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At least 1,171 records · Page 65
All sourcesNASA NTRSDOE OSTI
DOE OSTI2013

Implementing intensity modulated radiotherapy to the prostate bed: Dosimetric study and early clinical results

Salvage intensity modulated radiotherapy (IMRT) to the prostate bed has hardly been studied so far. We present here a feasibility study and early clinical results for 10 patients. These patients were selected on the basis of having either a biochemical relapse or high risk histology after prostatectomy. They were treated using “sliding-window” IMRT to 68 Gy in 34 fractions. Three-dimensional conformal radiotherapy (3D-CRT) plans were generated using the same planning computed tomography data set. Dose coverage of planning target volumes (PTVs) and of organs-at-risk (OAR, namely: rectum, bladder, and femoral heads) were compared. Acute toxicity and chronic toxicity were measured using the Common Toxicity Criteria for Adverse Events version 3.0 scale. IMRT significantly reduces the dose above the prescription dose given to the PTV1 (mean dose: IMRT 67.2 Gy vs 3D-CRT 67.7 Gy (p = 0.0137)), without altering dose coverage for PTV2 (mean dose: IMRT 68.1 Gy vs 3D-CRT 68.0 Gy (p = 0.3750)). Doses to OAR were lower with IMRT and differences were statistically significant (mean dose: IMRT 51.4 Gy vs 3D-CRT 56.6 Gy for rectum (p = 0.002), IMRT 45.1 Gy vs 3D-CRT 53.1 Gy for bladder (p = 0.002), and IMRT 26.1 Gy vs 3D-CRT 28.4 Gy for femoral heads (p = 0.0059)). There was no acute or chronic genitourinary or gastrointestinal toxicity >1 with a median follow-up of 38 months. IMRT to the prostatic fossa is feasible and reduces dose to OAR, with consequential limited toxicity.

61 RADIATION PROTECTION AND DOSIMETRY↗
DOE OSTI2013

Interior-Point Methods for Estimating Seasonal Parameters in Discrete-Time Infectious Disease Models

Infectious diseases remain a significant health concern around the world. Mathematical modeling of these diseases can help us understand their dynamics and develop more effective control strategies. In this work, we show the capabilities of interior-point methods and nonlinear programming (NLP) formulations to efficiently estimate parameters in multiple discrete-time disease models using measles case count data from three cities. These models include multiplicative measurement noise and incorporate seasonality into multiple model parameters. Our results show that nearly identical patterns are estimated even when assuming seasonality in different model parameters, and that these patterns show strong correlation to school term holidays across very different social settings and holiday schedules. We show that interior-point methods provide a fast and flexible approach to parameterizing models that can be an alternative to more computationally intensive methods.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2024

Sequential Inference of Hospitalization Electronic Health Records Using Probabilistic Models

In the dynamic hospital setting, decision support can be a valuable tool for improving patient outcomes. Data-driven inference of future outcomes is challenging in this dynamic setting, where long sequences such as laboratory tests and medications are updated frequently. This is due in part to heterogeneity of data types and mixed-sequence types contained in variable length sequences. In this work we design a probabilistic unsupervised model for multiple arbitrary-length sequences contained in hospitalization Electronic Health Record (EHR) data. The model uses a latent variable structure and captures complex relationships between medications, diagnoses, laboratory tests, neurological assessments, and medications. It can be trained on original data, without requiring any lossy transformations or time binning. Inference algorithms are derived that use partial data to infer properties of the complete sequences, including their length and presence of specific values. We train this model on data from subjects receiving medical care in the Kaiser Permanente Northern California integrated healthcare delivery system. The results are evaluated against held-out data for predicting the length of sequences and presence of Intensive Care Unit (ICU) in hospitalization bed sequences. Our method outperforms a baseline approach, showing that in these experiments the trained model captures information in the sequences that is informative of their future values.

97 MATHEMATICS AND COMPUTING↗
NASA NTRS1983

Environmental data display

Methods for using a combination of computer-generated color graphics and image processing techniques to display a large data base of environment information are described. The data source can be either field data or mathematical models, reduced to summary statistics that characterize the data field as a whole. Sharp gradients are plotted into contour plots, which can also feature shades, degree of brightness, and saturation levels for fine-tuning the image. The basic concepts of digital image processing are reviewed, including location of the pixels, intensity mapping operations, pseudocolor enhancements, neighborhood averaging, and smoothing. Sample applications are presented in terms of emissions and air quality distributions over the south coast air basin of southern California.

