Incident Rays Research Articles

Laser bathymetry based on the halo effect

The physical fundamentals of laser bathymetry based on measuring the halo radius resulting from diffuse scattering of a laser beam at the bottom of a water body and re-incidence of scattered light on the bottom after reflection from the underside of the water surface have been developed. The effect of the light scattering and absorption in water on the image contrast and visibility depth of the halo is theoretically studied. Algorithms for determining the optical properties of water by the measured dependence of the apparent radiance of the bottom on the distance to the point of the laser ray incidence on the bottom are proposed.

The role of incidence angle in the laser ablation of a planar target

The effect of the laser ray incidence angle on the mass ablation rate and ablation pressure of planar inertial confinement fusion (ICF) targets is explored. In this work, a modified version of the textbook model of laser ablation [Manheimer et al., Phys. Fluids 25, 1644 (1982)] is used to demonstrate that the mass ablation rate and ablation pressure scale with the 4/3 and 2/3 power of the cosine of the laser ray incidence angle relative to the target normal. Using an idealized planar model of ablation, it is demonstrated that constant irradiance is insufficient to produce similar velocities of a target when comparing cases driven at different incidence angles. Additionally, the effect of the incidence angle on the absorption fraction is demonstrated and it is shown that a longer duration is needed to achieve maximum absorption for greater angles. This further affects the mass ablation rate and ablation pressure in the first nanosecond of ablation. These results, when extrapolated, may provide insight into the variation of drive conditions encountered due to incidence in polar direct drive ICF.

Community characteristics and canopy structure of pine-oak forest at the Lingkong Mountain in Shanxi, China

We conducted a field investigation at 400 10 m×10 m quadrats in a 4-hm2 plot of mixed forest dominated by pine (Pinus tabuliformis) and oak (Quercus wutaishanica), which was established in 2011 in the Lingkong Mountain of Shanxi Province, China. The community characteristics in the year of 2016 were analyzed. The digital hemisphere photograph (DHP) approach was employed to measure the canopy structure and the understory light parameters. The results showed that a total of 5558 individuals of trees of 25 species from 15 genera and 10 families were recorded. The canopy openness (CO) varied from 15.0% to 25.0%, the leaf area index (LAI) varied from 1.5 to 2.5, and the understory light parameters varied from 10.0% to 30.0%. The distribution of dominant species drove the canopy structure and the undergrowth light factors. The canopy structure defined the impacts of light factors in the forest. The leaf area index was more optimal in describing the canopy’s dynamic function. The canopy openness and leaf area index were negatively correlated to understory light availability, especially to the abundance of the incident rays of diffused light. Since the canopy structure was relatively uniform in the temperate pine-oak mixed forest, the understory light spots generally distributed in clusters. The tree species and canopy structure had significant effects on light environment in the forest.

Non-stationary model of oblique x-ray incidence in amorphous selenium detectors: I. Point spread function.

In previous work, a theoretical model of the point spread function (PSF) for oblique x-ray incidence in amorphous selenium (a-Se) detectors was proposed. The purpose of this paper is to develop a complementary model that includes two additional features. First, the incidence angle and the directionality of ray incidence are calculated at each position, assuming a divergent x-ray beam geometry. This approach allows the non-stationarity of the PSF to be modeled. Second, this paper develops a framework that is applicable to a digital system, unlike previous work which did not model the presence of a thin-film transistor (TFT) array. At each point on the detector, the incidence angle and the ray incidence direction are determined using ray tracing. Based on these calculations, an existing model for the PSF of the x-ray converter (Med Phys. 1995;22:365-374) is generalized to a non-stationary model. The PSF is convolved with the product of two rectangle functions, which model the sampling of the TFT array. The rectangle functions match the detector element (del) size in two dimensions. It is shown that the PSF can be calculated in closed form. This solution is used to simulate a digital mammography (DM) system at two x-ray energies (20 and 40keV). Based on the divergence of the x-ray beam, the direction of ray incidence varies with position. Along this direction, the PSF is broader than the reference rect function matching the del size. The broadening is more pronounced with increasing obliquity. At high energy, the PSF deviates more strongly from the reference rect function, indicating that there is more blurring. In addition, the PSF is calculated along the polar angle perpendicular to the ray incidence direction. For this polar angle, the shape of the PSF is dependent upon whether the ray incidence direction is parallel with the sides of the detector. If the ray incidence direction is parallel with either dimension, the PSF is a perfect rectangle function, matching the del size. However, if the ray incidence direction is at an oblique angle relative to the sides of the detector, the PSF is not rectangular. These results illustrate the non-stationarity of the PSF. This paper demonstrates that an existing model of the PSF of a-Se detectors can be generalized to include the effects of non-stationarity and digitization. The PSF is determined in closed form. This solution offers the advantage of shorter computation time relative to approaches that use numerical methods. This model is a tool for simulating a-Se detectors in future work, such as in virtual clinical trials with computational phantoms.

