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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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All sourcesNASA NTRSDOE OSTI
NASA NTRS2018

Total Ozone Trends from 1979 to 2016 Derived from Five Merged Observational Datasets - The Emergence into Ozone Recovery

We report on updated trends using different merged datasets from satellite and ground-based observations for the period from 1979 to 2016. Trends were determined by applying a multiple linear regression (MLR) to annual mean zonal mean data. Merged datasets used here include NASA MOD v8.6 and National Oceanic and Atmospheric Administration (NOAA) merge v8.6, both based on data from the series of Solar Backscatter UltraViolet (SBUV) and SBUV-2 satellite instruments (1978–present) as well as the Global Ozone Monitoring Experiment (GOME)-type Total Ozone (GTO) and GOME-SCIAMACHY-GOME-2 (GSG) merged datasets (1995-present), mainly comprising satellite data from GOME, the Scanning Imaging Absorption Spectrometer for Atmospheric Chartography (SCIAMACHY), and GOME-2A. The fifth dataset consists of the monthly mean zonal mean data from ground-based measurements collected at World Ozone and UV Data Center (WOUDC). The addition of four more years of data since the last World Meteorological Organization (WMO) ozone assessment (2013-2016) shows that for most datasets and regions the trends since the stratospheric halogen reached its maximum (approximately 1996 globally and approximately 2000 in polar regions) are mostly not significantly different from zero. However, for some latitudes, in particular the Southern Hemisphere extratropics and Northern Hemisphere subtropics, several datasets show small positive trends of slightly below +1 percent decade(exp. -1) that are barely statistically significant at the 2 Sigma uncertainty level. In the tropics, only two datasets show significant trends of +0.5 to +0.8 percent(exp.-1), while the others show near-zero trends. Positive trends since 2000 have been observed over Antarctica in September, but near-zero trends are found in October as well as in March over the Arctic. Uncertainties due to possible drifts between the datasets, from the merging procedure used to combine satellite datasets and related to the low sampling of ground-based data, are not accounted for in the trend analysis. Consequently, the retrieved trends can be only considered to be at the brink of becoming significant, but there are indications that we are about to emerge into the expected recovery phase. However, the recent trends are still considerably masked by the observed large year-to-year dynamical variability in total ozone.

column ozone trends↗
NASA NTRS2006

Real Time On-line Space Research Laboratory Environment Monitoring with Off-line Trend and Prediction Analysis

One of the responsibilities of the NASA Glenn Principal Investigator Microgravity Services is to support NASA sponsored investigators in the area of reduced-gravity acceleration data analysis, interpretation and the monitoring of the reduced-gravity environment on-board various carriers. With the International Space Station currently operational, a significant amount of acceleration data is being down-linked and processed on ground for both the space station onboard environment characterization (and verification) and scientific experiments. Therefore, to help principal investigator teams monitor the acceleration level on-board the International Space Station to avoid undesirable impact on their experiment, when possible, the NASA Glenn Principal Investigator Microgravity Services developed an artificial intelligence monitoring system, which detects in near real time any change in the environment susceptible to affect onboard experiments. The main objective of the monitoring system is to help research teams identify the vibratory disturbances that are active at any instant of time onboard the International Space Station that might impact the environment in which their experiment is being conducted. The monitoring system allows any space research scientist, at any location and at any time, to see the current acceleration level on-board the Space Station via the World Wide Web. From the NASA Glenn s Exploration Systems Division web site, research scientists can see in near real time the active disturbances, such as pumps, fans, compressor, crew exercise, re-boost, extra-vehicular activity, etc., and decide whether or not to continue operating or stopping (or making note of such activity for later correlation with science results) their experiments based on the g-level associated with that specific event. A dynamic graphical display accessible via the World Wide Web shows the status of all the vibratory disturbance activities with their degree of confidence as well as their g-level contribution to the environment. The system can detect both known and unknown vibratory disturbance activities. It can also perform trend analysis and prediction by analyzing past data over many Increments of the space station for selected disturbance activities. This feature can be used to monitor the health of onboard mechanical systems to detect and prevent potential system failure as well as for use by research scientists during their science results analysis. Examples of both real time on-line vibratory disturbance detection and off-line trend analysis are presented in this paper. Several soft computing techniques such as Kohonen s Self-Organizing Feature Map, Learning Vector Quantization, Back-Propagation Neural Networks, and Fuzzy Logic were used to design the system.

