# Lambertian reflectance

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Lambertian reflectance

If a surface exhibits Lambertian reflectance, light falling on it is scattered such that the apparent brightness of the surface to an observer is the same regardless of the observer's angle of view. More technically, the surface luminance is isotropic. For example, unfinished wood exhibits roughly Lambertian reflectance, but wood finished with a glossy coat of polyurethane does not (depending on the viewing angle, specular highlights may appear at different locations on the surface). Not all rough surfaces are perfect Lambertian reflectors, but this is often a good approximation when the characteristics of the surface are unknown. Lambertian reflectance is named after Johann Heinrich Lambert.

In computer graphics, Lambertian reflection is often used as a model for diffuse reflection, and is calculated by taking the dot product of the surface's normalized normal vector $mathbf\left\{N\right\}$ and a normalized vector $mathbf\left\{L\right\}$ pointing from the surface to the light source. This number is then multiplied by the color of the surface and the intensity of the light hitting the surface:

:$I_\left\{D\right\}=mathbf\left\{L\right\}cdotmathbf\left\{N\right\}*C*I_\left\{L\right\}$,

where $I_\left\{D\right\}$ is the intensity of the diffusely reflected light (surface brightness), $C$ is the color and $I_\left\{L\right\}$ is the intensity of the incoming light. Because

:$mathbf\left\{L\right\}cdotmathbf\left\{N\right\}=|N||L|cos\left\{alpha\right\}$,

where $alpha$ is the angle between the direction of the two vectors, the intensity will be the highest if the normal vector points in the same direction as the light vector ($cos\left\{\left(0\right)\right\}=1$, the surface will be perpendicular to the direction of the light), and the lowest if the normal vector is perpendicular to the light vector ($cos\left\{\left(pi/2\right)\right\}=0$, the surface runs parallel with the direction of the light).

Lambertian reflection is typically accompanied by specular reflection, where the surface luminance is highest when the observer's angle is the same as the angle of the light source. This is simulated in computer graphics with Phong shading.

Spectralon is a material which is designed to exhibit an almost perfect Lambertian reflectance, while Scotchlite is a material designed with the opposite intent of only reflecting light on one line of sight.

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.

ee also

*Lambert's cosine law
*Specular reflection
*Diffuse reflection

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