Analyzing probability of detection as a function of defect size and depth in pulsed IR thermography

Abstract

This study introduces a novel approach to the presentation of the probability of detection (POD) function in infrared (IR) thermographic nondestructive testing. The modified POD is suggested as a function of two defect parameters, namely, defect depth and lateral size. The proposed approach is based on calculating theoretical values of maximum temperature contrast for many defect size/depth combinations by using an appropriate analytical model. Furthermore, these values are used for the quantification of defects to produce predicted POD curves by applying a signal/response method. The results appear as the POD maps illustrating detectability of defects with various size/depth combinations. By setting a particular POD threshold, for example, 90%, the detectability limit contours can be obtained. These contours illustrate the limiting combinations of the depth and diameter of the defects, which can be detected with a required probability of correct detection under a particular temperature signal threshold. The proposed methodology is illustrated with an example of using the POD approach in pulsed IR thermographic inspection of a 3D printed specimen with artificial sphere-like defects. Such an approach allows predicting the detectability of defects in a vast range of depth/size ratios by using an analytical model and a limited number of experiments.