Non-linearity in photothermal radiometric imaging

Non-linear effects occurring in photothermal microscopes based on principle of photothermal radiometry are studied as a hnction of the laser power and of the modulation frequency. For stainless steel, a second harmonic component of up to 11 % of the hndamental amplitude is found. Phase shifts of up to 20 degrees are observed as a hnction of the modulation frequency. The nonlinearity is mainly due to Stefan-Boltzmann's law. The experimental results are in good agreement with a theoretical model based on the static and oscillating temperature distribution. l. INTRODUCTION Thermal wave microscopy finds new applications in various fields of industrial nondestructive testing. Fast scanning speeds and therefore high signal-to-noise ratios are often required. A common way to improve the signal-to-noise ratio is to increase the laser power applied. When detecting infrared radiation from a periodically heated spot on a surface, Stefan-Boltzmann's law leads to an inherent nonlinearity of the detection, which is normally neglected by assuming small temperature changes. For higher laser powers, this is no longer possible (l), in particular for highly focused photothermal microscopes, where the radial distribution of the local static temperature can have significant effects on the detected photothermal signals. 2. THEORETICAL MODEL A modulated heating beam with a radius r, is assumed to fall onto a half-space with surface absorption and a thermal diffusion length ps (Fig. 1). The heated spot is observed by an infrared detector with a gaussian sensitivity profile with radius r, and with constant sensitivity in the wavelength range h,, to h,,,,,. For the material under study, a possible temperature and wavelength dependence of the surface emissivity will be ignored. Then the harmonic part of the detector signal is proportional to: Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1994714 JOURNAL DE PHYSIQUE IV