Tomographic Reconstruction of Unsteady Fields Using Proper Orthogonal Decomposition

An algorithm for the reconstruction of unsteady three dimensional concentration field from path-integrated data has been discussed. We propose the use of Proper Orthogonal Decomposition (Karhunen Loe´ve Expansion) to completely decouple the spatial and temporal components of the image sequence (projections) obtained from a typical experiment enabling the analysis of an asynchoronous time-dependent data set. We apply the algorithm to experimental data from a Laser Interferometric study of convection in a cylindrical annulus to capture transients that are invariably faster than the camera speed. The strength of the technique is demonstrated in the reconstruction of the flow field (related to concentration gradients) from model (simulated) Schlieren projections. Tomographic reconstruction based on Convolution Back Projection (CBP) has been coupled with Proper Orthogonal Decomposition to enable the reconstruction of unsteady concentration gradient field from asynchronous projections.