Inverse Radiative Transfer Problem Research Articles

SNOWTRAN: A Fast Radiative Transfer Model for Polar Hyperspectral Remote Sensing Applications

In this work, we develop a software suite for studies of atmosphere–underlying SNOW-spaceborne optical receiver light TRANsmission calculations (SNOWTRAN) with applications for the solution of forward and inverse radiative transfer problems in polar regions. Assuming that the aerosol load is extremely low, the proposed theory does not require the numerical procedures for the solution of the radiative transfer equation and is based on analytical equations for the spectral nadir reflectance and simple approximations for the local optical properties of atmosphere and snow. The developed model is validated using EnMAP and PRISMA spaceborne imaging spectroscopy data close to the Concordia research station in Antarctica. A new, fast technique for the determination of the snow grain size and assessment of the snowpack vertical inhomogeneity is then proposed and further demonstrated on EnMAP imagery over the Aviator Glacier and in the vicinity of the Concordia research station in Antarctica. The results revealed a large increase in precipitable water vapor at the Concordia research station in February 2023 that was linked to a warming event and a four times larger grain size at Aviator Glacier compared with Dome C.

Inverse radiative transfer with goal-oriented hp-adaptive mesh refinement: adaptive-mesh inversion

The inverse problem for radiative transfer is important in many applications, such as optical tomography and remote sensing. Major challenges include large memory requirements and computational expense, which arise from high-dimensionality and the need for iterations in solving the inverse problem. Here, to alleviate these issues, we propose adaptive-mesh inversion: a goal-oriented hp-adaptive mesh refinement method for solving inverse radiative transfer problems. One novel aspect here is that the two optimizations (one for inversion, and one for mesh adaptivity) are treated simultaneously and blended together. By exploiting the connection between duality-based mesh adaptivity and adjoint-based inversion techniques, we propose a goal-oriented error estimator, which is cheap to compute, and can efficiently guide the mesh-refinement to numerically solve the inverse problem. We use discontinuous Galerkin spectral element methods to discretize the forward and the adjoint problems. Then, based on the goal-oriented error estimator, we propose an hp-adaptive algorithm to refine the meshes. Numerical experiments are presented at the end and show convergence speed-up and reduced memory occupation by the goal-oriented mesh adaptive method.

Inverse radiative transfer problem for soil properties retrieval from bidirectional reflectance measurements

The difficulty of obtaining some experimental soil properties leads to the use of many approaches such as the inverse technique to estimate those properties. However, when confronted with complex problems, the inverse approach requires an accurate numerical method for solving both direct and indirect problems as well as the good choice of inverse data. In the present work, a novel approach to retrieve soil volumetric water content (SVWC) from the knowledge of soil bidirectional reflectance by using the inverse technique is developed. The soil sample is a planar multiphase system consisting of liquid (water), gas (air) and spherical clay particles with spatial linear variation of SVWC. The optical properties of clay particles are determined from Mie theory. The soil bidirectional reflectance is simulated by the radiative transfer equation (RTE), which is solved numerically by the discreet spherical harmonic method (DSHM). The inverse problem is described as an optimization problem and solved by the quantum behaved particle swarm optimization algorithm (QPSO). The inverse results showed that the accuracy of retrieved soil properties depends on wavelength of the incident radiation.

Quantitative assessment method of muzzle flash and smoke at high noise level on field environment