A Photographing Method of Integral Photography with High Angle Reproducibility of Light Rays

In these days, Integral Photography has been extensively studies. As a major problem of IP, there is a problem that the depth of the displayed 3D image is reversed from the original object. As a method to solve this problem, there is a method using a concave lens array for recording and using a convex lens array for display. However, in this method, there is a large difference between the incident angle of light ray incident on the lens at the time of recording and the display angle of the light ray emitted from the lens at the time of display. So, in this research, we proposed a photographing method of IP with high angle reproducibility of light rays by using convex mirror array for recording. From the analysis on the optical path of the light ray incident on each convex mirror, it was revealed that the proposed method has higher angle reproducibility of light rays than the conventional method. In the experiment comparing 3D images displayed by the proposed method and the conventional method, it was confirmed that the image displayed by the proposed method has larger parallax according to the movement of the observer than that of the conventional method.

Nonstationary model of oblique x-ray incidence in amorphous selenium detectors: II. Transfer functions.

One limitation of experimental techniques for quantifying resolution and noise in detectors is that the measurement is made in a region-of-interest (ROI). With theoretical modeling, these properties can be measured at a point, allowing for quantification of spatial anisotropy. This paper calculates nonstationary transfer functions for amorphous selenium (a-Se) detectors in breast imaging. We use this model to demonstrate the performance advantage of a "next-generation" tomosynthesis (NGT) system, which is capable of x-ray source motion with more degrees of freedom than a clinical tomosynthesis system. Using Swank's formulation, the optical transfer function (OTF) and presampled noise power spectra (NPS) are determined based on the point spread function derived in Part 1. The modulation transfer function (MTF) is found from the normalized modulus of the OTF. To take into account the presence of digitization, the presampled NPS is convolved with a two-dimensional comb function, for which the period along each direction is the reciprocal of the detector element size. The detective quantum efficiency (DQE) is then determined from combined knowledge of the OTF and NPS. First, the model is used to demonstrate the loss of image quality due to oblique x-ray incidence. The MTF is calculated along various polar angles, corresponding to different orientations of the input frequency. The MTF is independent of the incidence angle if the polar angle is perpendicular to the ray incidence direction. However, along other polar angles, oblique incidence results in MTF degradation at high frequencies. The MTF degradation is most substantial along the ray incidence direction. Unlike the MTF, the normalized NPS (NNPS) is independent of the incidence angle. To measure the relative signal-to-noise, the DQE is also calculated. Oblique incidence yields high-frequency DQE degradation, which is more pronounced than the MTF degradation. This arises because the DQE is proportionate with the square of the MTF. Ultimately, this model is used to evaluate how the image quality varies over the detector area. For various projection images, we calculate the variation in the incidence angle over this area. With the NGT system, the source can be positioned in such a way that this variation is minimized, and hence the DQE exhibits less anisotropy. To achieve this improvement in the image quality, the source needs to have a component of motion in the posteroanterior (PA) direction, which is perpendicular to the conventional direction of source motion in tomosynthesis. In a-Se detectors, the DQE at high frequencies is degraded due to oblique incidence. The DQE degradation is more pronounced than the MTF degradation. This model is used to quantify the spatial variation in DQE over the detector area. The use of PA source motion is a strategy for minimizing this variation and thus improving the image quality.