Jules, Kenol↗
NASA NTRS1988

Temporal trends and transport within and around the Antarctic polar vortex during the formation of the 1987 Antarctic ozone hole

During AAOE in 1987 an ER-2 high altitude aircraft made twelve flights out of Punta Arenas, Chile (53 S, 71 W) into the Antarctic polar vortex. The aircraft was fitted with fast response instruments for in situ measurements of many trace species including O3, ClO, BrO, NO sub y, NO, H2O, and N2O. Grab samples of long-lived tracers were also taken and a scanning microwave radiometer measured temperatures above and below the aircraft. Temperature, pressure, and wind measurements were also made on the flight tracks. Most of these flights were flown to 72 S, at a constant potential temperature, followed by a dip to a lower altitude and again assuming a sometimes different potential temperature for the return leg. The potential temperature chosen was 425 K (17 to 18 km) on 12 of the flight legs, and 5 of the flight legs were flown at 450 K (18 to 19 km). The remaining 7 legs of the 12 flights were not flown on constant potential temperature surfaces. Tracer data have been analyzed for temporal trends. Data from the ascents out of Punta Arenas, the constant potential temperature flight legs, and the dips within the vortex are used to compare tracer values inside and outside the vortex, both with respect to constant potential temperature and constant N2O. The time trend during the one-month period of August 23 through September 22, 1987, shows that ozone decreased by 50 percent or more at altitudes form 15 to 19 km. This trend is evident whether analyzed with respect to constant potential temperature or constant N2O. The trend analysis for ozone outside the vortex shows no downward trend during this period. The analysis for N2O at a constant potential temperature indicates no significant trend either inside or outside the vortex; however, a decrease in N2O with an increase in latitude is evident.

Proffitt, M. H.↗
DOE OSTI2024

Comment on “Five Decades of Observed Daily Precipitation Reveal Longer and More Variable Drought Events Across Much of the Western United States”

Abstract Changes in precipitation patterns with climate change could have important impacts on human and natural systems. Zhang et al. (2021, https://doi.org/10.1029/2020gl092293 ) report trends in daily precipitation patterns over the last five decades in the western United States, focusing on meteorological drought. They report that dry intervals (calculated at the annual or seasonal level) have increased across much of the southwestern U.S., with statistical assessment suggesting the results are statistically robust. However, Zhang et al. (2021, https://doi.org/10.1029/2020gl092293 ) preprocess their annual (or seasonal) averages to compute 5‐year moving window averages before using established statistical techniques for trend analysis that assume independence about some fixed trend. Here we show that the moving window preprocessing violates that independence assumption and inflates the statistical significance of their trend estimates. This raises questions about the robustness of their results. We conclude by discussing the difficulty of adjusting for spatial structure when assessing time trends in a regional context.

54 ENVIRONMENTAL SCIENCES↗
NASA NTRS2016

MUlti-SpEctral, MUlti-SpEcies, MUlti-SatEllite (MUSES) Retrieval Algorithm: Towards Extending Multi-Decadal NASA EOS Atmospheric Composition Data Records

Multi-Spectra, Multi-Species, Multi-Sensors (MUSES): Builds off of heritage from the Tropospheric Emission Spectrometer (TES) optimal estimation (OE) algorithm to combine a priori and satellite data, including rigorous error analysis diagnostics and observation operators needed for trend analysis, climate model evaluation, and data assimilation; has generic design to incorporate forward model radiances from hyperspectral measurements from multiple sensors into the joint retrieval algorithm.

Fu, Dejian↗
NASA NTRS2012

Changes in Extratropical Storm Track Cloudiness 1983-2008: Observational Support for a Poleward Shift

