Lambertian reflectance is the property that defines an ideal "matte" or diffusely reflecting surface. The apparent brightness of a Lambertian surface to an observer is the same regardless of the observer's angle of view. More technically, the surface's luminance is isotropic, and the luminous intensity obeys Lambert's cosine law. Lambertian reflectance is named after Johann Heinrich Lambert, who introduced the concept of perfect diffusion in his 1760 book Photometria.
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Examples
Unfinished wood exhibits roughly Lambertian reflectance, but wood finished with a glossy coat of polyurethane does not, since the glossy coating creates specular highlights. Not all rough surfaces are Lambertian reflectors, but this is often a good approximation when the characteristics of the surface are unknown.
Spectralon is a material which is designed to exhibit an almost perfect Lambertian reflectance.
Use in computer graphics
In computer graphics, Lambertian reflection is often used as a model for diffuse reflection. This technique causes all closed polygons (such as a triangle within a 3D mesh) to reflect light equally in all directions when rendered. In effect, a point rotated around its normal vector will not change the way it reflects light. However, the point will change the way it reflects light if it is tilted away from its initial normal vector since the area is illuminated by a smaller fraction of the incident radiation. The reflection is calculated by taking the dot product of the surface's normal vector,
where
where
Lambertian reflection from polished surfaces are typically accompanied by specular reflection (gloss), where the surface luminance is highest when the observer is situated at the perfect reflection direction (i.e. where the direction of the reflected light is a reflection of the direction of the incident light in the surface), and falls off sharply. This is simulated in computer graphics with various specular reflection models such as Phong, Cook-Torrance. etc.
Other waves
While Lambertian reflectance usually refers to the reflection of light by an object, it can be used to refer to the reflection of any wave. For example, in ultrasound imaging, "rough" tissues are said to exhibit Lambertian reflectance.