Inverse Radiation Problem Research Articles

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.

Проекционный метод решения дискретизированных обратных задач в области антенных измерений

In the article, the problems of determining and monitoring antenna parameters, solved using measurements in the near field, are presented in a unified formulation corresponding to the gene-ralized inverse radiation problem in the form of an integral equation of the first kind. Within the framework of the numerical approach to the solution, the equation is discretized, and then the solution is sought approximately as a solution to the normal system of equations. It is shown that an approximate solution to the discretized problem that satisfies the normal system is also a solution to an equation with an orthogonal projector on its right-hand side. On the basis of this formulation, a new method of iterative projections is proposed. The efficiency of the method is demonstrated by the example of solving the problem of reconstructing the radiation pattern of a horn antenna from near-field data calculated for the electrodynamic model of the antenna in the HFSS program. The results of the proposed method are compared with the results of solving the problem by the method of decomposition in singular numbers.

Efficient equation-solving integral equation method based on the radiation distribution factor for calculating radiative transfer in 3D anisotropic scattering medium

High-directional resolution radiation intensity (RI) can provide substantial measurement information inside the participating medium, such as the distribution of temperature and physical properties. Therefore, efficiently and accurately solving the radiative transfer equation (RTE) to obtain RI in any direction is the key and challenge of target-detection and inverse-radiation problems. In our previous works [1,2], the integral equation method based on the radiation distribution factor (RDFIEM) was proposed to accurately obtain an arbitrary directional RI. To overcome the inefficiency of the RDFIEM in building a radiation distribution factor (RDF) database from the time-consuming reverse Monte Carlo (RMC) method, a method of equation-solving RDFIEM (ES-RDFIEM) was improved and developed to obtain the solution of RTE in a three-dimensional (3D) anisotropic scattering medium in this work, which can effectively avoid the stochastic ray-tracing process of the traditional RMC method and obtain the value of RDF by solving linear equations directly. The mathematical principles and formulae of ES-RDFIEM are introduced and deduced in detail, whose core idea is to suppose a specified element with a unit blackbody emission, whereas the remaining elements have no energy emission. Subsequently, the linear equations for the RDF, which are only concerned with the physical properties and geometric factors of the radiative system, can be constructed and solved. The computational accuracy and efficiency of ES-RDFIEM and RMC in several cases with different parameters were comprehensively compared. The results showed an excellent agreement between the RDF values and the RI calculated by the two methods. The computational efficiency of ES-RDFIEM was significantly improved compared to RMC, which was almost unaffected by radiation properties.

Efficient two-dimensional scalar fields reconstruction of laminar flames from infrared hyperspectral measurements with a machine learning approach

The latest hyperspectral measurements of combustion flames by Rhoby et al. (2014) provided extensive spatially and spectrally resolved information of flame radiation, which has been explored to retrieve two-dimensional, multi-scalar values of these flames with the conventional gradient-based optimization method. The drawback of that method is that the inverse radiation problem was solved through iterations with computationally intensive radiative heat transfer calculations and high-resolution wide-spectrum modeling, making the retrieving process very time-consuming. In the present study, we propose a machine learning based efficient inverse radiation model to retrieve two-dimensional temperature, CO2, H2O, and CO mole fractions of laminar flames from hyperspectral measurements. The model is trained with synthetic numerical data and is tested against previously made OH-laser absorption measurements and chemical equilibrium calculations for ethylene laminar flames with different equivalence ratios. The training data generation process, machine learning model architecture, model training, and validations are discussed in detail. Results have shown that the proposed machine learning based inverse radiation model is both accurate and efficient.

An efficient equation-solving method for calculating radiative transfer in isotropic scattering medium

An efficient equation-solving integral equation method (ES-RDFIEM) is proposed to calculate the radiation distribution factor (RDF), which was required to be solved by the time-consuming ray tracing with reverse Monte Carlo method (RMC) in the past. Since the RDF is only related to the radiative properties and geometry of the medium, it can be assumed that the blackbody radiation intensity of a certain element n is 1, while there is no emission from the remaining elements of the radiation system. In this way, the RD(j, n) (j = 1, 2,…, N) can be obtained by solving N × N equations based on the equivalent relationship of incident radiation. As a result, the stochastic statistical process of the RMC can be effectively avoided. The numerical results show that the RDF and radiation intensity calculated by ES-RDFIEM and RMC are highly consistent for one-dimension and two-dimension emitting, absorbing, isotropic scattering medium with transparent boundary. The CPU time for ES-RDFIEM to calculate the RDFs of the whole radiation system is much shorter than RMC under the same condition, which, in addition, does not increase with the increase of scattering albedo or optical thickness. With the same calculation accuracy as RMC, ES-RDFIEM has the significant advantage of high efficiency, which shows great potential in solving inverse radiation problems.