It is quite a challenge to obtain the temperature and species concentration fields of muzzle flash at high noise level. In this numerical study, radiation intensity of muzzle flash received by the high-speed Complementary Metal-Oxide-Semiconductor (CMOS) camera was simulated based on the line-of-sight method in the direct radiative transfer problem. The inverse radiative transfer problem of reconstructing distributions of temperature and soot volume fraction from the knowledge of flame radiation intensity was transformed into a minimization optimization problem and a meta-heuristic algorithm was used to solve the problem. The effects of the number of detection lines, optical thickness and measurement errors on the reconstruction results were discussed in details. A method to estimate the noise level of radiation intensity was developed, experimental results showed that the signal-to-noise ratio (SNR) of radiation intensity can be successfully inferred when the SNR is greater than 20 dB. Subsequently, prior knowledge of the noise level was introduced in the regularization to achieve a meaningful approximation of the exact value. The reconstruction of the soot volume fraction filed with SNR greater than 40 dB is considered successful with the inclusion of an appropriate regularization term in the objective function, and the reconstruction of the temperature field is feasible even with SNR as low as 15 dB. The high tolerance to the noise level of the radiation intensity gives the reconstruction algorithm the potential to be used in practical experiments of muzzle flash.

An equation-solving method based on radiation distribution factor for radiative transfer in participating media with diffuse boundaries

An efficient and accurate method to solve the directional radiation intensity in the participating medium has always been a pursuit in radiative transfer fields, especially in radiation detection and inverse radiative transfer problems. As one of the few algorithms with both high accuracy and strong applicability, the reverse Monte Carlo (RMC) method suffers from the disadvantages of unavoidable random statistical errors and time-consuming ray tracing. Recently, a so-called equation-solving integral equation method based on the radiation distribution factor (ES-RDFIEM) can effectively overcome these shortcomings of RMC, which has comparable accuracy as RMC while taking only a few hundredths or thousandths of the calculation time of RMC. In this paper, ES-RDFIEM was extended to a radiation system with diffuse surfaces by constructing the radiative transfer equation (RTE) about the radiation distribution factor (RDF) of the wall and internal medium, respectively. The mathematical principle and formula were introduced in detail, and the computational performance was examined by several samples with different radiative parameters. The results showed that the RDF and radiation intensity solved by ES-RDFIEM are in good agreement with RMC, and ES-RDFIEM is more stable and reliable. More importantly, the computation time of ES-RDFIEM is significantly shorter than that of RMC, and it is not affected by wall emissivity, internal medium optical thickness and scattering albedo.

Numerical and experimental determination of optical properties and thermal conductivity of ceramic composites based on fumed silica and silica fiber

The thermal insulation material composed of fiber-reinforced fumed silica (in the raw and opacified with silicon carbide, zirconia or titania powders) was produced and analyzed. Optical properties (scattering and absorption coefficients) were experimentally examined in the spectral range of 0.9 – 4.7 µm by the solution of the inverse problem of radiative transfer. The inverse problem was based on the invariant embedding equation and the measured spectral directional-hemispherical reflectance. The effect of silicon carbide opacifier addition on the optical properties, effective and radiative thermal conductivity was estimated. The calculated radiative thermal conductivity of thermal insulations with various volume fractions of SiC opacifier was compared to the one deduced from the effective thermal conductivity using the calorimetric technique of conductive and radiative components separation. The effective thermal conductivity was measured by the quasi-stationary technique in the temperature range of 373 – 1173 K. The results of the inverse problem solution were compared to the calculations based on the Mie theory and the measured size distribution of silicon carbide particles. The experimental scattering coefficient was shown to be smaller than the calculated one. At the same time, absorption coefficients demonstrated mutual consent. Possible uncertainties in SiC powder size and the complex refractive index of the basic material were considered as a probable explanation of the obtained results. The size distribution of SiC opacifier was numerically optimized to obtain as low Rosseland mean radiative thermal conductivity as possible. The influence of the opacifier chemical composition was analyzed by collating radiative thermal conductivity deduced from the measured effective thermal conductivity to ones calculated using Mie theory. Finally, the effect of Fe2O3, Si3N4, TiO2, graphite, ZrO2, TiN, TiC, AlN opacifiers was numerically analyzed using Mie theory. Compounds based on titanium and an iron sesquioxide were shown to be promising opacifiers for high temperature applications.

