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NASA NTRS1980

Analysis of localized fringes in the holographic optical Schlieren system

The relation between localization of interference fringes in classical and holographic interferometry is reviewed and an application of holographic interferometry is considered for which the object is a transparent medium with nonhomogeneous refractive index. The technique is based on the analysis of the optical path length change of the object wave as it propagates through a transparent medium. Phase shifts due to variations of the speed of light within the medium give rise to an interference pattern. The resulting interferogram can be used to determine the physical properties of the medium or transparent object. Such properties include the mass density of fluids, electron densities of plasmas, the temperature of fluids, the chemical species concentration of fluids, and the state of stress in solids. The optical wave used can be either a simple plane or spherical wave, or it may be a complicated spatial wave scattered by a diffusing screen. The mathematical theory on the formation and analysis of localized fringes, the general theoretical concepts used, and a computer code for analysis are included along with the inversion of fringe order data.

Kurtz, R. L.↗

NASA NTRS1980

Repeatable, multiple-peaked structure in Type I X-ray bursts

A distinct, identifiable, multiple-peaked structure has been observed in Type I X-ray bursts from three sources. At energies below 6 keV, the light curves look like typical Type I bursts. At higher energies, the burst is double-peaked, with both the depth of the dip and the separation between the peaks increasing with energy. A light curve of the energy-integrated intensity shows no distinct double peak, suggesting that only a single energy release occurs. Blackbody fits to the evolving burst spectra yield changing radii and temperatures, inversely correlated, during the early part of the burst. The physical interpretation of these changes is uncertain. Burst decay spectra yield relatively constant radii with decreasing temperatures. It is proposed that Compton scattering may be responsible for the dips in the higher-energy light curves by shifting photons to lower energies.

Hoffman, J. A.↗

NASA NTRS1985

Bidirectional Reflectance Modeling of Non-homogeneous Plant Canopies

The objective of this research is to develop a 3-dimensional radiative transfer model for predicting the bidirectional reflectance distribution function (BRDF) for heterogeneous vegetation canopies. The model (named BIGAR) considers the angular distribution of leaves, leaf area index, the location and size of individual subcanopies such as widely spaced rows or trees, spectral and directional properties of leaves, multiple scattering, solar position and sky condition, and characteristics of the soil. The model relates canopy biophysical attributes to down-looking radiation measurements for nadir and off-nadir viewing angles. Therefore, inversion of this model, which is difficult but practical should provide surface biophysical pattern; a fundamental goal of remote sensing. Such a model also will help to evaluate atmospheric limitations to satellite remote sensing by providing a good surface boundary condition for many different kinds of canopies. Furthermore, this model can relate estimates of nadir reflectance, which is approximated by most satellites, to hemispherical reflectance, which is necessary in the energy budget of vegetated surfaces.

Norman, J. M.↗

NASA NTRS1993

Relationships between evaprorative fraction and remotely sensed vegetation index and microwave brightness temperature for semiarid rangelands

Measurements of the microwave brightness temperature (TB) with the Pushbroom Microwave Radiometer (PBMR) over the Walnut Gulch Experiment Watershed were made on selected days during the MONSOON 90 field campaign. The PBMR is an L-band instrument (21-cm wavelength) that can provide estimates of near-surface soil moisture over a variety of surfaces. Aircraft observations in the visible and near-infrared wavelengths collected on selected days also were used to compute a vegetation index. Continuous micrometeorological measurements and daily soil moisture samples were obtained at eight locations during experimental period. Two sites were instrumented with time domain reflectometry probes to monitor the soil moisture profile. The fraction of available energy used for evapotranspiration was computed by taking the ratio of latent heat flux (LE) to the sum of net radiation (Rn) and soil heat flux (G). This ratio is commonly called the evaporative fraction (EF) and normally varies between 0 and 1 under daytime convective conditions with minimal advection. A wide range of environmental conditions existed during the field campaign, resulting in average EF values for the study area varying from 0.4 to 0.8 and values of TB ranging from 220 to 280 K. Comparison between measured TB and EF for the eight locations showed an inverse relationship. Other days were included in the analysis by estimating TB with the soil moisture data. Because transpiration from the vegetation is more strongly coupled to root zone soil moisture, significant scatter in this relationship existed at high values of TB or dry near-surface soil moisture conditions. The variation in EF under dry near-surface soil moisture conditions was correlated to the amount of vegetation cover estimated with a remotely sensed vegetation index. These findings indicate that information obtained from optical and microwave data can be used for quantifying the energy balance of semiarid areas. The microwave data can indicate when soil evaporation is significantly contributing to EF, while the optical data is helpful for quantifying the spatial variation in EF due to the distribution of vegetation cover.

