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# Bidirectional reflectance distribution function

The bidirectional reflectance distribution function (BRDF; ${f_r(\omega_i , \omega_o)\ }$) is a 4-dimensional function that defines how light is reflected at an opaque surface. The function takes an incoming light direction, $\omega_i\$, and outgoing direction, $\omega_o\$, both defined with respect to the surface normal $n\$, and returns the ratio of reflected radiance exiting along $\omega_o\$ to the irradiance incident on the surface from direction $\omega_i\$. Physically based BRDFs have additional restrictions, including Helmholtz reciprocity, $f_r(\omega_i , \omega_o) = f_r(\omega_o , \omega_i)\$ , and energy conservation. The BRDF has units sr-1, with steradians (sr) being a unit of solid angle.

## Applications

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.

## Models

The BRDF was first defined by Edward in mid sixties[1]. BRDFs can be measured directly from real objects using calibrated cameras and lightsources [2]; however, many phenomenological and analytic models have been proposed including the Lambertian reflectance model frequently assumed in computer graphics. Some noteworthy examples are the phenomenological Phong reflectance model, Ward's anisotropic reflectance model [3] , and the Torrance-Sparrow microfacet based reflection model [4].

## Acquisition

Traditionally, BRDF measurements were taken for a specific lighting and viewing direction at a time using gonioreflectometers. 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 [5]. 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.

• Lubin, Dan; Robert Massom (2006-02-10). Polar Remote Sensing: Volume I: Atmosphere and Oceans, 1, Springer, 756. ISBN 3540430970.
• Matt, Pharr; Greg Humphreys (2004). Physically Based Rendering, 1, Morgan Kauffmann, 1019. ISBN 012553180X.
• Schaepman-Strub, G.; M.E. Schaepman, T.H. Painter, S. Dangel, J.V. Martonchik (2006-07-15). "Reflectance quantities in optical remote sensing--definitions and case studies". Remote Sensing of Environment 103 (1): 27-42. Retrieved on 2007-10-18.

## References

1. ^ Nicodemus, Fred. "Directional reflectance and emissivity of an opaque surface". Applied Optics 4 (7): 767-775.
2. ^ S.Rusinkiewicz. A Survey of BRDF Representation for Computer Graphics. Retrieved on 2007-09-05.
3. ^ Ward, Gregory. "Measuring and Modeling Anisotropic Reflection". SIGGRAPH 1992 Proceedings 26: 265-272.
4. ^ K. Torrance and E. Sparrow. Theory for Off-Specular Reflection from Roughened Surfaces. J. Optical Soc. America, vol. 57. 1976. pp. 1105-1114.
5. ^ Ward, G. "Measuring and Modeling Anisotropic Reflection", Siggraph 1992.