Vapor concentration measurement with photothermal deflectometry

Theoretical and experimental results for using the photothermal deflection technique to measure vapor species concentration, while minimizing the disturbance of the transport (material) parameters due to vapor heating, are developed and described. In contrast to common practice, the above constraints require using a pump-beam duty cycle of less than 50 percent. The theoretical description of the shortened heating time is based on a step-function formulation of the pumping cycle. The results are obtained as closed-form solutions of the energy equation for many chopping cycles until steady state is reached, by use of a Green's-function method. The Euler formulation of the Fermat principle is used to calculate the deflection angle. The equations are expanded to include the effects of vapor velocity on both the temperature and temperature gradient profiles. The effects of finite (unfocused) pump and probe beams and thermal (Soret) diffusion are also accounted for. Excellent agreement between theory and experiment is obtained.