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DOE OSTI2016

MOC Efficiency Improvements Using a Jacobi Inscatter Approximation

In recent weeks, attention has been given to resolving the convergence issues encountered with TCP 0 by trying a Jacobi (J) inscatter approach when group sweeping, where the inscatter source is constructed using the previous iteration flux. This is in contrast to a Gauss-Seidel (GS) approach, which has been the default to-date, where the scattering source uses the most up-to-date flux values. The former is consistent with CASMO, which has no issues with TCP 0 convergence. Testing this out on a variety of problems has demonstrated that the Jacobi approach does indeed provide substantially more stability, though can take more outer iterations to converge. While this is not surprising, there are improvements that can be made to the MOC sweeper to capitalize on the Jacobi approximation and provide substantial speedup. For example, the loop over groups, which has traditionally been the outermost loop in MPACT, can be moved to the interior, avoiding duplicate modular ray trace and coarse ray trace setup (mapping coarse mesh surface indexes), which needs to be performed repeatedly when group is outermost.

21 SPECIFIC NUCLEAR REACTORS AND ASSOCIATED PLANTS↗

NASA NTRS1965

Computer programs simplify optical system analysis

The optical ray-trace computer program performs geometrical ray tracing. The energy-trace program calculates the relative monochromatic flux density on a specific target area. This program uses the ray-trace program as a subroutine to generate a representation of the optical system.

Source record↗

DOE OSTI2016

SU-F-T-620: Development of a Convolution/Superposition Dose Engine for CyberKnife System

Purpose: Current CyberKnife treatment planning system (TPS) provided two dose calculation algorithms: Ray-tracing and Monte Carlo. Ray-tracing algorithm is fast, but less accurate, and also can’t handle irregular fields since a multi-leaf collimator system was recently introduced to CyberKnife M6 system. Monte Carlo method has well-known accuracy, but the current version still takes a long time to finish dose calculations. The purpose of this paper is to develop a GPU-based fast C/S dose engine for CyberKnife system to achieve both accuracy and efficiency. Methods: The TERMA distribution from a poly-energetic source was calculated based on beam’s eye view coordinate system, which is GPU friendly and has linear complexity. The dose distribution was then computed by inversely collecting the energy depositions from all TERMA points along 192 collapsed-cone directions. EGSnrc user code was used to pre-calculate energy deposition kernels (EDKs) for a series of mono-energy photons The energy spectrum was reconstructed based on measured tissue maximum ratio (TMR) curve, the TERMA averaged cumulative kernels was then calculated. Beam hardening parameters and intensity profiles were optimized based on measurement data from CyberKnife system. Results: The difference between measured and calculated TMR are less than 1% for all collimators except in the build-up regions. The calculated profiles also showed good agreements with the measured doses within 1% except in the penumbra regions. The developed C/S dose engine was also used to evaluate four clinical CyberKnife treatment plans, the results showed a better dose calculation accuracy than Ray-tracing algorithm compared with Monte Carlo method for heterogeneous cases. For the dose calculation time, it takes about several seconds for one beam depends on collimator size and dose calculation grids. Conclusion: A GPU-based C/S dose engine has been developed for CyberKnife system, which was proven to be efficient and accurate for clinical purpose, and can be easily implemented in TPS.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2020

Coupling laser physics to radiation-hydrodynamics

In order to accurately model implosion hydrodynamics in a radiation-hydrodynamics code, it is essential to include accurate accounting for energy deposition physics. In inertial confinement fusion (ICF), where capsules are driven by lasers or laser-driven x-rays, energy deposition profiles and energy transport have a strong impact on the development and evolution of capsule dynamics and hydrodynamic instabilities. Nevertheless, accurately modeling laser beam propagation in radiation-hydrodynamics codes presents unique challenges associated with disparate resolution requirements, the potential to seed spurious noise in highly unstable systems, and computational expense. We discuss a new method for coupling laser ray-tracing physics to a radiation hydrodynamics code, developed in the process of implementing the Mazinisin laser ray-trace into the xRAGE radiation hydrodynamics code. In contrast to previous approaches, in which laser ray-tracing is performed on the radiation-hydrodynamics mesh, our method involves a mesh generation and evolution strategy that addresses the unique requirements of the laser ray-trace in a separate mesh, enabling performance enhancements and strategies to reduce noise seeded by the discretization of beams into computational rays. In addition, we have employed several methods to ensure that spurious mesh imprinting is minimized. These involved optimizing the laser and radiation-hydrodynamics meshes as well as interpolation between them and requires the use of an exact initialization method for the radiation-hydrodynamics mesh. Furthermore, these techniques have enabled efficient computation of laser-driven implosions and other experiments with minimal introduction of spurious noise.