Kustas, W. P.↗

NASA NTRS1999

Improving Pixel Level Cloud Optical Property Retrieval using Monte Carlo Simulations

The accurate pixel-by-pixel retrieval of cloud optical properties from space is influenced by radiative smoothing due to high order photon scattering and radiative roughening due to low order scattering events. Both are caused by cloud heterogeneity and the three-dimensional nature of radiative transfer and can be studied with the aid of computer simulations. We use Monte Carlo simulations on variable 1-D and 2-D model cloud fields to seek for dependencies of smoothing and roughening phenomena on single scattering albedo, solar zenith angle, and cloud characteristics. The results are discussed in the context of high resolution satellite (such as Landsat) retrieval applications. The current work extends the investigation on the inverse NIPA (Non-local Independent Pixel Approximation) as a tool for removing smoothing and improving retrievals of cloud optical depth. This is accomplished by: (1) Delineating the limits of NIPA applicability; (2) Exploring NIPA parameter dependences on cloud macrostructural features, such as mean cloud optical depth and geometrical thickness, degree of extinction and cloud top height variability. We also compare parameter values from empirical and theoretical considerations; (3) Examining the differences between applying NIPA on radiation quantities vs direct application on optical properties; (4) Studying the radiation budget importance of the NIPA corrections as a function of scale. Finally, we discuss fundamental adjustments that need to be considered for successful radiance inversion at non-conservative wavelengths and oblique Sun angles. These adjustments are necessary to remove roughening signatures which become more prominent with increasing absorption and solar zenith angle.

Oreopoulos, Lazaros↗

NASA NTRS2002

Remote Sensing of Aerosol using MODIS, MODIS+CALIPSO and with the AEROSAT Concept

In the talk I shall review the MODIS use of spectral information to derive aerosol size distribution, optical thickness and reflected spectral flux. The accuracy and validation of the MODIS products will be discussed. A few applications will be shown: inversion of combined MODIS+lidar data, aerosol Anthropogenic direct forcing, and dust deposition in the Atlantic Ocean. I shall also discuss the aerosol information that MODIS is measuring: real ref index, single scattering albedo, size of fine and coarse modes, and describe the AEROSAT concept that uses bright desert and glint to derive aerosol absorption.

Kaufman, Yoram J.↗

NASA NTRS2012

Sensitivity of Ocean Reflectance Inversion Models for Identifying and Discriminating Between Phytoplankton Functional Groups

The daily, synoptic images provided by satellite ocean color instruments provide viable data streams for observing changes in the biogeochemistrY of marine ecosystems. Ocean reflectance inversion models (ORMs) provide a common mechanism for inverting the "color" of the water observed a satellite into marine inherent optical properties (lOPs) through a combination of empiricism and radiative transfer theory. lOPs, namely the spectral absorption and scattering characteristics of ocean water and its dissolved and particulate constituents, describe the contents of the upper ocean, information critical for furthering scientific understanding of biogeochemical oceanic processes. Many recent studies inferred marine particle sizes and discriminated between phytoplankton functional groups using remotely-sensed lOPs. While all demonstrated the viability of their approaches, few described the vertical distributions of the water column constituents under consideration and, thus, failed to report the biophysical conditions under which their model performed (e.g., the depth and thickness of the phytoplankton bloom(s)). We developed an ORM to remotely identifY Noctiluca miliaris and other phytoplankton functional types using satellite ocean color data records collected in the northern Arabian Sea. Here, we present results from analyses designed to evaluate the applicability and sensitivity of the ORM to varied biophysical conditions. Specifically, we: (1) synthesized a series of vertical profiles of spectral inherent optical properties that represent a wide variety of bio-optical conditions for the northern Arabian Sea under aN Miliaris bloom; (2) generated spectral remote-sensing reflectances from these profiles using Hydrolight; and, (3) applied the ORM to the synthesized reflectances to estimate the relative concentrations of diatoms and N Miliaris for each example. By comparing the estimates from the inversion model to those from synthesized vertical profiles, we were able to identifY those bio-optical conditions under which the inversion model performs both well and poorly.

