Article Preview
Top1. Background
Reflectance functions are used to describe the transport of light from the illumination direction to the viewing direction. Ideally, a reflectance function is a model of how a particular surface should look under all possible lighting conditions and all viewing angles. The BRDF (Nicodemus et al., 1977) is important for rendering realistic computer graphics imagery, as it serves as a predictive model of the appearance of materials. The model aims to predict the scattering of electromagnetic energy based on the composition of the material. An idealized model would encompass all the qualities necessary to describe shiny metals, rough dielectrics, and soft, translucent materials in high fidelity, subjectively appearing photo-realistic to the viewer. Analytically derived models are based on approximations and assumptions. Initially, the models were relatively simple functions with a small number of parameters describing the light transport to reduce the impact of computation resources. These reflectance models, therefore, are evaluated in terms of the efficiency and accuracy of the model’s prediction. Contemporary graphics are more demanding, and data driven approaches have been increasingly relied upon, evaluating how well an analytical model compares to real world data. However, capturing data is a lengthy procedure to document multiple dimensions of a reflectance function, and no agreed standards exist for data acquisition. Many unique designs have been purposely built and tested using novel techniques that aim to capture the data in the most efficient manner, whilst retaining high density.
This paper reviews the state of the art in reflectance capture and presents to the reader different categories of devices demonstrating their strengths and weaknesses. The methodology of fitting the data to analytical reflectance functions is also explored. Studies used in the development of commercial renderers are discussed, and a selection of contemporary fitting metrics are introduced.
To describe the complete interaction of the surface with electromagnetic energy, a significantly complex and higher dimension function is required, but it is impractical to measure or render. As many as 14 dimensions of the scattering function, 
, must be considered. These are the position x, y, and z, angles θ, and ϕ, wavelength λ, time t, a distribution of light reaching a surface and the position, angle, wavelength, and time of the same distribution leaving the surface. Further dimensions are also possible including the polarized state, and temperature, esp. with regards to infrared frequencies.
Some subsets of the scattering function apply to specific types of surfaces, such as the 6 dimensional spatially varying bidirectional reflectance distribution function, 
, for measuring reflectance of a non-uniform surface profile, i.e. a surface which exhibits irregularities. In practice, this is often a planar area measurement of an area xy for the incoming irradiance and outgoing reflectance direction, which is commonly referred to as the Bidirectional Texture Function (BTF). (Dana et al., 1999) A typical example is textiles that have an arrangement of fibers in some regular pattern.
Subsurface scattering is particularly useful for characterizing surfaces, such as skin or wax, that have a softened appearance. The 8D bidirectional sub-surface scattering reflectance distribution function, 
, may be used for measuring such surfaces where light entering at one point scatters under the surface, and then exits the again at a macro scale distance. (Weyrich et al., 2009) In many practical applications, however, the BRDF, a 4D function that considers the reflectance of a uniform surface, is considered a sufficient approximation. The BRDF formulation, first described by Nicodemus (1977), is a reflectance function fr, as shown in Equation 1, of the incoming irradiance incident at a single point on the surface and the outgoing radiance from the point leaving the surface in the viewing direction, shown in Figure 1-1. This can be used to characterise many common dielectrics such as plastic, ceramic or paper, and most homogeneous metallic surfaces.