COMPUTERIZED TOMOGRAPHY

The three-dimensional temperature field can be reconstructed from its interferomeric projections using principles of tomography. Tomography is the process of recovery of a function from a set of its line integrals evaluated along some well-defined directions. In interferometry, the source of light (the laser) and the detector (CCD camera) lie on a straight line with the test cell in between. Further a parallel beam of light is used. This configuration is called transmission tomography and the ray configuration as the parallel beam geometry [28]. Tomographic algorithms used in interferometry reconstruct two-dimensional fields from their one-dimensional projections. Reconstruction is then applied sequentially from one plane to the next until the third dimension is filled.

Tomography can be classified into: (a) transform (b) series expansion, and (c) optimization methods. Transform methods generally require a large number of projections for a meaningful answer [92]. In practice, projections can be recorded either by rotating the experimental setup or the source-detector combination. In interferometry, the latter is particularly difficult and more so with the Mach–Zehnder configuration. With the first option, It is not possible to record a large number of projections, partly owing to inconvenience and partly due to time and cost. Hence, as a rule, a large number of projections cannot be acquired with interferometry and one must look for methods that converge with just a few projections. Limited-view tomography is best accomplished using the series expansion method [29]. As limited-view tomography does not have a unique solution, the algorithms are expected to be sensitive to the initial guess of the field the start the iterations. Optimization-based  algorithms are known to be independent of initial guess, but the choice of the optimization functional plays an important role in the result obtained. Depending on the mathematical definition used, the entropy extremization route may yield good results, while the energy minimization principle may be suitable in other applications. For the algebraic techniques considered in the present study, an unbiased initial guess such as a constant profile was seen to be good enough to predict the correct temperature field. A complete random number guess can also be viewed as an unbiased initial guess. Tomography begin an inverse technique, was seen to preserve (and amplify under certain conditions) the noise in the initial data. The dominant trend in the field variable was seen to be however captured  during tomography inversion.