Plasticity in the timing of activity in the Red-rumped Agouti, Dasyprocta leporina (Mammalia: Rodentia), in the Atlantic Forest of southeastern Brazil

Abstract Timing of activity is a consequence of adaptations to daily and seasonal changes in the environment and examining these patterns is important to better understand the temporal niches of the species. Here we examine temporal activity in the Red-rumped Agouti (Dasyprocta leporina) in two fragments of Atlantic Forest and those factors that influence the circadian rhythm in the study areas. Camera traps were used to gather data in two protected areas (one montane and other coastal) in the state of Espírito Santo, southeastern Brazil. A total of 49 photos were taken in the mountains and 152 in the coastal area. Activity patterns were diurnal and bimodal, and animals were active for 14-15 hours each day. Activity peaked in the morning soon after sunrise and then before and during dusk. Activity patterns were different in the two study areas (W = 6.77, p = 0.034). There was a longer peak in the morning in the coastal area, and a higher peak in the evening in the mountains, where activity starts later and becomes less intense earlier. The difference between activity patterns in the two locations suggests plasticity in agouti behavior. Because the two study areas are at about the same latitude, we suggest that the behavioral plasticity is due to different temperature regimes associated with a local effect of altitude and topography of the terrain on the incidence of solar rays inside the forest. The influence of other factors is also discussed. In addition to a better understanding of the temporal niche of the Red-rumped Agouti, the behavior patterns we describe here can be useful to optimize strategies for D. leporina conservation in southeastern Brazil once the species is more susceptible to poaching at times when animals are most active.

A fast algorithm to compute shadow areas for Kirchhoff approximation-based underwater acoustic scattering simulation

Kirchhoff approximation method is a fast underwater acoustic scattering numerical method which adaptive to engineering application. Shadow areas calculation is one of the most important factors for computational efficiency. In this paper, several existing shadow domain calculation methods for underwater acoustic numerical simulation based on Kirchhoff approximation are introduced. On this basis, a fast sheltering method based on the linked-list search algorithm is proposed. Linked-list search algorithm uses element geometric center to express the element space position and projects the geometric center on incident wave plane along the incident sound ray. And linked-list relationship of elements is established by dividing background mesh cell on the screen. The algorithm achieves fast calculation by using linked-list relationship and optimizing the calculation path. Linked-list search algorithm and all-pair search algorithm are compared and analyzed by an example of numerical simulation. The computational efficiency of the fast shadow domain algorithm is verified by comparing the results of the two algorithms. And the suggestions for further improving the computational efficiency of the algorithm are proposed.

Towards a better estimation of energy and species of primary cosmic rays in the knee region with the Tibet hybrid experiment: Utilization of refined EAS lateral distributions

A new hybrid experiment (YAC-II+Tibet-III+MD) located at Yangbajing has started to improve the capability of explicit measurements of the cosmic-ray components (P, He, CNO, Fe, etc) at the knee energy region since 2014. Considering the different features of air shower development for different primary cosmic-ray nuclei, using a full Monte Carlo simulation, we modified the lateral distribution functions for proton-induced, helium-induced and iron-induced air showers, respectively. The results show that the air shower size of different nuclei obtained by the modified Nishimura-Kamata-Greisen function is consistent with the true shower size within 5% systematic errors. Furthermore, we studied the Extensive Air Shower age parameter determination from the lateral distribution functions of charged particles near the air shower core with the Tibet hybrid experiment. The derived age parameter can be well used to estimate the particle type of the incident primary cosmic rays.

Analytic inverse solutions for Risley prisms in four different configurations for positing and tracking systems.

The conventional ray deviation formula and analytical inverse solution for Risley prisms are traditionally derived by the first-order paraxial method, which is simplified and does not provide sufficient accuracy. When a light ray enters the wedge prism, the component that is perpendicular to the base side is deviated by the wedge prism and the component parallel to the base side is uninfluenced. In this study, the problem is presented and analyzed from the scalar form of Snell's law, and 2D vector algebra is used to solve the problem. The rotation and refracting angles of a single wedge prism are obtained by analyzing the propagation through the prism of incident rays from different directions, and ray deviation formulas are derived. Four configurations are described with ray deviation formulas and analytical inverse solutions deduced from the corresponding formulas for a single wedge prism. In the final section, two examples are considered for the four configurations. The numeric results demonstrate the accuracy of the inverse solution provided by the proposed method.

