Reconstruction Theories And Algorithms On Moiré Tomography For Phase Fields

Optical Computerized Tomography (OCT) is a branch of ComputerizedTomography. It is a non-contact measurement technique and shows superioritiesin many domains, such as flow visualization and measurement of thermo physicalparameters. The moire tomography belongs to the Optical ComputerizedTomography and its projection data is deflection angles. It has many meritssuch as simple optical configuration, superior ability of anti-error andadaptation to tough environment. The moire tomography has great practicalvalue to the qualitative visualizations and quantitative measurements ofcomplex flow fields. But up to now, the theory system and reconstructionalgorithms of the moire tomography have not been studied systematically. Soemphasis of this dissertation is put on the reconstruction algorithms of moiretomography for the complex flow fields. The main work is described as follows:1) Theory research of moire tomographyThe relation between the deflection projection and the traditionalprojection is studied and is described from many different views. By thisrelation, the deflection tomography can have a explicit position in the wholetomographic theoretical frame and theoretical law can be found to thesemethods which apply the traditional tomographic reconstruction algorithms tothe reconstruction of deflection tomography.2) Research work to the transform algorithms of deflection tomographyAccording to the relation between these two tomographic problems, thedeflection filtered back-projection algorithm is achieved and its numericalimplementation is studied. The corresponding convolution back-projectionalgorithm is also given. Then an error analysis is made to the DFBP algorithmand a modified algorithm is presented.3) Research work to the series expansion algorithms of deflectiontomographyA model which directly numeralize the gradient of refractive index ispresented to get the discrete linear equations of deflection tomography.According to the model, three reconstruction algorithms are studied to solvethese linear equations. Numerical experiments show that these algorithms have strong abilities of noise immunity. Another deflection iterative algorithmbased on the expansion of local basis is presented. This algorithm can notonly reserve the sparse property Of the coefficient array, but also discretethe deflection tomography in a natural way. Good quality of anti-noise andreconstruction accuracy of this algorithm have been found by numericalexperiments.4) Research work to the reconstructions of deflection tomography withincomplete dataIn the limited angle problem, a deflection tomographic iterative algorithmwhich is based on the Bayesian Law is presented. In the research of the interiorproblem, the wavelet based local tomographic reconstruction algorithm whichis present by Farrokh is introduced to the local reconstruction of deflectiontomography.5) Research work to the real flow field of moire tomographyThe deflection filtered back-projection algorithm and its correspondmodified algorithm are applied to reconstruct the density field caused by therocket exhausted plumes. Results show that the modified algorithm can depressthe slope phenomena efficiently. The iterative algorithm which is based onthe expansion of harming function is applied to reconstruct thedensity fieldin a hypersonic wind tunnel. The reconstruction results are compared with theinverse Abel transform method which can only be applied with axial symmetricalfield. Results coincident well with each other. But it is obviously that thenovel algorithm have handle arbitrary flied and more universality.Reconstructions to these real flow fields show those algorithms are valid.So the application foundation of moire tomography has been provided in thisdissertation.