Reflection-Mirage Measurements of Thermal Diffusivity

Abstract

The experimental technique for the measurement of thermal diffusivity using the mirage effect, or optical probe beam detection of thermal waves in opaque solids has been described elsewhere. [1–3] This is carried out by scanning the probe beam relative to the heating beam with a constant height, h. The separation, x0, of the two points on either side of the center of such a scan where the phase of the transverse deflection signal reaches ninety decrees effectively measures the thermal wavelength, λ = 2(πα /f)^1/2 in the solid. The determination of the thermal diffusivity, a, is accomplished by plotting this separation versus the inverse square root of the frequency. It has been shown theoretically [4,5] that the ratios of the slopes of such plots correspond, in the low frequency limit, to the ratios of the actual diffusivities of the solid. The numerical constant which relates the thermal diffusivity to the slope depends on the value of h. The previous measurements [1–3] of α, carried out using the “skimming” optical probe beam technique (see Fig. 1), were found to be in reasonable agreement with nominal values calculated from handbook data, provided that the slopes of the plots were set equal (heuristically) to (1.0 πα)^1/2. Careful examination of the theory [5], however, shows that when h is negligibly small compared to the other characteristics lengths in the experiment, the slope should be (1.4 πα )^1/2.