
Mathematically, the principals of CTT can be thought of as separating the thermal distribution from the emissivity variables. If we normalize the gradient image I_{x}(x,y) by the reflection corrected image I(x,y)
we separate the influences of thermal distributions and emissivity gradients into two terms. If two sets of images are collected, one corresponding to heat from the left and the other corresponding to heat from the right, and processed in this manner
the difference of these images Q(x,y) eliminates emissivity as a variable.
If the gradient is flowing from opposite directions then the second term will augment the first. In order to ensure this augmentation and hence detection of the flaw, the denominator must not be allowed to switch sign.