Over the interferograms, two regions were selected, one where the fringes are close to the cold wall (marked in fig.4.31) and the other where the fringes are close to the hot wall (marked in fig 4.31). Two sets of independent calculations were performed to obtain all the fringe temperatures in the interferogram.  The estimates of fringe temperature from both regions were found to be within . The fringe temperatures then allotted was the average of the estimates. Consider the fringes marked 2, 3, 4 (region , cold wall) in figure 4.31. Fitting a function of the type

where is a vertical coordinate, one obtains

These two equations can be solved for the constants Here is the temperature change per fringe shift and is a local coordinate measured from the upper wall.

The local wall temperature gradient is simply From Equation (15), this gradient can be expressed as The gradient in the temperature field very near the wall is likely to be constant since conduction heat transfer is dominant. Hence the gradient in temperature field at the first (fringe marked 2 in fig. 4.31) is expected to be same as the first gradient at the wall in region . The gradient in temperature field at the first fringe is The wall temperature gradient is allotted as an extrapolation step, the average of the two gradients. Once the gradient at the wall is known, the fringe temperature near the cold wall can be calculated as

Since the temperature different between successive fringes is known, the subsequent fringe temperatures are found out by simply adding or subtracting the amount from the fringe temperature depending upon the sign of the temperature gradient. Since the image is a available in the form of a matrix, the above procedure for calculating the fringe temperature can be implanted at any column. The column where the near-wall fringes are dense (as in regions and ) is preferred for this purpose. Column–to-column variation in the computed fringe temperatures was found to be generally small for the interferograms recorded in the experiments.