During two last decades the ideas and methods of computerized tomography (CT) have found wide application in different fields of plasma physics1'2. Having in mind many other diagnostic tools and techniques applicable in studying of plasma processes one may conclude that the CT is especially efficient when the whole 2D image of the plasma cross—section (and sometimes even 3D image) can be derived from the set of projections measured simultaneously. Unique possibilities of that kind play the3 nost important role in the situations with magnetic reconnection . Magnetic reconnection in high-conductivity plasma is the fundamental physical process and the basis of various phenomena of plasma physics and astrophysics. Solar flares, magnetospheric , sub.storms, disruption processes in tokamaks, cardinal structural changes in the reversed-field pinches, plasma focus devices compact tori etc are the typical examples. As a result of reconnection the transfer of the excess magnetic energy into kinetic and thermal energies of plasma, into radiation and also into the energy of accelerated particles takes place. Physicists often distinguish two types of magnetic reconnection: spontaneous and forced. Laboratory plasmas and the natural processes in outer space are usually closer to a spontaneous reconnection. In that case a definite accumulation of magnetic energy precedes the reconnection and the process similar to tearing modes develops at that initial stage. The forced reconnection due to an external forces is more convenient for purposeful experimental observation of recon— ection phenomena, e.g. by creation of current sheets '8.It is also more suitable for theoretical description and numerical simulation. Some independent calculations and checks of the diagnostic CT results are possible in that case. We restrict the scope of this paper to the two examples of reconnection investigations by tomographic methods related firstly to spontaneous and secondly to forced reconnection. The Part I presents basic concepts and somewhat puzzling nowadays situation with the socalled saw tooth problem arising in tokamak devices. An advanced radial modulators CT algorithm of 2D image reconstruction from limited views chord—integrated plasma emission measurements is described. This algorithm can be recommended as an efficient diagnostic tool for the future study of magnetic reconnection in various laboratory plasmas.The novel version of Monte Carlo CT reconstruction suitable for spectrotomographic activity is also described. The Part II presents our own spectrotomographic experiment with the plane pinch current sheet in the nonlinear regime.
The possibility of perform with tomographic reconstruction of spatial internal structure for the objects with reflecting flat or cylindrical surfaces is discussed. The problem solution is based on reducing the expression for reflected radiation to Radon transform of the desired distribution. Results of experimental investigations are adduced.
The probabilities for the object recognition from either their transforms in the Radon space or from their tomographic images are analyzed. For the cases under consideration, it is better to work directly in the Radon transformed space.
The determination of spatial structure density of inhomogeneous medium iising X-ray computer tomography is reduced to the solution of Radon integral equation G(y0,8) = J n"()do , (1) where n"() is the absorption coefficient (an imaginary part of the complex refractive index n=n'+in", n'=l), which is proportional to the medium density. Integration in (1) is done along straight rays y0=const, and G(y0,8) is a measurable function, i.e. an integral absorption along the rays, inserting the object at view 0, '2
An algorithm is described for the fast algebraic reconstruction in three-dimensional tomography. Some approaches for the rating are suggested and their influence on reconstruction quality is illustrated.
The iteration algorithm of three-dimensional tomography, the modified Gershberg-Papulis algorithm is developed. Its accuracy characteristics have been determined by numerical simulations. Much attention has been paid to the peculiarities of preliminary processing of the projection images from physical experiment. Algorithm is used for the reconstruction of the local emission coefficients in a micropinch discharge plasma. The analysis has revealed admissible accuracy of the algorithm, its sufficient stability to measurements noises, and the applicability in the processing of a real experiment.
A new technique for fast obtaining the quantitative characteristics of light-emitting object cross-section geometry, using the method of moments, is proposed. Optical calculation of integrated projection data (namely, the moments) considerably reduces the data for digital processing, thus making the real-time tomographic analysis possible. Theoretical aspects of the method along with its optical implementation are discussed.
The development and effective implementation of new plasma technological processes based upon the method of dynamic plasma operation (DPO) under atmospheric pressure call for using the emission spectral tomography. To this end, on the basis of an experimental apparatus implementing the method we designed an automated emission spectral-tomography complex with the fan measurement system. We studied experimentally how the flow configuration depends on various plasma parameters. In the framework of the local thermodynamic equilibrium (LTE) model we reconstructed several cross-sectional profiles of spatial distribution of emission coefficients and temperature from the visible recombination continuum of the argon plasma flow of different configurations. We have developed a commercial model of emission tomograph for plasma technological installations.
Algorithms for the tomographic reconstruction of nonaxial distributions of optical emission from the plasma periphery are proposed. The reconstruction from bi-view measurements is done to solve the problem of two-dimensional impurity transport diagnostics in tokamak. The developed technic is used to reconstruct the impurity emission evolution in the tokamak cross- section for light ions OII-OV, CIII-CV, H(beta ) spectral lines.
