Dynamic bidirectional reflectance distribution functions: Measurement and representation

With high-energy lasers, not only the direct laser beam can pose significant eye and skin hazards, but also light reflecting off material illuminated by the beam. Proper hazard analysis for a material irradiated by a laser relies upon the reflecting properties of the material surface, as these properties determine the magnitude and direction of the reflected laser energy commonly characterized by the bidirectional reflectance distribution function (BRDF). However, a high-energy laser heating and possibly melting a material can change the reflecting properties of that material, so these changes must be included in the hazard analysis. Traditional methods for measuring the BRDFs of materials are not practical for measurement of materials with rapidly-changing surface properties. However, BRDF measurement by imagery of a witness screen allows for practical measurements of the dynamically-changing BRDFs of materials under high-energy laser irradiation. Using this technique, the dynamic BRDFs of stainless steel and copper were measured under high irradiance. The BRDF of the materials was observed to change in magnitude, width, and the specular direction. In some instances, this would result in an increase in exposure to the laser radiation for some observers over that which would be predicted using static BRDF measurements where the reflective characteristics of the material are assumed to be constant. For effective use in safety calculations, the dynamic BRDFs need to be represented in a form suitable for use in safety analysis codes. Construction of a dynamic BRDF representation is complicated by the fact that data cannot be practically obtained over the entire range of incident and reflected angles or for all points in time. Therefore, a technique is required for interpolating through regions of missing data. A BRDF representation form has been developed based on expansions in spherical harmonics in a transformed coordinate space. The efficacy of this representation is examined using experimental data on stainless steel and copper samples exposed to high-energy laser irradiation. The representation technique is found to be capable of robust predictions at all incident and reflected angles and at interpolated material states. Simplified “envelope” models based on these representations are suitable for inclusion in laser safety codes for predicting reflection hazards from high-energy lasers.