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 <i>ABCD</i> 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.
© 2002 Optical Society of America
Alain Cournoyer, Pierre Baulaigue, Jacques Bures, Lionel Bertrand, and Roland Occelli, "Mathematical Formulations for the Schlieren Detection Method Applied to the Measurement of Photodeformation," Appl. Opt. 41, 1128-1144 (2002)