Common tools for quantitative time-resolved pulse and step-heating thermography - part I: theoretical basis

Several advanced pre- and post-processing tools have been developed over the last two decades, to enhance the performance of time-resolved pulse thermography, in terms of defect detection and characterisation. Two of the most efficient techniques are the Thermographic Signal Reconstruction, proposed in 2001, including a recent development based on the use of the polynomial coefficient images proposed in 2014, and the early detection of emerging contrast, proposed in 1994. The stake of this work is to show how these tools, commonly used for pulse-heating, can be applied to step-heating. The work was divided in two parts: the theoretical and analytic study is reported in the present article; the matching experimental results are discussed in a second, separate article.