The paper describes instrumentation and gas density reconstruction technique for tomographic investigations at a ballistic range. Due to ballistic experiments which are carried out in quiescent gas, the shape of a test pressure chamber is of no importance. This allows construction of a polyhedral working section with the plane windows and arrange around it some optical devices to obtain several projections of an object under study. As a means of flow visualization grating and polarization interferometers are chosen with pulse ruby lasers at light sources. The gas density reconstruction technique is based on gas density function expansion in finite series inside narrow rings of a considered plane flow cross-section. The mathematical statistics methods are applied to estimation of adequacy of determined mathematical models, importance of the expansion coefficients and confidence intervals of the gas density distributions. The technique is illustrated by density reconstruction results of the flow over a free flying supersonic cone at angles of attack.
A one-step method for direct measurement of refractive index field is proposed. The method consists in combination of the optical probing step, i.e. obtaining projection data, with the following step of tomogram reconstruction, which is done by analog processing in the tomographic interferometer. Holographic interferometry technique is used to visualize the optical wave field that carries refractive index tomogram information. The real-time interferometric visualization of refractive index spatial distribution in either longitudinal or cross section of the objects under investigation has become possible.
This paper deals with the analysis of an algebraic reconstruction technique version for the restoration of refractive index spatial distribution in the objects cross-sections, using the tomographic holographic interferometry data; it also includes the digital simulation results. An example of tomographic reconstruction using the experimentally obtained interferograms is presented.
In this work a new method, proposed for correction of aberrations in complicated interferometrical systems, is discussed and tested. This method is based on the computer-aided reconstruction of phase distortions.
The results of experimental investigation into the process of the local parameters reconstruction for three-dimensional flows from the data of double-exposure speckle photographs, obtained simultaneously in different directions, are presented. A mathematical procedure of reconstruction, based on the integral Radon transform, is described and its accuracy is analyzed. On the basis of the mathematical simulation results, the requirements for the automated system of specklegram processing are formulated and realized. The examples of temperature and density fields in different objects, obtained by means of the above mentioned technique, are given. The error in obtained experimental data amounted to less than 5%, and the error in reconstructing the local temperature did not exceed 10%.
Using some specific examples (dynamics of fine structure elements, formed by mixing), it is shown how achievements in modern optical non-intrusive methods (holographic interferometry and optical tomography) may be applied for studying a wide range of processes taking place in stratified media.
The problem of tomographic reconstruction of large-scale objects by means of small-angle scattering data is considered. Analysis is based on the scalar Helmholtz equation for sounding waves. The asymptotic solutions of the diffraction tomography problems in the high frequency approximation are obtained. The conditions of applicability are analyzed for weak-scattering approximations and for solutions found out in this paper which can be used in the case of strong-scattering irregularities also.
The study of the process of light propagation in random inhomogeneous media leads, as a rule, to the solution of two principal problems. The first one is to find out the optical properties of the medium from the results of detection of scattered field of a certain structure. The second problem is to find out the structure of light field, that propagates through the scattering medium, with the known optical characteristics. These problems are solved usually by spectrometric methods, and the solution is derived either in the form of determining the integral characteristics, or by eliciting the properties of a sought value in a small volume.
The reconstruction problem of scattering inhomogeneities basing on functional-analytical methods is discussed in the article. One of the main ways for these methods is the mathematical extension of real wave vectors to 'non physical' domain of complex wave vectors. The real wave vectors characterize wave field in the medium, if attenuation is absent; the complex wave vectors correspond to fictitious radiation and reception of inhomogeneous waves. This way allows the solution of the Helmholtz-type equation to be obtained, which is more general than that in a classical variant. Moreover, the functional-analytical methods are a base to create the reconstruction algorithm for two-dimensional (and, as a perspective, three- dimensional) scatterers. The algorithm deals with mean power scatterers, which spectra are localized in a certain domain of space frequencies. the limitations of the space scatterer spectrum depend on the scatterer power. The algorithm provides essential economy of calculation expenditure during the process of the scatterer reconstruction. At the same time, an attempt to reconstruct both two-dimensional mean power inhomogeneities with wide space spectrum and full power inhomogeneities leads to evident instability of the problem, that is inherent to any method of solving the two-dimensional inverse problems for the monochromatic observation regime.
The main goal of the inverse scattering problems is the reconstruction of quantitative properties of the media based on measurements in set of the scattering experiments. It is supposed, that there are a background media with the known structure and a localized area of a limited volume with unknown structure (inhomogeneity) inside it. The determination of the inhomogeneity properties is required. Problems of the reconstruction or a more accurate definition of the inhomogeneity shape with the known media properties are also some types of the inverse scattering problem. The measurement data or so-called "scattering data" give the possibility to solve our task with a certain accuracy and with or without a uniqueness.
Integrated photoelasticity, a nondestructive method of three-dimensional stress analysis, is treated as optical tomography of the stress tensor field. Distinguishing features of the optical tensor field tomography are considered. Since in the general case the measurement data is in a nonlinear way related to the stress field, two particular cases are considered in detail: (1) weak birefringence, (2) constant principal stress directions. In these cases it is possible to measure two line integrals of the components of the stress tensor. It is shown that the general problem of stress tensor field tomography can be reduced to a problem of scalar field tomography for a single component of the stress tensor. The other stress components can in some cases be determined using equations of the theory of elasticity. The paper is illustrated by some examples of application of the method.
