Determination of thermal diffusivity distribution along the thickness of an inhomogeneous material by Mirage effect

Using two basic mathematical transforms, the analytical solutions of the temperature fields in the sample and adjacent media are obtained from the thermal diffusion equation of inhomogeneous material when the thermal conductivity is assumed to be exponentially changed along the thickness. Further functional relationship between modulation frequency and phase of transverse deflection of probe beam is obtained by photothermal denection theory. The thermal diffusivities of two surfaces of the sample are measured by Mirage technique of detecting the normal and transverse deflections of probe beam. So the distribution of thermal diffusivity along the thickness in the inhomogeneous material can be determined by normal and transverse deflections of Mirage effect. In addition to the relevant theoretical derivation given in the paper,the experimental result of thermal diffusivity distribution for diamond sample is also given.