Response of interferometer based probe systems to photodisplacement in layered media

This paper presents a detailed theory which describes the response of a focused interferometer when a modulated laser source is incident upon a layered sample. In order to solve this problem it is necessary to solve the thermoelastic equations for a layered sample. The paper presents an analytical solution obtained using a symbolic manipulation program (reduce). In particular, we point out that the analytical form of the solution is necessary to achieve numerically stable results. In addition to calculating the actual displacement of the sample surface, the response of the instrument is considered in detail, in terms of the refractive index changes of the air above the sample and the optical transfer function of the probe optics.