Integrated photoelasticity with normal and oblique incidence has been used. Two equations for determining the distributions of stress components in the case of plane deformation have been derived, which allow the determination of the distributions of (sigma) z and (sigma) r + (sigma) (theta ) using scalar field tomography. The equations of equilibrium permit all the stress components to the obtained separately. Stresses in an axisymmetric fiber preform have been determined experimentally.
A problem of determination of three-dimensional stress state from optical measurements by the method of integrated photoelasticity is considered. The stress medium is contained in the cylinder domain, the element of the cylinder is parallel to z-axis. Only the equilibrium equations are satisfied and strains are not considered. The weak optical anisotropy is supposed. The optical measurements are carried out along all horizontal straight lines which are parallel to the plane z equals 0. It is proved under this assumption that the longitudinal component (sigma) zz of the stress tensor can be determined. The method of numerical determination is offered. It is proved that no information about stress tensor, except (sigma) zz, can be determined.
The problem of reconstruction of the local values for the symmetric stress tensor in transparent anisotropic media from the results of multiangle transillumination has been solved. This problem belongs to the class of inverse problems. The direct problems of light propagation in optically heterogeneous media with artificial anisotropy has been solved in order to formulate the complex inverse problem correctly.
The method of ellipsometric tomography designed for precision measurements of complex refractive index variations in the volume of thin surface layers is considered. It is shown, that multi-wavelength ellipsometric measurements of light, reflected and scattered by the surface layer, allowed us to reconstruct its internal structure by solving a first order integral equation.
Microtomography systems usually are laboratory devices designed for defectoscopy and three- dimensional nondestructive testing. Initial data acquisition for X-ray and optical microtomography takes a relatively long time because of the low radiation intensity of fine- focus sources. It is therefore impracticable to employ expensive specialized processors for data input and image reconstruction. A more practical approach involves the use of image processing systems based on personal computers. It is shown that such equipment can handle the tasks of data acquisition and 3-D image reconstruction and visualization very effectively. The efficiency of a microtomograph system depends on the capabilities of software and of the system of data input into the computer. To speed up image reconstruction, use is sometimes made of a specialized coprocessor to carry out convolution with back projection. The software package usually contains programs to perform the operations of image reconstruction and 3-D visualization.
The great number of problems of computational diagnostics of electronic components can be formulated as tomographical problems with incomplete initial data. The standard methods of tomographical reconstruction can not be applied to solving problems of this kind. We have developed effective techniques for solving these problems on the basis of using some a priori information. We have used both information about compact support of distribution to be found and more hard a priori information--about laminar structure of the object under investigation. The obtained results demonstrate high efficiency of the developed techniques for computational diagnostics of electronic components.
Some new physical and technical solutions applied to the development of laser diagnostic complex for the study of local electro-physical and structural characteristics of semiconductor materials and microelectronic devices are presented. The potentialities of introscopy and microtomography in laser scanning microscope when detecting different informative response signals are discussed. Original methods and operation modes for scanning microscopy and tomography of semiconductor crystals are described, in particular, the results of computer and apparatus microtomography using transmitted, scattered, polarized infrared radiation, and optically induced photocurrent.
The studies of the upper atmosphere, ionosphere, magnetosphere and near space gave rise to the development of active experiments involving the formation of artificial structures (AS). One of the problems resolved on such a basis in the diagnostics of aeronomic and dynamic processes, occurring in the near space. Research into the spatio-temporal and optical distribution characteristics of AS is of great interest. The authors have performed a series of studies to reveal the possible applications of optical tomography techniques to these purposes.
The paper describes a new approach to studying the spectral-spatial characteristics of the objects, proposed by the authors, and the results of its experimental testing. This approach is based on application of tomographic principles to the spectral investigations of the objects. The results obtained show the great advantages of this method for the spectral analysis of spatially extended objects.
For high speed frame recording the use of well-developed tomography methods of cross- section image reconstruction of 3-D objects is suggested in this paper. In case of changing one of spatial coordinates z to a time coordinate t an analogue of series of cross-section images, which are perpendicular to axis z, is a series of frames with various values of t. In this case projections needed for tomographic reconstruction can be realized as a set of streak records of 2-D images, obtained without a slit at various speeds of scanning. Digital simulation shows the possibility of reconstruction of the series of frames with temporal resolution approximating to that of streak recording. This paper also gives an example of chronotomographic reconstruction from projections, obtained in the model of chronotomograph.
Measuring of displacements and deformations of diffuse reflecting objects using the speckle photography technique is an important application field of interference methods in optical measuring systems. In the present paper the possibility of using the optical Radon transform for decoding the speckle photos at high speckle noise levels and their processing in Radon- Fourier optoelectronic device is discussed.
A formula, which denotes the phase profile of two-dimensional light field by means of measurements of its intensity has been derived on the basis of the Radon transformation of measurements of distributions.
The method of image recognition using the moment invariants is considered, image moments being calculated via the Radon transform. Estimation of the number of moments necessary for image recognition and reconstruction is adduced. The scheme of the fast optical-digital processor for image moments calculation is described along with the discussion of experimental results, obtained with this processor.