Solar Faculae: Microturbulence as an Indicator of Inclined Magnetic Fields

The observations of the solar facula in the Ba II λ 455.403 A line are used to construct a 3D model of the facula area by solving the inverse nonequilibrium radiative transfer problem and to investigate the fine structure of the field of unresolved velocities (microturbulence). New turbulent structures are formed in the layers of the upper photosphere. They are localized mainly between upward and downward flows with the formation of ring-shaped structures of increased turbulence around these flows. The mechanism of magnetic anisotropy of microturbulent velocity is proposed (small-scale eddy-type plasma motions mainly occur in the planes perpendicular to the magnetic field), which explains the height dependence of the field of unresolved velocities. Anisotropy of microturbulence begins to manifest itself in the lower photospheric layers outside the upward and downward flows, while it manifests itself in the higher layers inside these flows. The increase of microturbulence in the layers of the upper photosphere and the lower chromosphere in the areas between matter flows indicates the presence of inclined magnetic fields, which, along with the blurring of its spatial structure, indicates the existence of a magnetic canopy region. Microturbulence can be used as an additional tool for diagnostics of inclined magnetic fields.

Features of Convection in the Atmospheric Layers of the Solar Facula

According to the data of complex 2D observations on the VTT telescope of the solar facula, a 3D model of the solar atmosphere in the facular region was obtained by solving the inverse radiative transfer problem in the Ba II 4554 A line. The magnetic field was estimated using the Stokes V profiles of the Fe I 15648 A line. The influence of magnetic field on photospheric convection was investigated: spatial variations in temperature and velocities at different heights were considered. It is shown that the mutual transformation of the mechanical and thermal energy of the solar plasma into magnetic energy occurs in the layers of the middle photosphere. The integral effect of a small-scale magnetic dynamo leads to lowering the temperature and slowing down the motion of the predominant downward flows in the layers of the middle photosphere in the facular regions with a strong field (greater than 1 kG), while there is an increase in temperature and acceleration of the motion of the predominant upward flows in the layers of the middle photosphere in the facular regions with a weak field (less than 1 kG). It is shown that the magnetic field of the facula stabilizes photospheric convection, and the small-scale magnetic dynamo causes a double temperature inversion in the photospheric layers of the facula.

Characterization of siloxane-infiltrated ceramics microstructure by spectral scattering in the near infrared

The spectral scattering technique is considered to estimate the scatterers (pores) size distribution. It is based on the fitting of spectral scattering coefficients determined by Mie theory and radiative transfer inverse problem solution. The previously proposed method was improved for multiphase system analysis. The spectral directional-hemispherical reflectances of slabs of not less than two different geometrical thicknesses are used for inverse radiative transfer problem solution. Semitransparent ceramics with less than 10–15% of total porosity, that contains homogeneously distributed close to solid sphere scatterers, is the application object of the proposed technique. General expressions for multiphase systems were simplified to three-phase ones to reduce the number of optimization variables and adapted to the evaluation of semitransparent ceramics infiltrated by the polymer.The proposed technique was implemented for the evaluation of silica ceramics with 10% porosity before and after the infiltration by the methyl-phenyl-spirocyclosiloxanol followed by the polyfunctional condensation to obtain the polymethyl-phenyl-spirocyclosiloxane. Two techniques of ceramics infiltration with the low-molecular polymer viz by the solution and by the melt were compared. Size distributions of the polymer-filled pores was shown to be affected by the infiltration procedure and polymerization regime. It was shown that less than 25% of the initial pore volume appears to be polymer-filled in the case of ceramics infiltration by the solution. Infiltration from the melt fills not less than 80% of the pore volume. The mean pore diameter of air-filled pores was estimated by gas/mercury porometry and spectral scattering technique. Both methods are shown to be in a rather good agreement. By these techniques air-filled pores mean diameters were shown to be 0.37 and 0.44 µm respectively for ceramics before the infiltration and 0.54 and 0.55 µm for the ceramics infiltrated through the solution. The spectral scattering technique shows mean diameter of polymer-filled pores to be 0.11–0.17 and 0.49 µm in the cases of ceramics infiltration by the solution and by the melt respectively. Thus, sizes of polymer-filled pores are shown to be shifted to the higher values because of infiltration by the melt. The obtained data on polymer-filled pores sizes may be useful for the analysis of ceramics strengthening by the polymer infiltration and infiltration procedure optimization.

