Todd V. Small

Date of Award


Document Type


Degree Name

Doctor of Philosophy (PhD)


Department of Engineering Physics

First Advisor

Samuel D. Butler, PhD


The bi-directional reflectance distribution function (BRDF) describes the directional (spatial) nature of light’s reflectance from a material surface. When incident light of a particular wavelength strikes a material surface from a particular direction, portions of that incident light will be reflected into various directions in various amounts, depending on the material’s surface characteristics. Historically, the vast majority of BRDF measurement and modeling research has focused on reflection within the plane-of incidence (in-plane) and dealt primarily with simplified isotropic BRDFs. Remote sensing applications, such as satellite light curve analysis, typically rely on closed-form microfacet models for efficiency. There are many factors, but disagreements still manifest between observations and simulations. This work is motivated by the hypothesis that measuring and modeling reflection outside the plane-of-incidence (out-of-plane) may improve simulation accuracy. A new system is designed and constructed to successfully measure out-of-plane material BRDFs near the specular peak with high angular resolution. The system is then used to measure several materials, including a commercially available small satellite solar cell, using a 632.8 nm wavelength laser source. The measurements identify several unmodeled out-of-plane BRDF components, including significant diffraction behavior. Finally, the measurements are used to inform the creation of a new closed-form BRDF model for the solar cell which more accurately replicates the material’s measured out-of-plane reflection. Ultimately, it is expected that out-of-plane BRDF modeling leads to improvements in light curve analysis and other remote sensing applications.

AFIT Designator


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Optics Commons