Method and apparatus for determining the thermal expansion of a material

Abstract

A focus error signal resulting from the photothermically-induced expansion is measured in a sample of material under analysis. A laser is disposed as a periodically modulated heating source which is directed to the sample and a device for focus error measuring which is directed to the surface being heated. A device measuring focus error generates a signal representative of the displacement of the surface of material in perpendicular direction due to the expansion produced by the periodic heating, which is filtered, either analogically or digitally, to discriminate the displacement component at the frequency in which it was modulated or at any other related frequency, such any harmonic or a sum with any other modulation. The focus error signal, appropriately calibrated, gives a precise and sensitive measure of the magnitude the expansion. Said magnitude and its dependence with the modulation frequency allows the determination of physical properties such as the thermal expansion or thermal diffusivity coefficient, the thickness of a coating film or the absorption coefficient of the light from the heating beam. By varying the wave length of the directed radiation it is possible to determine the absorption spectrum of the sample even for very small sized particles in which the fraction of absorbed energy is very little.