Construction of γ Energy Spectrum Response Function Matrix in NaI Detector

In energy spectrum analysis, establishing accurate spectral response function plays a key role in the application of this technology. Generally, the response function of the detector is calculated by using experimentally measured data. This method needs to decompose the gamma spectrum into a single energy spectrum and then perform data fitting to obtain a response function. In reality, a sufficient number of gamma radiation sources cannot be found to establish an accurate response function. However, a simple theoretical calculation is difficult because the secondary process of gamma photons is complicated. Therefore, it is necessary to use simulation software. In this paper, 43 different energy gamma spectra are simulated, and the required data are extracted by function fitting, formula calculation, etc. The mathematical laws and physical principles between the data are analyzed. The incident ray energy is the main variable, the peak value of the full energy, the count ratio of the full energy and peak, the coefficient of the peak width of the full energy, the Compton side energy and other parameters are used as the response variables to establish an accurate single-energy gamma spectrum response matrix. It has important guiding significance for future research on the energy spectrum of NaI detector.

Continuous freeform lens design and optimization based on proportional source-target mapping for prescribed illumination

A general and simple method for constructing a proportional source-target energy mapping in order to design a continuous freeform lens for an extended LED light source is proposed. This mapping has the characteristic that we can directly obtain the relationship between the angles of the emitted and incident rays in both the longitudinal and latitudinal directions. By applying this angular function in turn to the normal vector, the lighting situation on the target plane can be quickly determined. Simulation results motivate the proposal of a feedback optimization algorithm to compensate for the deterioration near the diagonal on the target surface caused by surface construction errors and the finite extent of a real source. Based on energy conservation theory and the edge-ray principle, the optimization algorithm is divided into three steps. Finally, the illumination effect on the irradiated surface is consistent with our expectations for an extended LED light source with dimensions of 4 mm × 4 mm. Simulation results show that the energy efficiency η of the freeform lens on the target surface is approximately 0.85 and that the uniformity exceeds 90%. We subsequently analyze the error tolerance of the designed freeform lens from two perspectives: translation and rotation. The minimum translational and rotational error tolerances are 0.3 mm 0.3 mm and 4°, respectively, and the rotational error tolerance around the z-axis are greater than those around the x- and y-axes.

Effects of deformation of cylindrical compound parabolic concentrator (CPC) on concentration characteristics

Compound parabolic concentrators (CPC) have immense potential for middle-and-low temperature heat collection of solar energy. In this study, the propagation process of solar radiation rays in a CPC–tubular solar collector was simulated using an in-house MATLAB code by the Monte Carlo ray tracing (MCRT) method. The effects of ray incidence angle, CPC concentration ratio, and truncation residual ratio on the heat flux distribution on the tubular heat receiver were analyzed. Moreover, the effects of CPC deformations on concentration characteristics were analyzed, involving the rotation and translation of the reflective surface, the truncation of the involute starting point, and the position offset of the heat receiver. The heat flux distribution exhibited two evident peaks on the heat receiver external surface due to the concentration effect of the CPC. A small internal rotation, a small internal or external translation of the reflective surface, and the truncation of the involute starting point had mere effect on the heat flux distribution on the heat receiver. Therefore, the reflective surface can be allowed to have certain translation and internal rotation when machining a CPC. The downward, rightward, and leftward offsets of heat receivers should be avoided in the assembly of heat receivers and CPCs.

Forward projection matrix derivation through Monte-Carlo ray-tracing of KSTAR infra-red imaging video bolometer (IRVB).

The infrared imaging video bolometer (IRVB) as a foil bolometry technique can be an alternative solution to the conventional resistive bolometer due to its electro-magnetic immunity and 2D plasma profiles. The plasma profile of the IRVB cannot be directly derived from the foil images due to the difference between the foil pixel number and the plasma pixel number and the line integrated nature of the incident rays on the foil. So, it needs tomography such as the Phillips-Thikhonov algorithm. The projection matrix constructing the foil image from the plasma very directly influences the tomography. So, the projection matrix needs to be constructed precisely. For the technique calculating the precise projection matrix, a forward Monte-Carlo ray-tracing method is proposed here, and this technique can provide the detailed descriptions of the foil image. And it can give enhanced performance in the reconstructions of the plasmas with spatially localized power.

