Bidirectional reflectance distribution function
The bidirectional reflectance distribution function (BRDF), symbol
, is a function of four real variables that defines how light from a source is reflected off an opaque surface.
The function takes an incoming light direction,
lies along the z-axis), and returns the ratio of reflected radiance exiting along
is irradiance, or power per unit surface area, and
The Bidirectional Texture Function (BTF) is appropriate for modeling non-flat surfaces, and has the same parameterization as the SVBRDF; however in contrast, the BTF includes non-local scattering effects like shadowing, masking, interreflections or subsurface scattering.
The functions defined by the BTF at each point on the surface are thus called Apparent BRDFs.
in which light entering the surface may scatter internally and exit at another location.
In reality, the BRDF is wavelength dependent, and to account for effects such as iridescence or luminescence the dependence on wavelength must be made explicit:
Note that in the typical case where all optical elements are linear, the function will obey
Physically realistic BRDFs for reciprocal linear optics have additional properties,[2] including, The BRDF is a fundamental radiometric concept, and accordingly is used in computer graphics for photorealistic rendering of synthetic scenes (see the rendering equation), as well as in computer vision for many inverse problems such as object recognition.
BRDF has also been used for modeling light trapping in solar cells (e.g. using the OPTOS formalism) or low concentration solar photovoltaic systems.
[3][4] In the context of satellite remote sensing, NASA uses a BRDF model to characterise surface reflectance anisotropy.
For a given land area, the BRDF is established based on selected multiangular observations of surface reflectance.
While single observations depend on view geometry and solar angle, the MODIS BRDF/Albedo product describes intrinsic surface properties in several spectral bands, at a resolution of 500 meters.
[5] The BRDF/Albedo product can be used to model surface albedo depending on atmospheric scattering.
BRDFs can be measured directly from real objects using calibrated cameras and lightsources;[6] however, many phenomenological and analytic models have been proposed including the Lambertian reflectance model frequently assumed in computer graphics.
Some useful features of recent models include: W. Matusik et al. found that interpolating between measured samples produced realistic results and was easy to understand.
[7] Traditionally, BRDF measurement devices called gonioreflectometers employ one or more goniometric arms to position a light source and a detector at various directions from a flat sample of the material to be measured.
To measure a full BRDF, this process must be repeated many times, moving the light source each time to measure a different incidence angle.
[25] Unfortunately, using such a device to densely measure the BRDF is very time-consuming.
One of the first improvements on these techniques used a half-silvered mirror and a digital camera to take many BRDF samples of a planar target at once.
Since this work, many researchers have developed other devices for efficiently acquiring BRDFs from real world samples, and it remains an active area of research.
There is an alternative way to measure BRDF based on HDR images.
The first is that the dynamic range is limited by the camera being used; this can be as low as 8 bits for older image sensors or as high as 32 bits for the newer automotive image sensors.
The other disadvantage is that for BRDF measurements the beam must pass from an external light source, bounce off a pellicle and pass in reverse through the first few elements of the conoscope before being scattered by the sample.
Each of these elements is antireflection-coated, but roughly 0.3% of the light is reflected at each air-glass interface.
These reflections will show up in the image as a spurious signal.
BRDF fabrication refers to the process of implementing a surface based on the measured or synthesized information of a target BRDF.
There exist three ways to perform such a task, but in general, it can be summarized as the following steps: Many approaches have been proposed for manufacturing the BRDF of the target :