Climate model simulations suggest that the extratropical storm tracks will shift poleward as a consequence of global warming. In this study the northern and southern hemisphere storm tracks over the Pacific and Atlantic ocean basins are studied using observational data, primarily from the International Satellite Cloud Climatology Project, ISCCP. Potential shifts in the storm tracks are examined using the observed cloud structures as proxies for cyclone activity. Different data analysis methods are employed, with the objective to address difficulties and uncertainties in using ISCCP data for regional trend analysis. In particular, three data filtering techniques are explored; excluding specific problematic regions from the analysis, regressing out a spurious viewing geometry effect, and excluding specific cloud types from the analysis. These adjustments all, to varying degree, moderate the cloud trends in the original data but leave the qualitative aspects of those trends largely unaffected. Therefore, our analysis suggests that ISCCP data can be used to interpret regional trends in cloudiness, provided that data and instrumental artefacts are recognized and accounted for. The variation in magnitude between trends emerging from application of different data correction methods, allows us to estimate possible ranges for the observational changes. It is found that the storm tracks, here represented by the extent of the midlatitude-centered band of maximum cloud cover over the studied ocean basins, experience a poleward shift as well as a narrowing over the 25 year period covered by ISCCP. The observed magnitudes of these effects are larger than in current generation climate models (CMIP3). The magnitude of the shift is particularly large in the northern hemisphere Atlantic. This is also the one of the four regions in which imperfect data primarily prevents us from drawing firm conclusions. The shifted path and reduced extent of the storm track cloudiness is accompanied by a regional reduction in total cloud cover. This decrease in cloudiness can primarily be ascribed to low level clouds, whereas the upper level cloud fraction actually increases, according to ISCCP. Independent satellite observations of radiative fluxes at the top of the atmosphere are consistent with the changes in total cloud cover. The shift in cloudiness is also supported by a shift in central position of the mid-troposphere meridional temperature gradient. We do not find support for aerosols playing a significant role in the satellite observed changes in cloudiness. The observed changes in storm track cloudiness can be related to local cloud-induced changes in radiative forcing, using ERBE and CERES radiative fluxes. The shortwave and the longwave components are found to act together, leading to a positive (warming) net radiative effect in response to the cloud changes in the storm track regions, indicative of positive cloud feedback. Among the CMIP3 models that simulate poleward shifts in all four storm track areas, all but one show decreasing cloud amount on a global mean scale in response to increased CO2 forcing, further consistent with positive cloud feedback. Models with low equilibrium climate sensitivity to a lesser extent than higher-sensitivity models simulate a poleward shift of the storm tracks.

Bender, Frida A-M.↗
NASA NTRS1993

Nimbus-7 Earth radiation budget calibration history. Part 1: The solar channels

The Earth Radiation Budget (ERB) experiment on the Nimbus-7 satellite measured the total solar irradiance plus broadband spectral components on a nearly daily basis from 16 Nov. 1978, until 16 June 1992. Months of additional observations were taken in late 1992 and in 1993. The emphasis is on the electrically self calibrating cavity radiometer, channel 10c, which recorded accurate total solar irradiance measurements over the whole period. The spectral channels did not have inflight calibration adjustment capabilities. These channels can, with some additional corrections, be used for short-term studies (one or two solar rotations - 27 to 60 days), but not for long-term trend analysis. For channel 10c, changing radiometer pointing, the zero offsets, the stability of the gain, the temperature sensitivity, and the influences of other platform instruments are all examined and their effects on the measurements considered. Only the question of relative accuracy (not absolute) is examined. The final channel 10c product is also compared with solar measurements made by independent experiments on other satellites. The Nimbus experiment showed that the mean solar energy was about 0.1 percent (1.4 W/sqm) higher in the excited Sun years of 1979 and 1991 than in the quiet Sun years of 1985 and 1986. The error analysis indicated that the measured long-term trends may be as accurate as +/- 0.005 percent. The worse-case error estimate is +/- 0.03 percent.

Kyle, H. Lee↗
NASA NTRS1991

Analysis of launch site processing effectiveness for the Space Shuttle 26R payload

A trend analysis study has been performed on problem reports recorded during the Space Shuttle 26R payload's processing cycle at NASA-Kennedy, using the defect-flow analysis (DFA) methodology; DFA gives attention to the characteristics of the problem-report 'population' as a whole. It is established that the problem reports contain data which distract from pressing problems, and that fully 60 percent of such reports were caused during processing at NASA-Kennedy. The second major cause of problem reports was design defects.

Flores, Carlos A.↗
NASA NTRS1981

Review of AIDS development

The operation and implementation of the aircraft integrated data system AIDS are described. The system is described as an engineering tool with strong emphasis on analysis of recorded information. The AIDS is primarily directed to the monitoring of parameters related to: the safety of the flight; the performance of the aircraft; the performance of the flight guidance system; and the performance and condition of the engines. The system provide short term trend analysis on a trend chart that is updated by the flight engineer on every flight that lasts more than 4 flight hours. Engine data prints are automatically presented during take-off and in the case of limit excedance, e.g., the print shows an automatically reported impending hotstarts on engine nr. 1. Other significant features are reported.