Hussey, K. J.↗
NASA NTRS1986

Geological mapping potential of computer-enhanced images from the Shuttle Imaging Radar - Lisbon Valley Anticline, Utah

Computer-enhancement techniques applied to the SIR-A data from the Lisbon Valley area in the northern portion of the Paradox basin increased the value of the imagery in the development of geologically useful maps. The enhancement techniques include filtering to remove image speckle from the SIR-A data and combining these data with Landsat multispectral scanner data. A method well-suited for the combination of the data sets utilized a three-dimensional domain defined by intensity-hue-saturation (IHS) coordinates. Such a system allows the Landsat data to modulate image intensity, while the SIR-A data control image hue and saturation. Whereas the addition of Landsat data to the SIR-A image by means of a pixel-by-pixel ratio accentuated textural variations within the image, the addition of color to the combined images enabled isolation of areas in which gray-tone contrast was minimal. This isolation resulted in a more precise definition of stratigraphic units.

Curlis, J. D.↗
NASA NTRS1998

Holographic Storage as a Solution to Space Imaging Requirements

The data growth experienced in the recent past has been of staggering proportions. Over the past 10 years, tape data storage density (with the same form factor) has increased according to Moore's law, doubling every 18 months. However, during the same period, data transfer speeds have only increased at a rate of about 1.3 times every 18 months, and thus have fallen behind data density growth rates by a factor of at least 3. Coupled with data media density growth, data storage requirements have gone up significantly. According to a recent Computer Technology Review article (March 1998) the total storage at a typical Fortune 1000 site is projected to escalate from just 10 TB in 1997 to 1 PB by the year 2000. In the next 5 years, a typical large database system for U.S. government agencies is expected to accept 5 TB per day, maintain 300 TB on-line (within 15 seconds to 1 minute access time), and archive from 15 to 100 PB. Additionally, data intensive programs such as NASA's Earth Observation System (EOS) and the intelligence data archival systems at the Rome Air Development Center, and scientific laboratories such as Thomas Jefferson National Accelerator Facility will have enormously large scientific databases with very large storage requirements.

Halem, Milton↗
DOE OSTI2015

Data Fusion for a Vision-Radiological System for Source Tracking and Discovery

A multidisciplinary approach to allow the tracking of the movement of radioactive sources by fusing data from multiple radiological and visual sensors is under development. The goal is to improve the ability to detect, locate, track and identify nuclear/radiological threats. The key concept is that such widely available visual and depth sensors can impact radiological detection, since the intensity fall-off in the count rate can be correlated to movement in three dimensions. To enable this, we pose an important question; what is the right combination of sensing modalities and vision algorithms that can best compliment a radiological sensor, for the purpose of detection and tracking of radioactive material? Similarly what is the best radiation detection methods and unfolding algorithms suited for data fusion with tracking data? Data fusion of multi-sensor data for radiation detection have seen some interesting developments lately. Significant examples include intelligent radiation sensor systems (IRSS), which are based on larger numbers of distributed similar or identical radiation sensors coupled with position data for network capable to detect and locate radiation source. Other developments are gamma-ray imaging systems based on Compton scatter in segmented detector arrays. Similar developments using coded apertures or scatter cameras for neutrons have recently occurred. The main limitation of such systems is not so much in their capability but rather in their complexity and cost which is prohibitive for large scale deployment. Presented here is a fusion system based on simple, low-cost computer vision and radiological sensors for tracking of multiple objects and identifying potential radiological materials being transported or shipped. The main focus of this work is the development on two separate calibration algorithms for characterizing the fused sensor system. The deviation from a simple inverse square-root fall-off of radiation intensity is explored and accounted for. In particular, the computer vision system enables a map of distance-dependence of the sources being tracked. Infrared, laser or stereoscopic vision sensors are all options for computer-vision implementation depending on interior vs exterior deployment, resolution desired and other factors. Similarly the radiation sensors will be focused on gamma-ray or neutron detection due to the long travel length and ability to penetrate even moderate shielding. There is a significant difference between the vision sensors and radiation sensors in the way the 'source' or signals are generated. A vision sensor needs an external light-source to illuminate the object and then detects the re-emitted illumination (or lack thereof). However, for a radiation detector, the radioactive material is the source itself. The only exception to this is the field of active interrogations where radiation is beamed into a material to entice new/additional radiation emission beyond what the material would emit spontaneously. The aspect of the nuclear material being the source itself means that all other objects in the environment are 'illuminated' or irradiated by the source. Most radiation will readily penetrate regular material, scatter in new directions or be absorbed. Thus if a radiation source is located near a larger object that object will in turn scatter some radiation that was initially emitted in a direction other than the direction of the radiation detector, this can add to the count rate that is observed. The effect of these scatter is a deviation from the traditional distance dependence of the radiation signal and is a key challenge that needs a combined system calibration solution and algorithms. Thus both an algebraic approach as well as a statistical approach have been developed and independently evaluated to investigate the sensitivity to this deviation from the simplified radiation fall-off as a function of distance. The resulting calibrated system algorithms are used and demonstrated in various laboratory scenarios, and later in realistic tracking scenarios. The selection and testing of radiological and computer-vision sensors for the additional specific scenarios will be the subject of ongoing and future work. (authors)