Diagnostics of the Quiet Sun Atmosphere’s Photospheric Jets

Abstract—From 2D-spectral observation data of a quiet region of the solar disk center in the Fe I λ 557.609 nm line, 3D hydrodynamic models of photospheric jets are built by solving the inverse radiative transfer problem. The obtained models describe thermodynamic parameters and the complete velocity field (vertical and horizontal). It is shown that the photospheric jets under consideration arise from the interaction of the surrounding environment with the field of the magnetic tube. The jets are located in a region of a unipolar magnetized downflow at the impact point of two horizontal flows, and they tend to occur at the edge of magnetic tubes. The observed gas velocities are subsonic in downflows of the jets. Energy release in the photospheric jets is predominantly localized in the middle photosphere layers, where the excess pressure is maximal. Compared with the surrounding media, mass density in the jets is significantly increased in the upper layers and slightly decreased in the lower layers of the photosphere.

Exact Solution of the Inverse Scalar Radiative Transfer Problem in One-Dimensional Atmospheres

The inverse scalar problem of radiative transfer in a ID atmosphere is solved analytically. It is shown, in particular, that not all combinations of the reflection and transmission coefficients r, q ≤1 can be physically significant.

Inverse boundary design problem of combined radiation convection heat transfer in a duct with diffuse-spectral design surface

In the present work, an optimization technique is applied for inverse boundary design problem of radiative convective heat transfer of laminar duct flow by numerical method. The main goal is to verify how the solution of inverse problem is affected by the spectral behavior of the boundary surfaces. The conjugate gradient method is used to find the unknown temperature distribution over the heater surface to satisfy the prescribed temperature and heat flux distributions over the design surface. The bottom boundary surface (including design surface) is diffuse-spectral, while the top wall (heater surface) behaves as gray one. The variation of emissivity with respect to the wavelength is approximated by considering a set of spectral bands with constant emissivity and then the radiative transfer equation is solved by the discrete ordinates method for each band. The performance of the present method is evaluated by comparing the results with those obtained by considering a diffuse-gray design surface. Finally an attempt is made to investigate the spectral behavior of the design surface on the calculated temperature distribution over the heater surface.

Structure of the Long-Living Elements of Solar Granulation

Spatial and temporal variations in thermodynamic and kinematic parameters of structural elements of solar granulation are investigated by solving the inverse nonequilibrium radiative transfer problem using the observational data from the Vacuum Tower Telescope (duration of observations 2.6 h). In the lower photosphere, we have detected long-living (with lifetime up to 1.5 h) structures—trees of fragmenting granules. They occur as a result of the division of an ascending granular flow into several fragments, which can be repeated multiple times. We have found that approximately 67% of the regions with the highest positive variations of pressure correspond to the time and place of fragmentation of granular flows; approximately 12% of the regions correspond to the approach of adjacent structures.

A New Numerical Approach to Inverse Transport Equation with Error Analysis

The inverse radiative transfer problem finds broad applications in medical imaging, atmospheric science, astronomy, and many other areas. This problem intends to recover optical properties, denoted...

Diagnostics of horizontal velocity field in the solar atmosphere: Line Ba II λ 455.403 nm

We proposed a method for diagnostics of the horizontal velocity field based on 2D observations at the center of the solar disk with high spatial and temporal resolution. The method consists in semiempirical modeling of the solar atmosphere by solving the inverse radiative transfer problem and subsequent obtaining horizontal velocities by solution of the corresponding hydrodynamic equations. We investigated the diagnostic capabilities of the line Ba II λ 455.403 nm (considering hyperfine structure and isotope splitting) for studying the horizontal velocity field of the nonhomogeneous solar atmosphere.