Inverse radiation problem with infrared images to monitor plasma-facing components temperature in metallic fusion devices

Abstract Infrared (IR) diagnostics are used to measure plasma-facing components (PFC) surface temperature in fusion devices. However, the interpretation of such images is complex in all-reflective environments because of unknown emissivity and multiple reflections issues. In order to assess these challenges an iterative inversion method based on a fast photonic model, the radiosity method, has been developed. The radiosity method is based on strong hypotheses including all diffuse surfaces. The inversion method allows retrieving the true surface temperature of PFC in two steps: a step of the target emissivity estimation in a baking scene and the use of the emissivity map to retrieve the temperature of metallic components with errors up to 3% during a plasma scenario.

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.

Effective solution of three-dimensional inverse radiation problem in participating medium based on RDFIEM

A novel integral equation method based on radiation distribution factor (RDFIEM) is developed for solving radiation transfer equation (RTE) to obtain radiation intensity signal in a small solid angle on a small point, which is effectively applied to reconstruct the three-dimensional (3D) temperature distribution in an absorbing, emitting and scattering medium. The spatial distribution of radiation intensity inside the medium can be derived by the reverse Monte Carlo method based on the radiation distribution factor (RDF), and source term distribution can be obtained by integration of RDFs. Consequently, according to the idea of integral equation method (IEM), the boundary exit radiation intensity with respect to the RDF and temperature can be deduced. It is worth noting that the RDF is only related to the geometry and radiation properties of the medium, which can be calculated only once to make RDFIEM be more efficient. Meanwhile, the error caused by the random number of RMC can be reduced by integrating the RDFs. As a consequence, the RDFIEM is particularly suitable for temperature field reconstruction. The directional radiation intensity signals obtained by charge-coupled device (CCD) camera are used as the known information to reconstruct the temperature distribution, the effects of CCD combinations, detection directions, optical thickness, boundary conditions, scattering type and scattering albedo, measurement and coefficient errors on the implementation of RDFIEM have been examined. The least square QR decomposition (LSQR) algorithm is introduced to solve the 3D temperature reconstruction problem. The results show that the temperature field can be reconstructed accurately and efficiently.

Improving a Tikhonov regularization method with a fractional-order differential operator for the inverse black body radiation problem

Tikhonov regularization is an usual method to solve an ill-posed problem, recommended when the input data are contaminated with noise. However, in some cases, the use of this technique is not sufficient to provide good solutions. In this work, an improvement of the Tikhonov regularization method was proposed and tested in the inverse black body radiation problem. The method proposed consisted in including the norm of the fractional-order derivative of the solution in the original functional proposed by Tikhonov. In the present framework, the regularized solution depends on the regularization parameter, λ, and on the fractional derivative order, α. For α assuming real value between 0 and 2, the solution obtained is more precise than those from the usual Tikhonov regularization method.

О решениях обратных задач дифракции звуковых волн

Представлен обзор работ по решению обратных задач рассеяния звуковых волн упругими телами. Теоретические основы решения обратных задач дифракции звука базируются на фундаментальных исследованиях проблемы обратных задач для уравнений в частных производных, выполненных отечественными учеными. В самой общей классификации обратные задачи акустики делятся на обратные задачи излучения (ОЗИ) и обратные задачи рассеяния (ОЗР). При решении задач первого класса по характеристикам звукового поля определяют некоторые параметры излучателя. При решении задач второго класса измерения параметров рассеянного звукового поля используют для идентификации свойств рассеивающего объекта. Большая часть приложений акустических методов основана на решении обратных задач дифракции, когда по параметрам излучаемого или отраженного звукового поля судят о параметрах объекта или среды. Анализ звуковых полей составляет основу методов в гидро- и аэроакустике; исследований в биологии и медицине; неразрушающего контроля и диагностики объектов; ультразвуковой дефектоскопии; обследовании и испытании материалов, конструкций и сооружений. Решения всех обратных задач основаны на решении прямых задач дифракции. В работе представлены наиболее значимые результаты в решении прямых задач рассеяния звуковых волн упругими объектами. Выделены работы, посвященные проблемам обратных задач рассеяния звука неоднородными упругими телами. Это направление составляет предмет интересов в исследованиях авторов.

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.