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗
DOE OSTI2014

SU-E-QI-14: Quantitative Variogram Detection of Mild, Unilateral Disease in Elastase-Treated Rats

Purpose: Determining the presence of mild or early disease in the lungs can be challenging and subjective. We present a rapid and objective method for evaluating lung damage in a rat model of unilateral mild emphysema based on a new approach to heterogeneity assessment. We combined octree decomposition (used in three-dimensional (3D) computer graphics) with variograms (used in geostatistics to assess spatial relationships) to evaluate 3D computed tomography (CT) lung images for disease. Methods: Male, Sprague-Dawley rats (232 ± 7 g) were intratracheally dosed with 50 U/kg of elastase dissolved in 200 μL of saline to a single lobe (n=6) or with saline only (n=5). After four weeks, 3D micro-CT images were acquired at end expiration on mechanically ventilated rats using prospective gating. Images were masked, and lungs were decomposed to homogeneous blocks of 2×2×2, 4×4×4, and 8×8×8 voxels using octree decomposition. The spatial variance – the square of the difference of signal intensity – between all pairs of the 8×8×8 blocks was calculated. Variograms – graphs of distance vs. variance - were made, and data were fit to a power law and the exponent determined. The mean HU values, coefficient of variation (CoV), and the emphysema index (EI) were calculated and compared to the variograms. Results: The variogram analysis showed that significant differences between groups existed (p<0.01), whereas the mean HU (p=0.07), CoV (p=0.24), and EI (p=0.08) did not. Calculation time for the variogram for a typical 1000 block decomposition was ∼6 seconds, and octree decomposition took ∼2 minutes. Decomposing the images prior to variogram calculation resulted in a ∼700x decrease in time as compared to other published approaches. Conclusions: Our results suggest that the approach combining octree decomposition and variogram analysis may be a rapid, non-subjective, and sensitive imaging-based biomarker for quantitative characterization of lung disease.

60 APPLIED LIFE SCIENCES↗
DOE OSTI2017

Advanced Manufacturing for Thermal and Environmental Control Systems: Achieving National Energy Goals

This project was part of a regional initiative in the five counties of Central New York (CNY) that received funding from the U.S. Department of Energy (DOE) and four other federal agencies through the 2012 Advanced Manufacturing Jobs and Innovation Accelerator Challenge (AMJIAC). The CNY initiative was focused on cultivating the emergent regional cluster in “Advanced Manufacturing for Thermal and Environmental Control (AM-TEC).” As one component of the CNY AM-TEC initiative, the DOE-funded project supported five research & development seed projects that strategically targeted: 1) needs and opportunities of CNY AM-TEC companies, and 2) the goal of DOE’s Advanced Manufacturing Office (AMO) to reduce energy consumption by 50% across product life-cycles over 10 years. The project also sought to fulfill the AMO mission of developing and demonstrating new, energy-efficient processing and materials technologies at a scale adequate to prove their value to manufacturers and spur investment. The five seed projects demonstrated technologies and processes that can reduce energy intensity and improve production as well as use less energy throughout their lifecycles. The project was conducted over three years in two 18-month budget periods. During the first budget period, two projects proposed in the original AMJAIC application were successfully completed: Seed Project 1 focused on saving energy in heat transfer processes via development of nano structured surfaces to significantly increase heat flux; Seed Project 2 addressed saving energy in data centers via subzero cooling of the computing processors. Also during the first budget period, a process was developed and executed to select a second round of seed projects via a competitive request for proposals from regional companies and university collaborators. Applicants were encouraged to form industry-academic partnerships to leverage experience and resources of public and private sectors in the CNY region. Proposals were evaluated by a national panel of experts. Three projects were selected for awards and were completed successfully during the second budget period: Seed Project 3 focused on enabling self-powered furnaces to permit residents to shelter in place during power outages; Seed Project 4 addressed development of a novel method of controlling air conditioning systems that could enable flexible load matching in market segments not possible with existing technologies; and Seed Project 5 focused on the creation of smarter occupancy sensors to enable effective highly localized demand based ventilation.