Werdell, P. Jeremy↗

NASA NTRS1992

A considerable effect of stratospheric aerosol on lidar-detected ozone profile and a three-wavelength inversion technique for both ozone and aerosol

As far as the Differential Absorption Lidar (DIAL) technique is concerned, it is important that the off-line wavelength is close to the on-line wavelength in order to avoid a messy computation of the atmospheric aerosol scattering. However, the two wavelengths of ozone-DIAL are usually considerably different. Usually, an excimer laser of 308nm (on-line) and Raman shifting of 353nm or the third harmonic of a Nd-YAG laser with 355nm (off-line) are selected for measurements of the stratospheric ozone, and there is a difference of 45nm or 47nm between them. Because of the difference there is a difference in the atmospheric scatterings of the two wavelengths. This can cause some error in the retrieved ozone profile if the aerosol scattering is neglected. This paper is devoted to a study of the effect of the stratospheric aerosol on the ozone solution, and a three-wavelength detection technique is proposed for obtaining the more exact ozone profile and the aerosol profile in the stratosphere.

Qiu, Jinhuan↗

NASA NTRS1980

Investigation of multiple scattering effects in aerosols

The results are presented of investigations on the various aspects of multiple scattering effects on visible and infrared laser beams transversing dense fog oil aerosols contained in a chamber (4' x 4' x 9'). The report briefly describes: (1) the experimental details and measurements; (2) analytical representation of the aerosol size distribution data by two analytical models (the regularized power law distribution and the inverse modified gamma distribution); (3) retrieval of aerosol size distributions from multispectral optical depth measurements by two methods (the two and three parameter fast table search methods and the nonlinear least squares method); (4) modeling of the effects of aerosol microphysical (coagulation and evaporation) and dynamical processes (gravitational settling) on the temporal behavior of aerosol size distribution, and hence on the extinction of four laser beams with wavelengths 0.44, 0.6328, 1.15, and 3.39 micrometers; and (5) the exact and approximate formulations for four methods for computing the effects of multiple scattering on the transmittance of laser beams in dense aerosols, all of which are based on the solution of the radiative transfer equation under the small angle approximation.

Deepak, A.↗

DOE OSTI2023

Extremely Thin Perfect Absorber by Generalized Multipole Bianisotropic Effect

Symmetry breaking plays a crucial role in understanding the fundamental physics underlying numerous physical phenomena, including the electromagnetic response in resonators, giving rise to intriguing effects such as directional light scattering, supercavity lasing, and topologically protected states. Here, this work demonstrates that adding a small fraction of lossy metal (as low as 1 × 10 −6 in volume) to a lossless dielectric resonator breaks inversion symmetry (IS), thereby lifting its degeneracy, leading to a strong bianisotropic response. In the case of the metasurface composed of such resonators, this effect leads to unidirectional perfect absorption while maintaining nearly perfect reflection from the opposite direction. It has developed more general Onsager‐Casimir relations for the polarizabilities of particle arrays, taking into account the contributions of quadrupoles, which shows that bianisotropy is not solely due to dipoles, but also involves high‐order multipoles. The experimental validation demonstrates an extremely thin terahertz‐perfect absorber with a wavelength‐to‐thickness ratio of up to 25,000, where the material thickness is only 2% of the theoretical minimum thickness dictated by the fundamental limit. The findings can pave a new route to design devices for applications involving optical‐to‐heat conversion processes.

36 MATERIALS SCIENCE↗

DOE OSTI2024

A New Galerkin Quadrature Method Not Requiring a Matrix Inverse

We derive a new Galerkin quadrature (GQ) method for S 𝑛 calculations that differs from the two methods preceding it in that a matrix inverse for an 𝑁 𝑑 × 𝑁 𝑑 matrix, where 𝑁𝑑 is the number of directions in the quadrature set, is no longer required. Galerkin quadrature methods are designed for calculations with highly anisotropic scattering. Such methods are not simply special angular quadratures but also are methods for representing the S 𝑛 scattering source that offers several advantages relative to the standard scattering source representation when highly truncated Legendre cross-section expansions must be used. Galerkin quadrature methods are also useful when the scattering is moderately anisotropic, but the quadrature being used is not sufficiently accurate for the order of the scattering source expansion that is required. Furthermore, we derive the new method and present computational results showing that its performance for two challenging problems is comparable to those of the two GQ methods that preceded it.