Treatment of efficiency for temperature and concentration profiles reconstruction of soot and metal-oxide nanoparticles in nanofluid fuel flames

The choice of the step size plays an important role in one dimensional searching (ODS) algorithm in the inverse radiation problem to simultaneously estimate temperature and concentration distributions of soot and metal-oxide nanoparticles in nanofluid fuel flames. In practice, it is difficult to determine the optimal step size and the inappropriate step size can introduce significant reconstruction error and cause high computation time. This paper adopts a nonlinear optimization (NLP) technique without the needing of setting up the step size to improve the reconstruction efficiency. The reconstruction performances of NLP technique were compared with the ODS algorithm with different step sizes. It was found that the NLP technique can reach the same or better reconstruction accuracy and experience much lower computation time in comparison with the ODS algorithm even with the optimal step size.

Application of metaheuristic algorithms for solving inverse radiative boundary design problems with discrete power levels

In this study, an analysis for solving inverse radiative boundary design problem with discrete design variables is developed and presented when radiation is the dominant mode of heat transfer. An absorbing, emitting, and participating medium is considered in radiative equilibrium. The discrete ordinate method (DOM) is implemented to solve the radiative transfer equation (RTE). The goal of the design problem is to find the optimum power of heaters from a discrete set of powers in such a way that they produce the desired temperature and heat flux profile over the design surface. Therefore, several metaheuristic optimization methods including the genetic algorithm (GA), particle swarm optimization (PSO), and its modified forms such as PSO with Constriction Factor (PSO-CF), PSO with repulsion factor (PSO-RF) and PSO with adaptive inertia weight (PSO-W) are explored to solve the inverse problem. The accuracy of the direct solution of radiative heat transfer is examined by comparison of the present results with findings from the literature. Then the efficiency and accuracy of the optimization methods are assessed by their ability of finding and reconstructing of the results from the direct solution. Finally, the effects of some thermos-physical properties including the absorption coefficient, emissivity of the heater surface and design surface, on the optimum solutions are examined. The comparison of the results revealed that the genetic optimization algorithm converged faster and with fewer calculations of the objective function compared to other optimization techniques.

Inverse radiation problem of multi-nanoparticles temperature and concentration fields reconstruction in nanofluid fuel flame

A novel reconstruction model based on inverse radiation analysis was presented for simultaneous estimation of temperature and concentration fields of soot and multiple metal-oxide nanoparticles in nanofluid fuel flame from the knowledge of the flame emission radiation intensity obtained by a CCD camera. The self-absorption effect was considered in the reconstruction model and least-square QR decomposition (LSQR) algorithm combined with iterative method was introduced to solve the inverse radiation problem. The inverse reconstruction model was successfully applied in the flames containing two and three kinds of metal-oxide nanoparticles from simulation values as examples and can be extended to more kinds of metal-oxide nanoparticles containing system. The measured data were also simulated by adding random noise into the exact solution of the direct problem. The numerical results showed that all the unknown parameters fields can be estimated accurately, even with the noisy data.

Inverse estimation of various surface emissivity distributions using repulsive particle swarm optimization

The aim of the present study is to demonstrate further inverse solving capability of the repulsive particle swarm optimization (RPSO) method by estimating unknown surface radiative property of various distributions in a surface radiation problem. A distribution of the surface emissivity was selected as the unknown property to retrieve and was defined as arbitrary functional forms to simulate various profiles in an axisymmetric cylindrical enclosure with nonparticipating media condition. A total of four functional forms were examined with uniform, rectangular step, triangular ramp and polynomial curve profiles. Also, the number of unknowns was increased to verify if the RPSO method could still retrieve property values exactly when compared with a previous study. In conclusion, the present results proved that the RPSO method showed accurate and robust performance as the inverse solver due to a superior search capability for the inverse surface radiation problem involving numerous unknown parameters of various distributions.

Neural Network Modeling for the Solution of the Inverse Loop Antenna Radiation Problem

Soft computing techniques are used, in this paper, to model and solve the inverse problem of a thin, circular, loop antenna that radiates in free space. The electromagnetic field intensity serves as the input to the inverse model, whereas the antenna radius is the output. Three different architectures, based on artificial neural networks (ANNs), are implemented and various training algorithms are tested in order to obtain the optimum performance. The effect of the size of the training data set and the number of the observers on the accuracy of the results are investigated. Specific information for the selection of the appropriate ANN architecture is provided, depending on the constraints imposed by various parameters of the problem. Extensive numerical tests indicate that the results predicted by the proposed models are in excellent agreement with the theoretical data obtained from the existing analytical solutions of the forward problem.

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...