Construction and utilization of probabilistic dynamic bidirectional reflectance distribution functions

Reflections of high energy lasers from surfaces can present hazards to persons and instruments at significant distances. Heating from these lasers causes changes in the reflection characteristics of surfaces they illuminate. As such, reflections from these surfaces cannot be properly modeled with static bidirectional reflectance distribution functions (BRDFs), but require time- dynamic BRDFs. Moreover, the time-evolution of the surface reflections is not deterministic, but can vary even when the materials and illumination conditions are nearly identical, such that only probabilistic characterization is realistic. Due to the swiftly changing nature of the reflections, traditional BRDF measurements with goniometric instruments are impossible, so BRDFs must be deduced from images of the reflected light incident on a screen intercepting a portion of the reflection solid angle. A new BRDF model describes these complex probabilistic dynamic BRDFs with only four intuitive parameters for a given laser wavelength, irradiance, and duration, where these parameters have central values and statistical variances over discrete regimes corresponding to surface conditions. An automated procedure determines appropriate parameter values and variances from captured screen images, requiring only a single angle of laser incidence. Parameters from sample tests illustrate the model.