arXiv2011
Recent publications have described a method for stand-off optical detection of explosives using resonant infra-red photothermal imaging. This technique uses tuned lasers to selectively heat small particles of explosive lying on a substrate surface. The presence of these heated particles is then detected using thermal infra-red imagery. Although the method has been experimentally demonstrated, no adequate theoretical analysis of the laser heating and subsequent particle cooling has been developed. This paper provides the analytical description of these processes that is necessary to understand and optimize the operational parameters of the explosive detection system. The differential equations for particle and substrate temperatures are derived and solved in the Laplace transform domain. The results are used to describe unexplained cooling phenomena measured during the experiments. A limiting particle temperature is derived as a function of experimental parameters. The effects of radiative and natural convection cooling of the particle and of non-uniform particle temperature are examined and found to be negligible. Calculations using the analytical model are compared with experimental measurements. An analysis of thermal contact heating of the substrate is included in the appendix.