Vermeulen, H. C.↗
NASA NTRS2016

Natural and Anthropogenic Aerosol Trends from Satellite and Surface Observations and Model Simulations over the North Atlantic Ocean from 2002 to 2012

Aerosols contribute to Earths radiative budget both directly and indirectly, and large uncertainties remain in quantifying aerosol effects on climate. Variability in aerosol distribution and properties, as might result from changing emissions and transport processes, must be characterized. In this study, variations in aerosol loading across the eastern seaboard of theUnited States and theNorthAtlanticOcean during 2002 to 2012 are analyzed to examine the impacts of anthropogenic emission control measures using monthly mean data from MODIS, AERONET, and IMPROVE observations and Goddard Chemistry Aerosol Radiation and Transport (GOCART) model simulation.MODIS observes a statistically significant negative trend in aerosol optical depth (AOD) over the midlatitudes (-0.030 decade(sup-1)). Correlation analyses with surface AOD from AERONET sites in the upwind region combined with trend analysis from GOCART component AOD confirm that the observed decrease in the midlatitudes is chiefly associated with anthropogenic aerosols that exhibit significant negative trends from the eastern U.S. coast extending over the western North Atlantic. Additional analysis of IMPROVE surface PM(sub 2.5) observations demonstrates statistically significant negative trends in the anthropogenic components with decreasing mass concentrations over the eastern United States. Finally, a seasonal analysis of observational datasets is performed. The negative trend seen by MODIS is strongest during spring (MAM) and summer (JJA) months. This is supported by AERONET seasonal trends and is identified from IMPROVE seasonal trends as resulting from ammonium sulfate decreases during these seasons.

Jongeward, Andrew R.↗
NASA NTRS2012

Satellite-Based Evidence for Shrub and Graminoid Tundra Expansion in Northern Quebec from 1986-2010

Global vegetation models predict rapid poleward migration of tundra and boreal forest vegetation in response to climate warming. Local plot and air-photo studies have documented recent changes in high-latitude vegetation composition and structure, consistent with warming trends. To bridge these two scales of inference, we analyzed a 24-year (1986-2010) Landsat time series in a latitudinal transect across the boreal forest-tundra biome boundary in northern Quebec province, Canada. This region has experienced rapid warming during both winter and summer months during the last forty years. Using a per-pixel (30 m) trend analysis, 30% of the observable (cloud-free) land area experienced a significant (p < 0.05) positive trend in the Normalized Difference Vegetation Index (NDVI). However, greening trends were not evenly split among cover types. Low shrub and graminoid tundra contributed preferentially to the greening trend, while forested areas were less likely to show significant trends in NDVI. These trends reflect increasing leaf area, rather than an increase in growing season length, because Landsat data were restricted to peak-summer conditions. The average NDVI trend (0.007/yr) corresponds to a leaf-area index (LAI) increase of ~0.6 based on the regional relationship between LAI and NDVI from the Moderate Resolution Spectroradiometer (MODIS). Across the entire transect, the area-averaged LAI increase was ~0.2 during 1986-2010. A higher area-averaged LAI change (~0.3) within the shrub-tundra portion of the transect represents a 20-60% relative increase in LAI during the last two decades. Our Landsat-based analysis subdivides the overall high-latitude greening trend into changes in peak-summer greenness by cover type. Different responses within and among shrub, graminoid, and tree-dominated cover types in this study indicate important fine-scale heterogeneity in vegetation growth. Although our findings are consistent with community shifts in low-biomass vegetation types over multi-decadal time scales, the response in tundra and forest ecosystems to recent warming was not uniform.

McManus, K. M.↗
NASA NTRS2025

Jemez Pueblo Agriculture: Monitoring Rangeland Conditions to Inform Drought and Land Management in New Mexico