30 DIRECT ENERGY CONVERSION↗
NASA NTRS1977

Uranus occults SAO158687

Experience gained in obtaining atmospheric parameters, oblatenesses, and diameters of Jupiter and Mars from recent stellar occultations by these planets is used to predict what can be learned from the March 1977 occultation of the star SAO158687 by Uranus. The spectra of this star and Uranus are compared to indicate the relative instrument intensities of the two objects, the four passbands where the relative intensities are most nearly equal are listed, and expected photon fluxes from the star are computed on the assumption that it has UBVRI colors appropriate for a K5 main-sequence object. It is shown that low photon noise errors can be achieved by choosing appropriate passbands for observation, and the rms error expected for the Uranus temperature profiles obtained from the occultation light curves is calculated. It is suggested that observers of this occultation should record their data digitally for optimum time resolution.

Elliot, J. L.↗
NASA NTRS1982

Measurement potential of laser speckle velocimetry

Laser speckle velocimetry, the measurement of fluid velocity by measuring the translation of speckle pattern or individual particles that are moving with the fluid, is described. The measurement is accomplished by illuminating the fluid with consecutive pulses of Laser Light and recording the images of the particles or the speckles on a double exposed photographic plate. The plate contains flow information throughout the image plane so that a single double exposure may provide data at hundreds or thousands of points in the illuminated region of the fluid. Conventional interrogation of the specklegram involves illuminating the plate to form Young's fringes, whose spacing is inversely proportional to the speckle separation. Subsequently the fringes are digitized and analyzed in a computer to determine their frequency and orientation, yielding the velocity magnitude and orientation. The Young's fringe technique is equivalent to performing a 2-D spatial correlation of the double exposed specklegram intensity pattern, and this observation suggests that correlation should be considered as an alternative processing method. The principle of the correlation technique is examined.

Adrian, R. J.↗
NASA NTRS1993

A comparative study of computational solutions to flow over a backward-facing step

A comparative study was conducted for computational fluid dynamic solutions to flow over a backward-facing step. This flow is a benchmark problem, with a simple geometry, but involves complicated flow physics such as free shear layers, reattaching flow, recirculation, and high turbulence intensities. Three Reynolds-averaged Navier-Stokes flow solvers with k-epsilon turbulence models were used, each using a different solution algorithm: finite difference, finite element, and hybrid finite element - finite difference. Comparisons were made with existing experimental data. Results showed that velocity profiles and reattachment lengths were predicted reasonably well by all three methods, while the skin friction coefficients were more difficult to predict accurately. It was noted that, in general, selecting an appropriate solver for each problem to be considered is important.

Mizukami, M.↗
DOE OSTI2020

Effectively Using Remote I/O For Work Composition in Distributed Workflows

Distributed scientific workflows are becoming more important with the interest in incorporating AI into their loops. A critical programming and performance question is how to compose workflow tasks when data is produced on one system but must be consumed on another. Since the dominant technique is composition with remote I/O, this paper explores its performance expectations. We describe BigFlowSim, a workflow I/O simulator that captures key implementation choices for remote I/O, including intensity, reuse, locality, access pattern, and data movement.With BigFlowSim, we generate a synthetic benchmark. We quantify the effects of each parameter with a performance sensitivity study. We explain trends in terms of data movement reduction and show that, under certain conditions, it is possible to establish a total order among most parameters. We apply these insights to a high energy physics workflow, Belle II Monte Carlo and simulate several I/O optimizations. Speedups range from 5% to 2×, without changing compute time.