Investigation of acoustic properties of snow-covered sea ice

The paper presents results of field observations of hydroacoustic characteristics of snow-covered ice cover in shallow seas of the Arctic shelf. The purpose of the research was to determine the quantitative characteristics of the reflection and absorption coefficients of sound from the bottom of the drifting ice cover, as well as the Doppler broadening of the frequency spectrum of acoustic signals depending on the thickness of the ice, the structure of the reflecting surface, the thickness of the snow cover, and the ice drift speed. The objective of the research was to obtain the data necessary for choosing optimal parameters of specialized hydroacoustic equipment designed to monitor ice conditions in the areas of operation of offshore oil and gas platforms. Researches were conducted in areas of active construction of engineering marine constructions and carrying out the transport operations. The research methodology was based on the use of an autonomous measuring complex, which for a long period was installed on the bottom of the sea at depths of 50 to 130 m. The recording system consisted of the following components: upward looking pulse sonar of the IPS-5 type produced by the Canadian company ASL; the Doppler meter of the ice drift speed ADCP (the RDI firm); and a RSM-7 electromechanical current meter. All devices operated in continuous mode with a measurement cycle of 1s, the results were recorded in memory and processed after lifting the devices to the surface. The time delays of signals reflected from the ice cover, as well as the amplitudes and variations of the sound attenuation depending on the reflectance and absorption coefficients were recorded in the memory of the up-looking sonar. Variations of time delays were used to calculate a settlement of ice formations and to determine the shape of the reflective surface, including the angles of inclination of ice keels. Doppler shift of frequency of reflected acoustic signals and broadening of the frequency spectrum were calculated using values of the ice drift speed and changes of immersion depths of hummocks. Acoustic characteristics were measured repeatedly during several seasons of each year from 2010 to 2017. This investigation made possible to obtain statistical estimates of the distributions of the reflection coefficient of the sound and the quantitative values of broadening of the frequency spectrum of acoustic signals depending on the angle of incidence of the acoustic rays, the nature of the irregularities and the structure of the reflective surfaces of ice and snow cover thickness and the drift speed. The results obtained by this research allowed reasonable choosing and calculating the basic characteristics of the hydroacoustic equipment intended for runtime diagnostics of ice cover in zones of marine engineering structures.

Asymptotic solutions of the Helmholtz equation: Generalised Friedlander–Keller ray expansions of fractional order

Applications of a WKBJ-type ‘ray ansatz’ to obtain asymptotic solutions of the Helmholtz equation in the high-frequency limit are now standard and underpin the construction of ‘geometrical optics’ ray diagrams in many electromagnetic, acoustic and elastic reflection, transmission and other scattering problems. These applications were subsequently extended by Keller to include other types of rays – called ‘diffracted’ rays – to provide an accessible and impressively accurate theory which is relevant in wide-ranging sets of circumstances. Friedlander and Keller then introduced a modified ray ansatz to extend yet further the scope of ray theory and its applicability to certain other classes of diffraction problems (tangential ray incidence upon an obstructing boundary, for instance) and did so by the inclusion of an extra term proportional to a power of the wave number within the exponent of the initial ansatz. Our purpose here is to generalise this further still by the inclusion of several such terms, ordered in a natural sequence in terms of strategically chosen fractional powers of the large wave number, and to derive a systematic sequence of boundary value problems for the coefficient phase functions that arise within this generalised exponent, as well as one for the leading-order amplitude occurring as a pre-exponential factor. One particular choice of fractional power is considered in detail, and waves with specified radially symmetric or planar wavefronts are then analysed, along with a boundary value problem typifying two-dimensional radiation whereby arbitrary phase and amplitude variations are specified on a prescribed boundary curve. This theory is then applied to the scattering of plane and cylindrical waves at curved boundaries with small-scale perturbations to their underlying profile.