Galerkin quadrature↗

DOE OSTI2021

Local Resistance Measurement for Degradation of c-Si Heterojunction with Intrinsic Thin Layer (HIT) Solar Modules

Silicon heterojunction with intrinsic thin layer (or HIT) modules typically degrade at a rate of less than 1% annually in solar fields with dominant degradation in open-circuit voltage and some degradation in series resistance. However, detailed mechanisms can differ from module to module. Here, we study increases in local series resistance that occur over long-term field deployment, indicated by cell areas where the photoluminescence intensity does not degrade but the electroluminescence degrades significantly. To directly measure the local series resistance, we have cored out the local electroluminescence-degraded area, and we measured the sheet resistance by 4-point-probe and local nm-scale resistance using scanning spreading resistance microscopy (SSRM). The results by 4-point-probe show scattered sheet resistance that can be caused, for example, by nonuniform current paths through the transparent conductive oxide layer, the a-Si:H emitter, or the near-junction c-Si inversion layer. In contrast, the SSRM results indicate a relatively uniform and non-degraded resistivity on smaller nanometer spatial scales. SSRM is an atomic force microscopy-based two-terminal resistance mapping technique that measures the local resistance in nm-volume beneath the probe. The consistent resistances measured on the control and degraded samples can exclude the degradation of transparent conductive oxide resistance.

41 EE - Solar Energy Technologies Office (EE-4S)↗

NASA NTRS1985

The investigation of advanced remote sensing, radiative transfer and inversion techniques for the measurement of atmospheric constituents

The research program is documented for developing space and ground-based remote sensing techniques performed during the period from December 15, 1977 to March 15, 1985. The program involved the application of sophisticated radiative transfer codes and inversion methods to various advanced remote sensing concepts for determining atmospheric constituents, particularly aerosols. It covers detailed discussions of the solar aureole technique for monitoring columnar aerosol size distribution, and the multispectral limb scattered radiance and limb attenuated radiance (solar occultation) techniques, as well as the upwelling scattered solar radiance method for determining the aerosol and gaseous characteristics. In addition, analytical models of aerosol size distribution and simulation studies of the limb solar aureole radiance technique and the variability of ozone at high altitudes during satellite sunrise/sunset events are also described in detail.

Deepak, Adarsh↗

NASA NTRS2016

GOCI Yonsei Aerosol Retrieval (YAER) Algorithm and Validation During the DRAGON-NE Asia 2012 Campaign

The Geostationary Ocean Color Imager (GOCI) onboard the Communication, Ocean, and Meteorological Satellite (COMS) is the first multi-channel ocean color imager in geostationary orbit. Hourly GOCI top-of-atmosphere radiance has been available for the retrieval of aerosol optical properties over East Asia since March 2011. This study presents improvements made to the GOCI Yonsei Aerosol Retrieval (YAER) algorithm together with validation results during the Distributed Regional Aerosol Gridded Observation Networks - Northeast Asia 2012 campaign (DRAGONNE Asia 2012 campaign). The evaluation during the spring season over East Asia is important because of high aerosol concentrations and diverse types of Asian dust and haze. Optical properties of aerosol are retrieved from the GOCI YAER algorithm including aerosol optical depth (AOD) at 550 nm, fine-mode fraction (FMF) at 550 nm, single-scattering albedo (SSA) at 440 nm, Angstrom exponent (AE) between 440 and 860 nm, and aerosol type. The aerosol models are created based on a global analysis of the Aerosol Robotic Networks (AERONET) inversion data, and covers a broad range of size distribution and absorptivity, including nonspherical dust properties. The Cox-Munk ocean bidirectional reflectance distribution function (BRDF) model is used over ocean, and an improved minimum reflectance technique is used over land. Because turbid water is persistent over the Yellow Sea, the land algorithm is used for such cases. The aerosol products are evaluated against AERONET observations and MODIS Collection 6 aerosol products retrieved from Dark Target (DT) and Deep Blue (DB) algorithms during the DRAGON-NE Asia 2012 campaign conducted from March to May 2012. Comparison of AOD from GOCI and AERONET resulted in a Pearson correlation coefficient of 0.881 and a linear regression equation with GOCI AOD = 1.083 x AERONET AOD - 0.042. The correlation between GOCI and MODIS AODs is higher over ocean than land. GOCI AOD shows better agreement with MODIS DB than MODIS DT. The other GOCI YAER products (AE, FMF, and SSA) show lower correlation with AERONET than AOD, but still show some skills for qualitative use.