47 OTHER INSTRUMENTATION↗

DOE OSTI2012

Zgoubi Users' Guide

The computer code zgoubi calculates trajectories of charged particles in magnetic and electric fields. At the origin specially adapted to the definition and adjustment of beam lines and magnetic spectrometers, it has so evolved that it allows the study of systems including complex sequences of optical elements such as dipoles, quadrupoles, arbitrary multipoles, FFAG magnets and other magnetic or electric devices, and is able as well to handle periodic structures. Compared to other codes, it presents several peculiarities, as follows - a non-exhaustive list : • a numerical method for integrating the Lorentz equation, based on Taylor series, which optimizes computing time and provides high accuracy and strong symplecticity, • spin tracking, using the same numerical method as for the Lorentz equation, • account of stochastic photon emission, and its effects on particle dynamics, • calculation of the synchrotron radiation electric field and spectra in arbitrary magnetic fields, from the ray-tracing outcomes, • the possibility of using a mesh, which allows ray-tracing from simulated or measured (1-D, 2-D or 3-D) electric and magnetic field maps, • a number Monte Carlo procedures : unlimited number of trajectories, in-flight decay, stochastic radiation, etc., • built-in fitting procedures allowing arbitrary variables and a large variety of constraints, easily expandable, • multi-turn tracking in circular accelerators including features proper to machine parameter calculation and survey, • simulation of time-varying power supplies, and • simulation of arbitrary radio-frequency programs. The initial version of zgoubi was dedicated to ray-tracing in magnetic elements, beam lines, spectrometers. It was perfected for the purpose of studying, and operating, the four spectrometers SPES I, II, III, IV at the Laboratoire National SATURNE (CEA-Saclay, France), and, later, SPEG at GANIL (Caen, France). Developments regarding spin tracking and ray-tracing in combined electric and magnetic fields were implemented, in the late 1980s and early 1990s respectively. In the mid-1990s, the computation of synchrotron radiation electromagnetic impulse and spectra was introduced, for the purpose of synchrotron radiation diagnostic R&D at LEP, and further applied to the design of the SR diagnostics installations at LHC in the early 2000s. In the mean time, several new optical elements were added, such as electro-magnetic and other electrostatic lenses. Used since several years for special studies in periodic machines (e.g., SATURNE at Saclay, COSY at Julich, LEP and LHC at CERN), zgoubi has also undergone extensive developments regarding storage ring related features. Many developments have been accomplished since the early 2000s in the frame of a number of project design and beam dynamics studies, as the neutrino factory, lepton and hadron colliders, spin studies at AGS and RHIC, etc. As a consequence the list of optical elements and the compendium of numerical methods, so-called “Glossary of Keywords” list, pp. 7 and 169, has stretched with new simulation and computing procedures, ranging from fitting (FIT2 procedure ; additional constraints) to overlapping magnetic field capabilities (DIPOLES, FFAG), spin manipulation (SPINR), optical elements (BEAMBEAM), radiation damping tools (SRLOSS) and many others (FAISTORE, MAP2D-E, OPTICS, PICKUPS, TWISS, etc.). The graphic interface to zgoubi (zpop, Part D) has undergone extensive developments, making it a convenient companion tool to the use of zgoubi.

43 PARTICLE ACCELERATORS↗

DOE OSTI2016

SU-D-206-02: Evaluation of Partial Storage of the System Matrix for Cone Beam Computed Tomography Using a GPU Platform

