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. The reflection decreases when the surface is tilted away from being perpendicular to the light source, however, because 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 unit normal vector, ${\displaystyle \mathbf{N}}$, and a normalized light-direction vector, ${\displaystyle \mathbf{L}}$, 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:

${\displaystyle B_D=\mathbf{L}\cdot \mathbf{N}C{I}_{\text{L}}}$,

where ${\displaystyle B_D}$ is the brightness of the diffusely reflected light, ${\displaystyle C}$ is the color and ${\displaystyle I_{\text{L}}}$ is the intensity of the incoming light. Because

${\displaystyle \mathbf{L}\cdot \mathbf{N}=|N||L|\cos \alpha =\cos \alpha }$,

where ${\displaystyle \alpha }$ is the angle between the directions of the two vectors, the brightness will be highest if the surface is perpendicular to the light vector, and lowest if the light vector intersects the surface at a grazing angle.

Lambertian reflection from polished surfaces is 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.

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.