Choi, Myungje↗

NASA NTRSDate not supplied

NASA’s Prototype Spectral Water Inversion Processor and Emulator (SWIPE): Towards Global Coastal and Inland Water Quality and Algal Biodiversity Monitoring

Degradation of Earth’s inland water resources due to anthropogenic perturbations and climate anomalies at both local and global scales continues to place human health at substantial risk. There is now a growing necessity to develop pragmatic approaches that allow timely and effective extrapolation of local processes, to spatially resolved global products, and to promote operational and sustainable resource policy management. This presentation will provide updates on NASA’s prototype open-source aquatic modeling platform, Spectral Water Inversion Processor and Emulator (SWIPE), which is a comprehensive, multi-faceted modeling platform for both forward and inverse modeling of diverse aquatic ecosystems from the benthos to top-of-atmosphere (TOA). SWIPE provides a cohesive application which leverages recent advancements in particle modeling, Big Data analytics, and machine learning to develop a high-fidelity synthetic training ground for sensitivity studies and algorithm development for multispectral or upcoming hyperspectral missions. Some of the prominent features of SWIPE to be discussed include: 1. Advanced hyperspectral modeling of globally diverse algal and non-algal particles using a novel two-layer coated sphere scattering model and radiative transfer modeling, 2. Massive, highly detailed synthetic spectral libraries of Analysis-Ready-Data (ARD) which include spectral libraries of particle microphysics, water biogeophysical and optical properties, as well as surface and TOA reflectances at 1 nm resolution, 3. An ensemble of pre-built analytic, machine learning, and deep learning inversion algorithms for various water quality and biodiversity related retrieval parameters and uncertainty quantification, 4. Sensor-agnostic water quality inversion at wide ranging spatial and spectral resolutions including a codebase for seamless application in the Google Earth Engine and NASA Earth Exchange (NEX) for planetary scale analysis. SWIPE will be a fully open-source platform based in python with comprehensive documentation, tutorials, and options for distributed computing on high performance computing clusters or on single, local machines. Further, we will discuss how we envision SWIPE contributing towards a global analysis of coastal and inland water quality dynamics.

top-of-atmosphere (TOA)↗

DOE OSTI2023

Local inversion-symmetry breaking in a bismuthate high-Tc superconductor

Abstract The doped perovskite BaBiO 3 exhibits a maximum superconducting transition temperature ( T c ) of 34 K and was the first high- T c oxide to be discovered, yet pivotal questions regarding the nature of both the metallic and superconducting states remain unresolved. Although it is generally thought that superconductivity in the bismuthates is of the conventional s -wave type, the pairing mechanism is still debated, with strong electron-phonon coupling and bismuth valence or bond disproportionation possibly playing a role. Here we use diffuse x-ray scattering and Monte Carlo modeling to study the local structure of Ba 1-x K x BiO 3 across its insulator-metal boundary. We find no evidence for either long- or short-range disproportionation, which resolves a major conundrum, as disproportionation and the related polaronic effects are likely not relevant for the metallic and superconducting states. Instead, we uncover nanoscale structural correlations that break inversion symmetry, with far-reaching implications for the electronic physics. This unexpected finding furthermore establishes that the bismuthates belong to the broader classes of materials with hidden spin-orbit coupling and a tendency towards inversion-breaking displacements.

36 MATERIALS SCIENCE↗

NASA NTRS2016

Aerosol Optical Properties Derived from the DRAGON-NE Asia Campaign, and Implications for a Single-Channel Algorithm to Retrieve Aerosol Optical Depth in Spring from Meteorological Imager (MI) On-Board the Communication, Ocean, and Meteorological Satellite (COMS)