Purpose: Iterative reconstruction algorithms in computed tomography (CT) require a fast method for computing the intersections between the photons’ trajectories and the object, also called ray-tracing or system matrix computation. This work evaluates different ways to store the system matrix, aiming to reconstruct dense image grids in reasonable time. Methods: We propose an optimized implementation of the Siddon’s algorithm using graphics processing units (GPUs) with a novel data storage scheme. The algorithm computes a part of the system matrix on demand, typically, for one projection angle. The proposed method was enhanced with accelerating options: storage of larger subsets of the system matrix, systematic reuse of data via geometric symmetries, an arithmetic-rich parallel code and code configuration via machine learning. It was tested on geometries mimicking a cone beam CT acquisition of a human head. To realistically assess the execution time, the ray-tracing routines were integrated into a regularized Poisson-based reconstruction algorithm. The proposed scheme was also compared to a different approach, where the system matrix is fully pre-computed and loaded at reconstruction time. Results: Fast ray-tracing of realistic acquisition geometries, which often lack spatial symmetry properties, was enabled via the proposed method. Ray-tracing interleaved with projection and backprojection operations required significant additional time. In most cases, ray-tracing was shown to use about 66 % of the total reconstruction time. In absolute terms, tracing times varied from 3.6 s to 7.5 min, depending on the problem size. The presence of geometrical symmetries allowed for non-negligible ray-tracing and reconstruction time reduction. Arithmetic-rich parallel code and machine learning permitted a modest reconstruction time reduction, in the order of 1 %. Conclusion: Partial system matrix storage permitted the reconstruction of higher 3D image grid sizes and larger projection datasets at the cost of additional time, when compared to the fully pre-computed approach. This work was supported in part by the Fonds de recherche du Quebec - Nature et technologies (FRQ-NT). The authors acknowledge partial support by the CREATE Medical Physics Research Training Network grant of the Natural Sciences and Engineering Research Council of Canada (Grant No. 432290).

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

Study of lower hybrid wave propagation in ionized gas by Hamiltonian theory

In order to find an approximate solution to the Vlasov-Maxwell equation system describing the lower hybrid wave propagation in magnetic confined plasmas, the use of the WKB method leads to the ray tracing equations. The Hamiltonian character of the ray tracing equations is investigated analytically and numerically in order to deduce the physical properties of the wave propagating without absorption in the confined plasma. The consequences of the Hamiltonian character of the equations on the travelling wave, in particular, on the evolution of the parallel wavenumber along the propagation path have been accounted and the chaotic diffusion of the timeaveraged parallel wave-number towards higher values has been evaluated. Numerical analysis by means of a Runge-Kutta based algorithm implemented in a ray tracing code supplies the analytical considerations. A numerical tool based on the symplectic integration of the ray trajectories has been developed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2022

Evaluating the location capabilities of a regional infrasonic network in Utah, US, using both ray tracing-derived and empirical-derived celerity-range and backazimuth models

SUMMARY More realistic models for infrasound signal propagation across a region can be used to improve the precision and accuracy of spatial and temporal source localization estimates. Motivated by incomplete infrasound event bulletins in the Western US, the location capabilities of a regional infrasonic network of stations located between 84–458 km from the Utah Test and Training Range, Utah, USA, is assessed using a series of near-surface explosive events with complementary ground truth (GT) information. Signal arrival times and backazimuth estimates are determined with an automatic F-statistic based signal detector and manually refined by an analyst. This study represents the first application of three distinct celerity-range and backazimuth models to an extensive suite of realistic signal detections for event location purposes. A singular celerity and backazimuth deviation model was previously constructed using ray tracing analysis based on an extensive archive of historical atmospheric specifications and is applied within this study to test location capabilities. Similarly, a set of multivariate, season and location specific models for celerity and backazimuth are compared to an empirical model that depends on the observations across the infrasound network and the GT events, which accounts for atmospheric propagation variations from source to receiver. Discrepancies between observed and predicted signal celerities result in locations with poor accuracy. Application of the empirical model improves both spatial localization precision and accuracy; all but one location estimates retain the true GT location within the 90 per cent confidence bounds. Average mislocation of the events is 15.49 km and average 90 per cent error ellipse areas are 4141 km2. The empirical model additionally reduces origin time residuals; origin time residuals from the other location models are in excess of 160 s while residuals produced with the empirical model are within 30 s of the true origin time. We demonstrate that event location accuracy is driven by a combination of signal propagation model and the azimuthal gap of detecting stations. A direct relationship between mislocation, error ellipse area and increased station azimuthal gaps indicate that for sparse networks, detection backazimuths may drive location biases over traveltime estimates.