The Jemez Pueblo, a community located in the semi-arid high desert region of northcentral New Mexico, faces challenges with drought mitigation and livestock management. NASA DEVELOP partnered with the Pueblo of Jemez Natural Resources Department and The Nature Conservancy to provide recent and historical rangeland conditions to aid present decision-making, which relies on cultural practices, site familiarity, available resources, and physical data. This partnership offers the opportunity to support management practices by leveraging remote sensing and virtual fencing technologies. Our project explored Rangeland Analysis Platform (RAP) products incorporating NASA Earth observation Landsat 5 TM, Landsat 7 ETM+, Landsat 8 OLI, and Landsat 9 OLI-2 remote-sensed imagery as an agricultural land management tool. We performed linear regression analysis to evaluate RAP data to field data and explored RAP annual herbaceous biomass, ground cover trends, and climatic factors at the pasture level. We then computed study area summary statistics, performed pixel-by-pixel trend analysis across the study period, and evaluated ground cover trends near water sources. Based on available data, RAP was poorly correlated to bare ground and herbaceous biomass, generally underestimating the former and overestimating the latter. To improve the evaluation of RAP products, we suggest increasing the spatiotemporal distribution of the field dataset. According to RAP, from 1986 to 2023, the site became hotter and drier, bare ground increased, and annual forbs and grasses increased while perennials decreased. RAP products did not agree with field-collected data; however, the trends over time may be useful for informing rangeland management actions.

cattle grazing management↗
NASA NTRS2019

NCA-LDAS: Overview and Analysis of Hydrologic Trends for the National Climate Assessment

Terrestrial hydrologic trends over the conterminous United States are estimated for 1980-47 2015 using the National Climate Assessment-Land Data Assimilation System (NCA-LDAS) reanalysis. NCA-LDAS employs the uncoupled Noah Version 3.3 land surface model at 0.125 degreesx0.125 degrees forced with NLDAS-2 meteorology, rescaled Climate Prediction Center precipitation, and assimilated satellite-based soil moisture, snow depth and irrigation products. Mean annual trends are reported using the nonparametric Mann-Kendall test at p<0.1 significance. Results illustrate the interrelationship between regional gradients in forcing trends, and trends in other land energy and water stores and fluxes. Mean precipitation trends range from +3 to +9 mm/yr in the Upper Great Plains and Northeast to -1 to -9 in the West and South; net radiation flux trends range from +0.05 to +0.20 W/m(exp2)/yr in the East to -0.05 to -0.20 in the West; U.S.-wide temperature trends average about +0.03K/yr. Trends in soil moisture, snow cover, latent and sensible heat fluxes and runoff are consistent with forcings, contributing to increasing evaporative fraction trends from West to East. Evaluation of NCA-LDAS trends compared to independent data indicates mixed results. The RMSE of U.S.-wide trends in number of snow cover days improved from 3.13 to 2.89 days/yr while trend detection increased 11%; Trends in latent heat flux were hardly affected, RMSE decreasing only 0.17 to 0.16 W/m(exp 2)/yr, while trend detection increased 2%; NCA-LDAS runoff trends degraded significantly from 2.6 to 16.1 mm/yr while trend detection was unaffected. Analysis also indicated that NCA-LDAS exhibits relatively more skill in low precipitation station density areas, suggesting there are limits to the effectiveness of satellite data assimilation in densely gaged regions. Overall, NCA-LDAS demonstrates capability for quantifying physically consistent, U.S. hydrologic climate trends over the satellite era.

Snow depth↗
NASA NTRS2019

NCA-LDAS: Overview and Analysis of Hydrologic Trends for the National Climate Assessment

Terrestrial hydrologic trends over the conterminous United States are estimated for 1980–2015 using the National Climate Assessment Land Data Assimilation System (NCA-LDAS) reanalysis. NCA-LDAS employs the uncoupled Noah version 3.3 land surface model at 0.125° 3 0.125° forced with NLDAS-2 meteorology, rescaled Climate Prediction Center precipitation, and assimilated satellite-based soil moisture, snow depth, and irrigation products. Mean annual trends are reported using the nonparametric Mann–Kendall test at p < 0.1 significance. Results illustrate the interrelationship between regional gradients in forcing trends and trends in other land energy and water stores and fluxes. Mean precipitation trends range from +3 to +9 mm/yr in the upper Great Plains and Northeast to -1 to -9 mm/yr in the West and South, net radiation flux trends range from +0.05 to +0.20 W/sq. m yr in the East to -0.05 to -0.20 W/sq. m yr in the West, and U.S.-wide temperature trends average about +0.03K/yr. Trends in soil moisture, snow cover, latent and sensible heat fluxes, and runoff are consistent with forcings, contributing to increasing evaporative fraction trends from west to east. Evaluation of NCA-LDAS trends compared to independent data indicates mixed results. The RMSE of U.S.-wide trends in number of snow cover days improved from 3.13 to 2.89 days/yr while trend detection increased 11%. Trends in latent heat flux were hardly affected, with RMSE decreasing only from 0.17 to 0.16 W/sq. m yr, while trend detection increased 2%. NCA-LDAS runoff trends degraded significantly from 2.6 to 16.1 mm/yr while trend detection was unaffected. Analysis also indicated that NCA-LDAS exhibits relatively more skill in low precipitation station density areas, suggesting there are limits to the effectiveness of satellite data assimilation in densely gauged regions. Overall, NCA-LDAS demonstrates capability for quantifying physically consistent, U.S. hydrologic climate trends over the satellite era.

