Mathematical formulations for the schlieren detection method applied to the measurement of photodeformation

In a schlieren detection scheme for photodeformation measurements, the divergence of the probe beam that is induced by the axisymmetric but radially inhomogeneous periodic photothermal displacement of the surface of a sample is transformed into an intensity variation by insertion of an iris in front of the detection photodiode. We present three expressions for the intensity profile of a Gaussian laser beam that is reflected by the inhomogeneous photodeformation of a solid. The first expression proceeds from geometrical optics (or photometry), whereas the second one derives from the use of the well-known ABCD law and the third one from diffraction principles. Comparing these formulations of the schlieren signal with their behavior as a function of different geometrical parameters, we obtain the domain of validity of each expression, and we deduce the advantages of the different formalisms.