58 GEOSCIENCES↗

DOE OSTI2012

Surface scanning through a cylindrical tank of coupling fluid for clinical microwave breast imaging exams

Purpose: Microwave tomographic image quality can be improved significantly with prior knowledge of the breast surface geometry. The authors have developed a novel laser scanning system capable of accurately recovering surface renderings of breast-shaped phantoms immersed within a cylindrical tank of coupling fluid which resides completely external to the tank (and the aqueous environment) and overcomes the challenges associated with the optical distortions caused by refraction from the air, tank wall, and liquid bath interfaces. Methods: The scanner utilizes two laser line generators and a small CCD camera mounted concentrically on a rotating gantry about the microwave imaging tank. Various calibration methods were considered for optimizing the accuracy of the scanner in the presence of the optical distortions including traditional ray tracing and image registration approaches. In this paper, the authors describe the construction and operation of the laser scanner, compare the efficacy of several calibration methods-including analytical ray tracing and piecewise linear, polynomial, locally weighted mean, and thin-plate-spline (TPS) image registrations-and report outcomes from preliminary phantom experiments. Results: The results show that errors in calibrating camera angles and position prevented analytical ray tracing from achieving submillimeter accuracy in the surface renderings obtained from our scanner configuration. Conversely, calibration by image registration reliably attained mean surface errors of less than 0.5 mm depending on the geometric complexity of the object scanned. While each of the image registration approaches outperformed the ray tracing strategy, the authors found global polynomial methods produced the best compromise between average surface error and scanner robustness. Conclusions: The laser scanning system provides a fast and accurate method of three dimensional surface capture in the aqueous environment commonly found in microwave breast imaging. Optical distortions imposed by the imaging tank and coupling bath diminished the effectiveness of the ray tracing approach; however, calibration through image registration techniques reliably produced scans of submillimeter accuracy. Tests of the system with breast-shaped phantoms demonstrated the successful implementation of the scanner for the intended application.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

NASA NTRS1999

Wave Dynamics and Transport in the Stratosphere

The report discusses: (1) Gravity waves generated by tropical convection: A study in which a two-dimensional cloud-resolving model was used to examine the possible role of gravity waves generated by a simulated tropical squall line in forcing the quasi-biennial oscillation was completed. (2) Gravity wave ray tracing studies:It was developed a linear ray tracing model of gravity wave propagation to extend the nonlinear storm model results into the mesosphere and thermosphere. (3) tracer filamentation: Vertical soundings of stratospheric ozone often exhibit laminated tracer structures characterized by strong vertical tracer gradients. (4) Mesospheric gravity wave modeling studies: Although our emphasis in numerical simulation of gravity waves generated by convection has shifted from simulation of idealized two-dimensional squall lines to the most realistic (and complex) study of wave generation by three-dimensional storms. (5) Gravity wave climatology studies: Mr. Alexander applied a linear gravity wave propagation model together with observations of the background wind and stability fields to compute climatologies of gravity wave activity for comparison to observations. (6) Convective forcing of gravity waves: Theoretical study of gravity wave forcing by convective heat sources has completed. (7) Gravity waves observation from UARS: The objective of this work is to apply ray tracing, and other model technique, in order to determine to what extend the horizontal and vertical variation in satellite observed distribution of small-scale temperature variance can be attributed to gravity waves from particular sources. (8) The annual and interannual variations in temperature and mass flux near the tropical tropopause. and (9) Three dimensional cloud model.

Holton, James R.↗

DOE OSTI2019

Uncollided flux techniques for arbitrary finite element meshes

The uncollided angular flux can be difficult to compute accurately in discrete-ordinate radiation transport codes, especially in weakly-scattering configurations with localized sources. It has long been recognized that an analytical or semi-analytical treatment of the uncollided flux, coupled with a discrete-ordinate solution for the collided flux, can yield dramatic improvements in solution accuracy and computational efficiency. In this paper, we present such an algorithm for the semi-analytical calculation of the uncollided flux. This algorithm is unique in several aspects: (1) it applies to arbitrary polyhedral cells (and can be thus coupled with collided flux solvers that support arbitrary polyhedral meshes without the need for explicit tetrahedral re-meshing), (2) it provides accurate uncollided solutions near sources, (3) it is devised with parallel implementation in mind, and (4) it minimizes the total number of traced rays and maintains a reasonable ray density on each local subdomain. This paper provides a complete derivation of the algorithm and demonstrates its important features on a set of simple examples and a standard transport benchmark. Assessment of its parallel performance will be the subject of a subsequent paper.

42 ENGINEERING↗

DOE OSTI2014

A Thermo-Optic Propagation Modeling Capability.

A new theoretical basis is derived for tracing optical rays within a finite-element (FE) volume. The ray-trajectory equations are cast into the local element coordinate frame and the full finite-element interpolation is used to determine instantaneous index gradient for the ray-path integral equation. The FE methodology (FEM) is also used to interpolate local surface deformations and the surface normal vector for computing the refraction angle when launching rays into the volume, and again when rays exit the medium. The method is implemented in the Matlab(TM) environment and compared to closed- form gradient index models. A software architecture is also developed for implementing the algorithms in the Zemax(TM) commercial ray-trace application. A controlled thermal environment was constructed in the laboratory, and measured data was collected to validate the structural, thermal, and optical modeling methods.