Friese, Ryan D.↗
NASA NTRS2017

Nominal 30-M Cropland Extent Map of Continental Africa by Integrating Pixel-Based and Object-Based Algorithms Using Sentinel-2 and Landsat-8 Data on Google Earth Engine

A satellite-derived cropland extent map at high spatial resolution (30-m or better) is a must for food and water security analysis. Precise and accurate global cropland extent maps, indicating cropland and non-cropland areas, is a starting point to develop high-level products such as crop watering methods (irrigated or rainfed), cropping intensities (e.g., single, double, or continuous cropping), crop types, cropland fallows, as well as assessment of cropland productivity (productivity per unit of land), and crop water productivity (productivity per unit of water). Uncertainties associated with the cropland extent map have cascading effects on all higher-level cropland products. However, precise and accurate cropland extent maps at high spatial resolution over large areas (e.g., continents or the globe) are challenging to produce due to the small-holder dominant agricultural systems like those found in most of Africa and Asia. Cloud-based Geospatial computing platforms and multi-date, multi-sensor satellite image inventories on Google Earth Engine offer opportunities for mapping croplands with precision and accuracy over large areas that satisfy the requirements of broad range of applications. Such maps are expected to provide highly significant improvements compared to existing products, which tend to be coarser in resolution, and often fail to capture fragmented small-holder farms especially in regions with high dynamic change within and across years. To overcome these limitations, in this research we present an approach for cropland extent mapping at high spatial resolution (30-m or better) using the 10-day, 10 to 20-m, Sentinel-2 data in combination with 16-day, 30-m, Landsat-8 data on Google Earth Engine (GEE). First, nominal 30-m resolution satellite imagery composites were created from 36,924 scenes of Sentinel-2 and Landsat-8 images for the entire African continent in 2015-2016. These composites were generated using a median-mosaic of five bands (blue, green, red, near-infrared, NDVI) during each of the two periods (period 1: January-June 2016 and period 2: July-December 2015) plus a 30-m slope layer derived from the Shuttle Radar Topographic Mission (SRTM) elevation dataset. Second, we selected Cropland/Non-cropland training samples (sample size 9791) from various sources in GEE to create pixel-based classifications. As supervised classification algorithm, Random Forest (RF) was used as the primary classifier because of its efficiency, and when over-fitting issues of RF happened due to the noise of input training data, Support Vector Machine (SVM) was applied to compensate for such defects in specific areas. Third, the Recursive Hierarchical Segmentation (RHSeg) algorithm was employed to generate an object-oriented segmentation layer based on spectral and spatial properties from the same input data. This layer was merged with the pixel-based classification to improve segmentation accuracy. Accuracies of the merged 30-m crop extent product were computed using an error matrix approach in which 1754 independent validation samples were used. In addition, a comparison was performed with other available cropland maps as well as with LULC maps to show spatial similarity. Finally, the cropland area results derived from the map were compared with UN FAO statistics. The independent accuracy assessment showed a weighted overall accuracy of 94, with a producers accuracy of 85.9 (or omission error of 14.1), and users accuracy of 68.5 (commission error of 31.5) for the cropland class. The total net cropland area (TNCA) of Africa was estimated as 313 Mha for the nominal year 2015.

Cropland mapping; cropland areas; 30-m; Landsat-8;↗
DOE OSTI2014

An Advanced Network and distributed Storage Laboratory (ANDSL) for Data Intensive Science (Final Report)

The original intent of this project was to build and operate an Advanced Network and Distributed Storage Laboratory (ANDSL) for Data Intensive Science that will prepare the Open Science Grid (OSG) community for a new generation of wide area communication capabilities operating at a 100Gb rate. The plan was to engage a team of four dedicated scientists that will design, develop and operate a state of the art laboratory that will be fully integrated into the organizational and operational infrastructure of the OSG. The ANDSL was planned to include host-based hardware and software required to profile, emulate and study real-life distributed storage workloads at rates of 100 Gbps. The laboratory was designed to utilize the Department Of Energy’s Advanced Network Initiative (ANI) 100GbTestbed as connections to the fabric become available so that OSG stakeholders can use it to profile real-life data intensive science applications as well as experiment with advanced storage and data management technologies. The goal of the original program of work was to close the adoption gap, decreasing the time between availability of production 100Gbps links and the end-to-end use of such a network to enable scientific discovery.