An aerosol model optimized for northeast Asia is updated with the inversion data from the Distributed Regional Aerosol Gridded Observation Networks (DRAGON)-northeast (NE) Asia campaign which was conducted during spring from March to May 2012. This updated aerosol model was then applied to a single visible channel algorithm to retrieve aerosol optical depth (AOD) from a Meteorological Imager (MI) on-board the geostationary meteorological satellite, Communication, Ocean, and Meteorological Satellite (COMS). This model plays an important role in retrieving accurate AOD from a single visible channel measurement. For the single-channel retrieval, sensitivity tests showed that perturbations by 4 % (0.926 +/- 0.04) in the assumed single scattering albedo (SSA) can result in the retrieval error in AOD by over 20 %. Since the measured reflectance at the top of the atmosphere depends on both AOD and SSA, the overestimation of assumed SSA in the aerosol model leads to an underestimation of AOD. Based on the AErosol RObotic NETwork (AERONET) inversion data sets obtained over East Asia before 2011, seasonally analyzed aerosol optical properties (AOPs) were categorized by SSAs at 675 nm of 0.92 +/- 0.035 for spring (March, April, and May). After the DRAGON-NE Asia campaign in 2012, the SSA during spring showed a slight increase to 0.93 +/- 0.035. In terms of the volume size distribution, the mode radius of coarse particles was increased from 2.08 +/- 0.40 to 2.14 +/- 0.40. While the original aerosol model consists of volume size distribution and refractive indices obtained before 2011, the new model is constructed by using a total data set after the DRAGON-NE Asia campaign. The large volume of data in high spatial resolution from this intensive campaign can be used to improve the representative aerosol model for East Asia. Accordingly, the new AOD data sets retrieved from a single-channel algorithm, which uses a precalculated look-up table (LUT) with the new aerosol model, show an improved correlation with the measured AOD during the DRAGON-NE Asia campaign. The correlation between the new AOD and AERONET value shows a regression slope of 1.00, while the comparison of the original AOD data retrieved using the original aerosol model shows a slope of 1.08. The change of y-offset is not significant, and the correlation coefficients for the comparisons of the original and new AOD are 0.87 and 0.85, respectively. The tendency of the original aerosol model to overestimate the retrieved AOD is significantly improved by using the SSA values in addition to size distribution and refractive index obtained using the new model.

Kim, M.↗

NASA NTRS1991

Remote sensing of earth terrain

In remote sensing, the encountered geophysical media such as agricultural canopy, forest, snow, or ice are inhomogeneous and contain scatters in a random manner. Furthermore, weather conditions such as fog, mist, or snow cover can intervene the electromagnetic observation of the remotely sensed media. In the modelling of such media accounting for the weather effects, a multi-layer random medium model has been developed. The scattering effects of the random media are described by three-dimensional correlation functions with variances and correlation lengths corresponding to the fluctuation strengths and the physical geometry of the inhomogeneities, respectively. With proper consideration of the dyadic Green's function and its singularities, the strong fluctuation theory is used to calculate the effective permittivities which account for the modification of the wave speed and attenuation in the presence of the scatters. The distorted Born approximation is then applied to obtain the correlations of the scattered fields. From the correlation of the scattered field, calculated is the complete set of scattering coefficients for polarimetric radar observation or brightness temperature in passive radiometer applications. In the remote sensing of terrestrial ecosystems, the development of microwave remote sensing technology and the potential of SAR to measure vegetation structure and biomass have increased effort to conduct experimental and theoretical researches on the interactions between microwave and vegetation canopies. The overall objective is to develop inversion algorithms to retrieve biophysical parameters from radar data. In this perspective, theoretical models and experimental data are methodically interconnected in the following manner: Due to the complexity of the interactions involved, all theoretical models have limited domains of validity; the proposed solution is to use theoretical models, which is validated by experiments, to establish the region in which the radar response is most sensitive to the parameters of interest; theoretically simulated data will be used to generate simple invertible models over the region. For applications to the remote sensing of sea ice, the developed theoretical models need to be tested with experimental measurements. With measured ground truth such as ice thickness, temperature, salinity, and structure, input parameters to the theoretical models can be obtained to calculate the polarimetric scattering coefficients for radars or brightness temperature for radiometers and then compare theoretical results with experimental data. Validated models will play an important role in the interpretation and classification of ice in monitoring global ice cover from space borne remote sensors in the future. We present an inversion algorithm based on a recently developed inversion method referred to as the Renormalized Source-Type Integral Equation approach. The objective of this method is to overcome some of the limitations and difficulties of the iterative Born technique. It recasts the inversion, which is nonlinear in nature, in terms of the solution of a set of linear equations; however, the final inversion equation is still nonlinear. The derived inversion equation is an exact equation which sums up the iterative Neuman (or Born) series in a closed form and, thus, is a valid representation even in the case when the Born series diverges; hence, the name Renormalized Source-Type Integral Equation Approach.

Yueh, Herng-Aung↗