An orthogonal iteration pose estimation algorithm based on an incident ray tracking model

Although the pinhole imaging model prevails among current pose estimation algorithms, this idealized model gradually shows its limitation and inaccuracy, especially in harsh environments. In recent years, a few generic imaging models have been proposed to replace the dominant pinhole one. Among them, the camera model, named the incident ray tracking model, has proved to be superior. This model consists of mappings between pixels on the image and straight lines in 3D space. Based on the incident ray tracking camera model, a pose estimation algorithm, which can be called the perspective-ray-based orthogonal iteration (PROI), is proposed in this paper. The proposed algorithm introduces the popular orthogonal iteration algorithm into the incident ray tracking model. In this method, the object space collinearity error is expressed by a more accurate perspective ray instead of the traditional line of sight. The orthogonal rotation matrices are computed by an iterative algorithm and the iterative initial value is given in a weak perspective model. Experiment results on the pose estimation with better accuracy and efficiency by PROI have shown the superiority of the proposed method compared with the best currently employed optimization algorithms.

Phase-Gradient Meta-Dome for Increasing Grating-Lobe-Free Scan Range in Phased Arrays

This paper presents a simple and effective way to increase the scan range of phased array antennas by using a metasurface (MTS) curved dome. The technique is based on a phase-gradient passive MTS that deflects the incident rays coming from the array aperture, and on a predistortion of amplitude and phase applied to the original phased array. We assume, therefore, to have at disposal an array capable of electronic beam scanning over a limited angular range with control of amplitude and phase. Geometrical optics ray tracing is used for the design of the metadome and physical optics for the analysis. For the sake of simplicity, the idea is illustrated here for a 2-D scan case; however, the extension to full 3-D scanning appears to be straightforward.

A note on design of linear dielectric compound parabolic concentrators

In this communication, three-dimensional radiation transfer within linear dielectric compound parabolic concentrators (DCPC) is investigated based on vector algebra and solar geometry, and the design of DCPC oriented in east-west direction is addressed. The analysis shows that, the projected incident and refractive angles of solar rays on the cross-section of DCPC are not subjected to the correlation as Snell law except for incident rays on the cross-section, hence, the acceptance half-angle (θa) of DCPC should be determined based on time variations of projected refractive angle and minimum time (2tc) required to concentrate direct sunlight in all days of a year. It is also found that, to make all refractive radiation within θa are totally internally reflected onto the absorber, DCPC with a restricted exit angle (DCPC-θa/θe should be employed, and solar leakage from walls of DCPC-θa/90 can be avoided or reduced by increasing θa and number of periodical tilt-angle adjustment in a year. Calculations show that, the minimum θa of DCPC depends on tc and strategy of tilt-angle adjustment; and for a given tc, the ratio (Rc) of maximum geometric concentration of DCPC to that of reflective CPC (n = 1) is dependent on number of periodical tilt-angle adjustment in a year, but always larger than refractive index (n) of dielectric. Calculations also indicate that, for DCPCs with n > 1.4, when solar rays incident towards onto right/left wall, the radiation incident on its opposite wall (left/right) will be totally internally reflected, and multiple reflections of solar rays on way to the absorber will also be total internal reflection for radiation within its acceptance angle.

Calculation of scintillation properties of Ø1″×1″ of the lanthanum bromide scintillation detector using MCNP simulation and experiment

The purpose of this study is to develop a model for gamma spectroscopy for calculation of full width at half maximum (FWHM), energy resolution and full-energy peak absolute detection efficiency of Ø1″×1″ of the lanthanum bromide LaBr3 (Ce) detector crystal. For this purpose, a complete detector model was developed for Monte Carlo N-Particle (MCNP) transport code. In MCNP simulation, F8 tally was used as it gives the energy distribution of pulses created in the detector. Whenever incident gamma ray enters into detector volume, due to interactions short pulses are produced inside the detector volume. The pulse height spectra of various gamma sources were obtained, which were used to calculate different scintillator properties of our interest. In the simulation, the distance from the source to the detector face was varied to see the effects on scintillation properties of the detector crystal. The detector crystal offers the energy resolution of 3.455% and the FWHM of 22.81 KeV when gamma source Cs137 (662 KeV) was used. As we increased the incident gamma ray energy, the FWHM of the detector crystal increased, while the energy resolution and absolute detection efficiency of the detector crystal decreased. The scintillation properties of Ø1″×1″ of the LaBr3 (Ce) detector crystal were studied experimentally. In our case, it was observed that experimental and simulation results coincided. This proves that the detector model we built for gamma spectroscopy in MC transport code is accurate.