Schrader, Karl↗

NASA NTRS1982

Tolerance analysis of optical telescopes using coherent addition of wavefront errors

A near diffraction-limited telescope requires that tolerance analysis be done on the basis of system wavefront error. One method of analyzing the wavefront error is to represent the wavefront error function in terms of its Zernike polynomial expansion. A Ramsey-Korsch ray trace package, a computer program that simulates the tracing of rays through an optical telescope system, was expanded to include the Zernike polynomial expansion up through the fifth-order spherical term. An option to determine a 3 dimensional plot of the wavefront error function was also included in the Ramsey-Korsch package. Several assimulation runs were analyzed to determine the particular set of coefficients in the Zernike expansion that are effected by various errors such as tilt, decenter and despace. A 3 dimensional plot of each error up through the fifth-order spherical term was also included in the study. Tolerance analysis data are presented.

Davenport, J. W.↗

NASA NTRS1994

Refraction of high frequency noise in an arbitrary jet flow

Refraction of high frequency noise by mean flow gradients in a jet is studied using the ray-tracing methods of geometrical acoustics. Both the two-dimensional (2D) and three-dimensional (3D) formulations are considered. In the former case, the mean flow is assumed parallel and the governing propagation equations are described by a system of four first order ordinary differential equations. The 3D formulation, on the other hand, accounts for the jet spreading as well as the axial flow development. In this case, a system of six first order differential equations are solved to trace a ray from its source location to an observer in the far field. For subsonic jets with a small spreading angle both methods lead to similar results outside the zone of silence. However, with increasing jet speed the two prediction models diverge to the point where the parallel flow assumption is no longer justified. The Doppler factor of supersonic jets as influenced by the refraction effects is discussed and compared with the conventional modified Doppler factor.

Khavaran, Abbas↗

NASA NTRS2019

Understanding the Impact of Meteorological Spatiotemporal Variability on Distant Focusing Overpressure Risk

Since the 1950s, the amplification of blast energy from explosions has been understood to be a significant hazard to public safety at launch ranges. Historically, the risk assessment of the Distant Focusing Overpressure (DFO) hazard started with a single temperature and wind profile (e.g., a radiosonde launch) as input to acoustic 1-D ray tracing models. By analyzing rays propagation and performing ray tracing, population centers under high DFO risk can be identified. Although this method is useful, less is known about how the blast waves can be focused when the spatiotemporal variability of the input profiles are considered. In summary, this work aims to consider how realistic atmospheric boundary layer variability (e.g., turbulence, land-surface contrasts) may affect blast waves propagation and focusing and, as a result, DFO risk assessment results.

Blumberg, W. Greg↗

DOE OSTI2014

Deterministic Simulation of First-Order Scattering in a Clinical X-ray Computed Tomography Scanner - Paper 81

In nondestructive testing (NDT) and medical diagnostic x-ray imaging (photon energy<140 keV), scattered x-ray caused by Compton and Rayleigh scattering should be eliminated. Scattered x-ray photons reduce image contrast, increase image noise, and introduce artifact into the reconstructed computed tomography (CT) images. In cone-beam CT, where the coverage of the x-ray beam and the area of the detector are significantly larger than those in fan-beam CT, x-ray photon scatter is one of the major sources of image degradation. The artifacts caused by scattered x-ray photon can be divided into two categories: 1) low spatial frequency scatter profile adds a positive bias to the detected radiation signal, thus reducing the effective attenuation of the imaged object, resulting in a negative bias in the measured linear attenuation coefficient in the image; 2) a high spatial frequency scatter profile causes a differential artifact, such as shading in uniform regions. A real x-ray scan is composed of both low and high frequency scatter profiles. Thus, the key to a successful scatter correction is the ability to accurately capture the scatter profile of a real x-ray imaging scan. The most accurate method for estimating a scatter profile is the Monte Carlo simulation. However, the computation cost of the Monte Carlo method makes it unfeasible for simulating real and complex scan geometries in clinical settings. A practical yet accurate scatter profile estimation method is through ray tracing techniques, where the scatter profiles are computed by tracking rays through the object's volume. The x-ray from the source is tracked when it interacts with the material in the volume. The interaction creates scattered x-rays, in all possible directions. These rays are again either attenuated or scattered, creating cascaded scatter events. In x-ray CT, the first-order scattering (where only one scatter interaction is encountered) accounts for the most severe image artifacts since this first-order scatter contains a high frequency component of the scatter profile. Previous studies have shown that ray tracing techniques are quite effective in simulating the contribution of first-order scattering in radiological images. In this study, a similar ray tracing technique is applied to simulate the scatter profile of a real x-ray computed tomography (CT) scan in clinical settings. A good agreement has been found between the simulated scatter profile and the experimental measurement result. (authors)