Simultaneous retrieval of multiparameters in a frequency domain radiative transfer problem using an improved pdf-based aco algorithm

ABSTRACTInspired by the particle swarm optimization algorithm, an improved ant colony optimization algorithm based on probability density function (IPDF-ACO) was developed for solving the inverse problem of frequency domain radiative transfer in a one-dimensional participating medium. The plural hemispherical reflectance and transmittance simulated by the finite-volume method served as input of the inverse analysis. The extinction coefficient, scattering albedo, and asymmetry parameter were retrieved simultaneously by using the amplitude and phase information as measured values. Through five test cases, the IPDF-ACO proved to be more accurate and efficient than the basic PDF-ACO even with noisy data.

Diagnostics of the solar atmosphere by the Non-LTE inversion method: Line of Ba II λ 455.403 nm

The inverse problem of nonequilibrium radiative transfer in the Ba II λ 455.403 nm line is solved taking into account the hyperfine structure and isotopic splitting. Diagnostic capabilities of this line for the study of the solar atmosphere are investigated based on the three-dimensional hydrodynamic model. It is shown that the use of inversion methods for the analysis of the observed Ba II λ 455.403 nm line makes it possible to reproduce physical conditions in the layers of the photosphere and the lower chromosphere (0 < h < 600 km) with a correlation coefficient of 0.9.

Some speed-up strategies for solving inverse radiative transfer problems

Inversion based on the radiative transfer equation (RTE) is generally highly CPU time consuming because the forward model itself is complicated to solve when the space dimension is greater than one, and because the inversion is based on a large number of forward model runs until convergence is reached. The goal of this paper is to set up some speed-up strategies specific of inversion when radiative transfer problems are dealt with. More specifically, the accurate identification of the volumetric radiative properties i.e. both the absorption and scattering coefficients is the objective of this study.

Space-Dependent Sobolev Gradients as a Regularization for Inverse Radiative Transfer Problems

Diffuse optical tomography problems rely on the solution of an optimization problem for which the dimension of the parameter space is usually large. Thus, gradient-type optimizers are likely to be used, such as the Broyden-Fletcher-Goldfarb-Shanno (BFGS) algorithm, along with the adjoint-state method to compute the cost function gradient. Usually, theL2-inner product is chosen within the extraction procedure (i.e., in the definition of the relationship between the cost function gradient and the directional derivative of the cost function) while alternative inner products that act as regularization can be used. This paper presents some results based on space-dependent Sobolev inner products and shows that this method acts as an efficient low-pass filter on the cost function gradient. Numerical results indicate that the use of Sobolev gradients can be particularly attractive in the context of inverse problems, particularly because of the simplicity of this regularization, since a single additional diffusion equation is to be solved, and also because the quality of the solution is smoothly varying with respect to the regularization parameter.

Convection structure in the solar photosphere at granulation and mesogranulation scales

Vertical structure of the solar photospheric convection is investigated using the profiles of neutral iron line λ ≈ 639.3 nm measured in a non-pertubed region near the center of the solar disk. The observations were carried out using German Vacuum Tower Telescope (Canary Islands, Spain). They are characterized by a high spatial resolution. Spatial-temporal variations of the kinematic and ther-modynamic parameters were reproduced by solving the nonequilibrium inverse radiative transfer problem. The wave motions were eliminated using the k — ω filtration. Spatial variations of temperature, vertical velocity, density, and gas pressure in convective cells are analyzed on the scales of granules (0.5–5 Mm) and mesogranules (5–12 Mm), respectively, at various heights in the solar photosphere (h = −25–500 km). When moving to the upper photosphere layers, the convective structure undergoes the following changes: at heights h = 200–250 km, the temperature inversion occurs, as well as some-times the inversion of convective velocities; at heights h = 50–100 km, the inversion of relative density variations takes place, the relative variations in density and pressure inside convective cells increase with height and become positive in ascending flows and negative in descending flows.