With the development of the laser the problem of the interaction of a polarized beam of monochromatic radiation with a scattering material has gained considerable importance in the heat transfer community. Lasers are now used as diagnostic tools to probe hot combustion gases as well as the atmosphere, and to measure the radiative properties of packed- beds, thermal insulations, ceramics, and human tissue. Laser- based micromachining systems abound in the microelectronics industry and hold great potential in the fabrication of micromechanical structures. The medical applications of lasers range from treating heart disease and cancer to dentistry and eye surgery. The use of laser beams as "tweezers" to seize and manipulate bits of living cells is being considered as a way to improve gene-mapping methods. Most of these applications must be classified as multidimensional because of the finite size of the laser beam which is linearly polarized, and they often involve multiple and anisotropic scattering. A definite need exists to develop a theoretical model for radiative transfer that can incorporate all these factors and to develop guidelines and approximate procedures for handling polarization effects. This project is a theoretical and experimental study of three- dimensional radiative heat transfer including polarization and multiple scattering. Specifically, the effects of multiple scattering on a laser beam of known polarization (linear, circular, or elliptical) are under investigation. The laser beam is incident perpendicular to the top, flat surface of a cylindrical scattering medium. The scattering centers are homogeneous spherical particles which are randomly distributed within the medium. A theoretical model is being developed based on the three-dimensional vector transport equation for the Stokes parameters. The usual scattering phase function will be replaced by a 4x4 phase matrix. The transport equation will be reduced to a one-dimensional form using the double Fourier transform method, and the resulting equation will be solved by Ambartsumian's method. The back-scattered radiation will then be calculated using a double inverse Fourier transform. The theoretical analysis will be first carried out for small spherical particles, i.e., Rayleigh scattering. A series of carefully controlled experiments will be conducted with latex microspheres suspended in pure water to validate the theoretical model. The concentration of the microspheres will be varied so that the optical thickness of the scattering medium will range from thin to thick. The results of this research will provide insight into a number of practical problems involving the interaction of a polarized laser beam with a scattering medium. The development of a more realistic radiation model should have a significant impact in many fields where lasers are utilized including heat transfer, manufacturing, and medicine.