Michael F. Jasinski↗
NASA NTRS2010

Characterizing DSN System Frequency Stability with Spacecraft Tracking Data

This paper describes a recent effort in characterizing frequency stability performance of the ground system in the NASA Deep Space Network (DSN). Unlike the traditional approach where performance is obtained from special calibration sessions that are both time consuming and require manual setup, the new method taps into the daily spacecraft tracking data. This method significantly increases the amount of data available for analysis, roughly by two orders of magnitude; making it possible to conduct trend analysis with reasonable confidence. Since the system is monitored daily, any significant variation in performance can be detected timely. This helps the DSN maintain its performance commitment to customers.

performance analysis↗
NASA NTRS1988

An expert system for satellite and instrument data anomaly and fault isolation

A prototype Generic Payload Operations Control System (GPOCC) is being developed at the NASA Jet Propulsion Laboratory to provide a low-cost command and control processing center for science instruments and small payloads. The GPOCC supports the difficult transition from integration and test to flight operations. The prototype will incorporate four expert systems to perform telemetry, command, and mission planning functions as well as telecommunications scheduling. The first of these expert systems to be developed will perform telemetry data analysis and fault isolation, as well as propose corrective action. This Data Analysis Module (DAM) will monitor telemetry data and perform continual data monitoring and trend analysis based on a knowledge base and historic data archived on an optical disk storage device. The system maintains a continuous knowledge database of past system performance characteristics. The goal of the Data Analysis Module is to achieve consistent, dependable and validatable performance, to demonstrate thorough, reliable and fast reasoning, and to reduce the concentration demanded of flight analysis personnel.

Busse, Carl↗
NASA NTRS2000

Recent Trends in the Analysis of Quasioptical Systems

The recent trend in microwave instruments is the use of multiple millimeter and submillimeter wavelength bands. These systems are typically analyzed by using physical optics, Gaussian beams or ray tracing techniques. Physical optics offers high accuracy at the expense of computation time. This trade-off becomes particularly apparent in the analysis of multiple reflector antennas, such as beam waveguide antennas, where physical optics is used to compute the current on each reflector from the current on the previous reflector. At the other end of the spectrum is ray tracing approaches that ignore diffraction effects entirely. These methods are fast but sacrifice the ability to predict some effects accurately. An intermediate approach is to use an appropriate set of expansion functions to model the field between the reflectors. If the set is chosen wisely only a few coefficients need to be determined from each reflector current. The field is then computed at the next reflector through the use of the expansion functions and their coefficients rather than by using the previous reflector current. For a beam waveguide system with no enclosing tubes an excellent set of expansion functions is the Gaussian beam mode set. In many cases a preliminary design which includes the effects on diffraction may be obtained by considering only the fundamental mode and a thin lens model for the reflectors. Higher-order modes are included to model the effects of the curved reflector, which include asymmetric distortion of the beam, cross polarization, and beam truncation. This paper describes a computer code implementing higher-order Gaussian beam scattering by multiple reflector systems. There are four essential steps in the algorithm. (1) Compute the current on the first reflector using physical optics using either a feed model or by an incident set of Gaussian beam modes. (2) Find the direction of propagation for the reflected Gaussian beam-set using ray tracing. (3) Determine the waist size and location for the output beam set by examining the amplitude and phase distribution of the current on the reflector. (4) Compute the amplitudes of the individual modes in the output mode set. These steps are then repeated for each addition reflector in the chain. In each of these cases the previous Gaussian beam set provides the input field for the current calculation. Details of the four steps discussed above will be discussed. Examples will compare results from the Gaussian beam approach to pure physical optics, illustrating both its merits and limitations. Hybrid approaches capable of eliminating some of the limitations will also be discussed.

Hoppe, D. J.↗