61 RADIATION PROTECTION AND DOSIMETRY↗

DOE OSTI2014

A nonvoxel-based dose convolution/superposition algorithm optimized for scalable GPU architectures

Purpose: Real-time adaptive planning and treatment has been infeasible due in part to its high computational complexity. There have been many recent efforts to utilize graphics processing units (GPUs) to accelerate the computational performance and dose accuracy in radiation therapy. Data structure and memory access patterns are the key GPU factors that determine the computational performance and accuracy. In this paper, the authors present a nonvoxel-based (NVB) approach to maximize computational and memory access efficiency and throughput on the GPU. Methods: The proposed algorithm employs a ray-tracing mechanism to restructure the 3D data sets computed from the CT anatomy into a nonvoxel-based framework. In a process that takes only a few milliseconds of computing time, the algorithm restructured the data sets by ray-tracing through precalculated CT volumes to realign the coordinate system along the convolution direction, as defined by zenithal and azimuthal angles. During the ray-tracing step, the data were resampled according to radial sampling and parallel ray-spacing parameters making the algorithm independent of the original CT resolution. The nonvoxel-based algorithm presented in this paper also demonstrated a trade-off in computational performance and dose accuracy for different coordinate system configurations. In order to find the best balance between the computed speedup and the accuracy, the authors employed an exhaustive parameter search on all sampling parameters that defined the coordinate system configuration: zenithal, azimuthal, and radial sampling of the convolution algorithm, as well as the parallel ray spacing during ray tracing. The angular sampling parameters were varied between 4 and 48 discrete angles, while both radial sampling and parallel ray spacing were varied from 0.5 to 10 mm. The gamma distribution analysis method (γ) was used to compare the dose distributions using 2% and 2 mm dose difference and distance-to-agreement criteria, respectively. Accuracy was investigated using three distinct phantoms with varied geometries and heterogeneities and on a series of 14 segmented lung CT data sets. Performance gains were calculated using three 256 mm cube homogenous water phantoms, with isotropic voxel dimensions of 1, 2, and 4 mm. Results: The nonvoxel-based GPU algorithm was independent of the data size and provided significant computational gains over the CPU algorithm for large CT data sizes. The parameter search analysis also showed that the ray combination of 8 zenithal and 8 azimuthal angles along with 1 mm radial sampling and 2 mm parallel ray spacing maintained dose accuracy with greater than 99% of voxels passing the γ test. Combining the acceleration obtained from GPU parallelization with the sampling optimization, the authors achieved a total performance improvement factor of >175 000 when compared to our voxel-based ground truth CPU benchmark and a factor of 20 compared with a voxel-based GPU dose convolution method. Conclusions: The nonvoxel-based convolution method yielded substantial performance improvements over a generic GPU implementation, while maintaining accuracy as compared to a CPU computed ground truth dose distribution. Such an algorithm can be a key contribution toward developing tools for adaptive radiation therapy systems.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1972

Moment expansion for ionospheric range error

On a plane earth, the ionospheric or tropospheric range error depends only on the total refractivity content or zeroth moment of the refracting layer and the elevation angle. On a spherical earth, however, the dependence is more complex; so for more accurate results it has been necessary to resort to complex ray-tracing calculations. A simple, high-accuracy alternative to the ray-tracing calculation is presented. By appropriate expansion of the angular dependence in the ray-tracing integral in a power series in height, an expression is obtained for the range error in terms of a simple function of elevation angle, E, at the expansion height and of the mth moment of the refractivity, N, distribution about the expansion height. The rapidity of convergence is heavily dependent on the choice of expansion height. For expansion heights in the neighborhood of the centroid of the layer (300-490 km), the expansion to N = 2 (three terms) gives results accurate to about 0.4% at E = 10 deg. As an analytic tool, the expansion affords some insight on the influence of layer shape on range errors in special problems.

Mallinckrodt, A.↗