The correctness of fringe thinning, assigning fringe temperatures, and a check on the magnitude of interpolation errors have been examined by using the following result:  At steady state, the width-average of the line integrals of temperature field plotted as a function of the vertical coordinate is independent of the projection angle. This is because the total energy transferred across the cavity is unchanged from one horizontal plane to the next. Figure 4.35 shown the variation of line integrals of the temperature field averaged over a horizontal plane as a function of the vertical coordinate. The line integrals are simply the temperature as conputed from the interferograms.

Figure 4.33: Collection of thinned images.

The coordinate is measured from the cold top wall. Both zero and 90 degree projections have been shown and the Rayleigh number based on the temperature different across the across the fluid layer is 13900. The corresponding graph for is shown in Figure 4.36. The S-shaped curve, characteristic of buoyancy–driven convection can be seen in all the figures. The curve for the two projections match closely and their slopes at the hot and cold walls are practically equal. Temperature in the zero and 90 degree data have been subsequently corrected to ensure that between the two projections, the S-shaped curve is strictly unique. This step does not alter the isotherms in the projection data to any significant degree, but is expected to improve the convergence of the tomographic  inversion process.                

Figure 4.34: Isotherms obtained from the interpolated data