An optical technique to identify the presence of chemical coatings over rough surfaces is described. It is based on the selective use of elements of the 4 x 4 Mueller matrix. The full-wave theory of electromagnetic scattering is used to predict six independent Mueller elements from randomly rough uncoated (dry) and coated (wet) surface materials as functions of the media complex dielectric coefficients, backscattering angle, and midinfrared wavelengths of laser-beam excitations that are polarization modulated. The set of independent elements at beam wavelengths and backscattering angles [M(mn) (lambda(i), lambda(i))] most sensitive to i optically thick contaminant coatings are statistically obtained from the full-wave database, and detection-parameter sets [lambda(i), lambda(i)] are inputs to another algorithm designed to identify the contaminant coating (when present and interacted by the irradiating beams). These algorithms facilitate the operation of a multi-CO(2) laser-ellipsometer facility now under development at the U.S. Army Chemical Research, Development, and Engineering Center for the remote detection of chemical or biological surface contaminants.