Abstract
Computerized tomography has been used as a diagnostic technique for studying inhomogeneous turbulent density fields from optical path length data obtained at different viewing angles. The contribution of each element of the turbulent field to the path integral depends on the local turbulent intensity and the distance of the element from the detector. An iterative algebraic reconstruction algorithm, based on full discretization, has been used to solve the distant-dependent Radon transform. The algorithm has been studied by applying it to turbulent optical path length data obtained by computer simulations of two phantoms. The results show accurate reconstructions. The effects of ray ordering and relaxation parameters on reconstruction accuracy has been studied.
Similar content being viewed by others
References
Browne, J. A., Herman, G. T., and Odhner, D. (1993). SNARK93: A programming system for image reconstruction from projections, Technical Report No. MIPG 198, Medical Image Processing Group, Department of Radiology, University of Pennsylvania, Philadelphia, Pennsylvania 19104, August.
Censor, Y. (1983). Finite-series-expansion methods,Proc. IEEE 71, 409–419.
Censor, Y. (1988). On the selective use of iterative algorithms for inversion problems in image reconstruction and radiotherapy, In:Proceedings of the 12th World Congress on Scientific Computation-IMACS Vichnevetsky, R. Borne P. and Vignes, J. (Eds.), Gorfidn, Paris, France,4, 563–565.
Censor, Y. (1981). Row-Action methods for huge and sparse systems and their applications.SIAM Review 23, 444–466.
Cimmino, G. (1938). Calcolo Approssimato per le soluzioni dei systemi di equazioni lineari, La Ricerca Scientifica, Roma XVI, Ser. II, Ano IX,1, 326–333.
Deans, S. R. (1983).The Radon Transform and Some of Its Applications, Wiley, New York.
Eggermont, P. P. B., Herman, G. T., and Lent, A. (1981). Iterative algorithms for large partitioned linear systems, with applications to image reconstruction.Linear Algebra and Its Applications 40, 37–67.
Elfving, T. (1980). Block-Iterative methods for consistent and inconsistent linear equations.Numerische Mathematik 35, 1–12.
Faris, G. W., and Byer, R. L. (1988). Three-dimensional beam-deflection optical tomography of a supersonic jet.Appl. Optics 27, 5202–5212.
Hall, R. J., Bonczyk, P. A. (1990). Sooting flame thermometry using emission/absorption tomography.Appl. Optics 29, 4590–4598.
Herman, G. T. (1980).Image Reconstruction from Projections: The fundamentals of Computerized Tomography: Academic Press, New York.
Herman, G. T., Levkowitz, H., Tuy, H. K., McCormick, S. (1984). Multilevel Image Reconstruction, In Rosenfeld, A. (ed.),Multiresolution Image Processing and Analysis, Springer-Verlag, Berlin, Heidelberg, New York, Tokyo, 121–135.
Herman, G. T., and Meyer, L. B. (1993). Algebraic reconstruction techniques can be made computationally efficient.IEEE Transactions on Medical Imaging 12, 600–609.
Ishimaru, A. (1973). A new approach to the problem of wave fluctuations in localized smoothly varying turbulence.IEEE. Trans. Antennas and Propagation AP-21, 47–53.
Ishimaru, A. (1978).Wave Propagation and Scattering in Random Media, Chapter 6, Academic Press, New York.
Kaczmarz, S. (1937). Angenaherte auflosung von systemen linearer gleichungen.Bull. Acad. Polon. Sci. Lett. A 35, 355–357.
Kafri, O. (1980). Noncoherent method for mapping phase objects.Opt. Lett. 5, 555–557.
Kak, A. C., and Roberts, B. A. (1986). Reconstruction from projections: applications in computerized tomography, InHandbook of Pattern Recognition and Image Processing, Young, T. Y., and Fu, K. S. (Eds.), Academic Press, New York, pp. 649–693.
Keren, E., Livnat, A., and Kafri, O. (1988). J. Unified theory for the optical transfer function: ray-optical approach.Opt. Soc. Am. A-5, 1213–1225.
Lewitt, R. M. (1983). Reconstruction algorithms: transform methods.Proc. IEEE 71, 390–408.
Lindgren, A. G., and Rattey, P. A. (1981). The inverse discrete radon-transform with applications to tomographic imaging using projection data,Advances in Electronics and Electron Physics, Academic Press,56, 359–410.
Liu, T. C., Merzkirch, W., and Oberste-Lehn, K. (1989). Optical tomography applied to speckle photographic measurement of asymmetric flows with variable density.Experiments in Fluids 7, 157–163.
Matulka, R. D., and Collins, D. (1971). Determination of three-dimensional density fields from holographic interferograms.J. Appl. Phys. 42, 1109–1119.
Natterer, F. (1986).The Mathematics of Computerized Tomography, J. Wiley and Sons, Chichester, England.
Ray, S. R., and Semerjian, M. G. (1983). Laser tomography for simultaneous concentration and temperature measurement in reacting flows.Prog. Astronaut. Aeronaut. 92, 300–324.
Stricker, J. (1984). Analysis of 3-D phase objects by Moire deflectometry.Appl. Optics 23, 3657–3659.
Snyder, R., and Hesselink, L. (1984). Optical tomography for flow visualization of the density field around a revolving helicopter rotor blade.Appl. Optics 23, 3650–3656.
Sweeney, D. W., and Vest, C. M. (1974). Measurement of three-dimensional temperature fields above heated surfaces by holographic interferometry.Int. J. Heat Mass Transfer 17, 1443–1454.
Tanabe, K. (1971). Projection method for solving a singular system of linear equations and its application.Numerische Mathematik 17, 203–214.
Tatarksi, V. I. (1961).Wave Propagation in a Turbulent Medium, McGraw-Hill, New York.
Vest, C. M., and Prikryl, I. (1984). Tomography by iterative convolution: empirical study and application to interferometry.Appl. Optics 23, 2433–2440.
Vukicevic, D., Jager, H., Neger, T., Philipp, H., and Woisetschlager, J. (1989). Tomographic reconstruction of the temperature distribution in a convective heat flow using multidirectional and holographic interferometry.Appl. Optics 28, 1508–1515.
Yule, A. J., Ahseng, C., Felton, P. G., Ungut, A. and Chigier, N. A. (1981). Laser tomographical Investigation of Liquids Sprays,18th International Symposium on Combustion, University of Waterloo, Waterloo, Canada, August 17–22, pp. 1501–1510.
Zhu, H. M., Sun, T. Y., and Chigier, N. (1987). Tomographical Transformation of Malvern Spray Measurements.Atmoization and Spray Techn. 3, 89–105.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Stricker, J., Censor, Y. & Zakharin, B. Inhomogeneous turbulent field diagnostics by distance-dependent tomographic reconstruction techniques. J Sci Comput 11, 207–227 (1996). https://doi.org/10.1007/BF02088816
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF02088816