The calculated SE yield is much larger than that for both electron and Ga ion bombardment. The incident angle dependence of the SE yield approximately obeys the inverse cosine law even at high angles of 85 degrees and more. On the other hand, for electron bombardment, the incident angle dependences are much weaker for low energy and high Z2. These indicate that the image contrast on He-SIM is clearer than those of SEM. Among the electron excitations by incident He ions, recoiled target atoms and excited electrons, the first one having narrow excitation volume dominates the SE yield, so that the spatial image resolution in SIM using zero-diameter He beams with the energies of 10-50 keV is prospected to be smaller or better (<0.1 nm) than for 30 keV Ga ion and 1 keV electron beams.

Incident angle dependence of secondary electron emission from carbon induced by swift H 2 +

The incident angle dependence of secondary electron emission induced by a swift H2+ ion impinging on carbon is studied using the Monte Carlo method combined with the semiempirical theory. The relationships both between the electron emission yield and the project angle and between the statistics and the projectile angle are investigated. The results show that the backward electron emission yield deviates from the inverse cosine law, due to the effect of the valence electrons of H2+. The ratio of the forward electron emission yield to the backward electron emission yield at the inclining incidence is different from that at the normal incidence. The statistical distribution of electron emission is independent of the incident angle. The value of b, the deviation parameter from the Poisson distribution, increases with projectile energy.

Influences of ion backscattering and recoil cascade on incident angle dependence of ion-induced kinetic electron emission from solids

Abstract The incident angle dependence of ion-induced kinetic electron emission (KEE) from Cu is calculated in the energy range from 100 eV to 1 MeV, using a Monte Carlo simulation of transport of incident ions (H+ and Xe+) and recoiling target atoms and a semiempirical theory of KEE. The calculated results are in good agreement with the experimental data and reveal dominant effects of backscattering ions and recoiling target atoms on the deviation from the inverse cosine law for light and heavy ion impacts, respectively.

Monte Carlo study of incident-angle dependence of ion-induced kinetic electron emission from solids

The incident angle dependence of ion-induced kinetic electron emission (KEE) from solids is calculated using a Monte Carlo simulation of the transport of incident ions and recoiling target atoms, and a semi-empirical theory of KEE. The emphasis is put on the origin of the deviation from the inverse cosine law. The effect of the high-energy recoiling target atoms on the deviation is much greater than that of the trajectory distribution and backscattering of the incident ions, except for light and low-energy ion impact. The positive (negative) contribution of the recoiling target atoms to the incident angle dependence is dominant for high (low) impact energy. The deviation can be explained by the increase in the electron excitation by recoiling target atoms localized near the surface and the increase in the emission of the atoms, i.e., sputtering.

Deviation from the Inverse Cosine Law upon Incident Angle Dependence of Secondary Electron Emission from Solids under Electron and Proton Bombardments

Deviation from the Inverse Cosine Law upon Incident Angle Dependence of Secondary Electron Emission from Solids under Electron and Proton Bombardments

Calculation of Incident Angle Dependence of Ion-Induced Kinetic Electron Emission from Aluminum

The Monte Carlo simulation of transport of incident ions and recoiling target atoms is combined with the semiempirical theory of ion-induced kinetic electron emission (KEE) for calculating the incident angle dependence of the KEE yields. The calculation was made for light and heavy ion impact on Al in the energy range from 100 eV to 1 MeV. The present results are consistent with the experimental data and have revealed the origin of the deviation from the inverse cosine law, which corresponds to the contributions from backscattering ions and recoiling target atoms.

Atomic versus bulk Al Auger electron emissin induced by noble gas ion bombardment

Abstract We present an angle resolved study on the Auger electron emission from an Al surface uneer noble gas ion bombardment along the normal incidence direction for primary energies varying from 5–15 keV. We show that the intensity ratio between the atomic LMM and the bulk LVV features decreases according to an inverse cosine law as the detection goes from normal to grazing directions and that such ratio changes considerably with the primary ions (Ar+, Kr+ and Xe+). These results provide important information on the deexcitation mechanism of the core excited Al particles.

Statistics of Kinetic Secondary Electron Emission with Stochastic Elastic Collision of Ions in Solids

Electron emission statistics for H+ impact on Au in the energy range 1 keV-40 keV are investigated using a Monte Carlo calculation with the kinetic emission model. The factor f0/ε evaluated by fitting the calculation to experimental electron yield increases with increasing impact energy, and it approaches an energy-independent value as recognized by many investigators because of the decrease of large-angle elastic scattering of H+ in Au (f0: the transmission probability through the surface, ε: the average energy deposited to produce an electron). Special features of the emission statistics are a large probability to produce no electron for keV energy, a smaller probability for no electron with increasing energy, and higher (lower) yield than the inverse cosine law for tens keV (keV) with oblique incidence.