100Gb networks↗
DOE OSTI2022

Development, verification, and validation of comprehensive acoustic fluid-structure interaction capabilities in an open-source computational platform

The acoustic fluid-structure interaction (FSI) formulation is a practical numerical approach for the seismic analysis of fluid-filled tanks. However, there are no verification and validation studies reported in the literature that demonstrate the ability of an acoustic FSI numerical model to predict responses important to structural and mechanical design for intense translational and rotational earthquake inputs. Herein, an acoustic FSI formulation is implemented in the open-source Multiphysics Object-Oriented Simulation Environment (MOOSE), and is formally verified and validated using analytical solutions and code-to-code verification, and experimental data, respectively. The analytical solutions are for small amplitude, unidirectional seismic inputs. The code-to-code verification utilizes a previously verified and validated Arbitrary Lagrangian-Eulerian (ALE) numerical model in the commercial finite element code LS-DYNA. The validation studies utilize a comprehensive data set assembled from results of 3D earthquake-simulator tests of a fluid-filled vessel. The acoustic numerical model in MOOSE is verified and validated for hydrodynamic pressures and support reactions except for cases that involve significant convective response. For small amplitude inputs, numerically predicted wave heights match those of the analytical solutions. The numerical model is not verified and validated for wave height calculations under intense 3D seismic inputs. The run times for the acoustic FSI simulations in MOOSE are an order of magnitude, or more, shorter than for the corresponding ALE simulations in LS-DYNA. The utility of the MOOSE acoustic FSI implementation is demonstrated by seismic analysis of a building equipped with a fluid-filled, advanced nuclear reactor.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗
DOE OSTI2015

ON A NEW THEORETICAL FRAMEWORK FOR RR LYRAE STARS. I. THE METALLICITY DEPENDENCE

We present new nonlinear, time-dependent convective hydrodynamical models of RR Lyrae stars computed assuming a constant helium-to-metal enrichment ratio and a broad range in metal abundances (Z = 0.0001–0.02). The stellar masses and luminosities adopted to construct the pulsation models were fixed according to detailed central He-burning horizontal-branch evolutionary models. The pulsation models cover a broad range in stellar luminosity and effective temperatures and the modal stability is investigated for both fundamental (FU) and first overtone polsators (FOs). We predict the topology of the instability strip (IS) as a function of the metal content and new analytical relations for the edges of the IS in the observational plane. Moreover, a new analytical relation to constrain the pulsation mass of double pulsators as a function of the period ratio and the metal content is provided. We derive new Period–Radius–Metallicity relations for FU and FO pulsators. They agree quite well with similar empirical and theoretical relations in the literature. From the predicted bolometric light curves, transformed into optical (UBVRI) and near-infrared (NIR; JHK) bands, we compute the intensity-averaged mean magnitudes along the entire pulsation cycle and in turn new and homogenous metal-dependent (RIJHK) Period–Luminosity relations. Moreover, we compute new dual and triple-band optical, optical–NIR, and NIR Period–Wesenheit–Metallicity relations. Interestingly, we find that the optical Period-W(V, B–V) is independent of the metal content and that the accuracy of individual distances is a balance between the adopted diagnostics and the precision of photometric and spectroscopic data sets.

79 ASTRONOMY AND ASTROPHYSICS↗
NASA NTRS1994

Errors induced by the neglect of polarization in radiance calculations for Rayleigh-scattering atmospheres

Although neglecting polarization and replacing the rigorous vector radiative transfer equation by its approximate scalar counterpart has no physical background, it is a widely used simplification when the incident light is unpolarized and only the intensity of the reflected light is to be computed. We employ accurate vector and scalar multiple-scattering calculations to perform a systematic study of the errors induced by the neglect of polarization in radiance calculations for a homogeneous, plane-parallel Rayleigh-scattering atmosphere (with and without depolarization) above a Lambertian surface. Specifically, we calculate percent errors in the reflected intensity for various directions of light incidence and reflection, optical thicknesses of the atmosphere, single-scattering albedos, depolarization factors, and surface albedos. The numerical data displayed can be used to decide whether or not the scalar approximation may be employed depending on the parameters of the problem. We show that the errors decrease with increasing depolarization factor and/or increasing surface albedo. For conservative or nearly conservative scattering and small surface albedos, the errors are maximum at optical thicknesses of about 1. The calculated errors may be too large for some practical applications, and, therefore, rigorous vector calculations should be employed whenever possible. However, if approximate scalar calculations are used, we recommend to avoid geometries involving phase angles equal or close to 0 deg and 90 deg, where the errors are especially significant. We propose a theoretical explanation of the large vector/scalar differences in the case of Rayleigh scattering. According to this explanation, the differences are caused by the particular structure of the Rayleigh scattering matrix and come from lower-order (except first-order) light scattering paths involving right scattering angles and right-angle rotations of the scattering plane.

Mishchenko, M. I.↗