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2.1 Surface crack detection
The thermography method used for detecting surface cracks is based on the variations in absorption of radiation caused by cracks acting like black-bodies[6]. However, the background around the crack acts like grey-bodies. When the crack is illuminated by high intensity light, an increase in the absorbed energy was detected [6, 7]. This means that cracks are detected easily by comparing the crack absorption to the background absorption.
2.2 Radiation
The book by P. V. M. Xavier [1] mentioned that when temperature is T, from Planck Law, the spectral intensity of radiation emitted from a blackbody is obtained with the relation:
(1)
Nevertheless, the intensity of radiation from a real surface is small compare with a blackbody at the same temperature. The spectral emissivity can be calculated, for the intensity of radiation emitted by a real surface, as the emissivity multiplies by that emitted by a blackbody at the same temperature, according to:
(2)
However, real surfaces do not behave as blackbodies. For instance, the incident flux results in absorption ( ), reflection ( ) and transmission ( ). Furthermore, these absorption, reflection and transmission fractions of the incident light not only depend on the wavelength ( ), orientation ( ), temperature ( ) but also on the surface quality:
(3)
Some materials are special, for example, for perfect mirrors, and equal to zero. However, for a blackbody, all the incident flux is absorption ( ). For an opaque material, transmission can be ignored. So the incident fluxes are absorbed and reflected. Specifically, absorbance was used to define the ratio of the incident flux to the absorbed flux:
(4)
Similarly, in terms of the incident flux and reflected flux, the spectral-bidirectional reflectance ( ) can be defined as: