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

Luminance

Luminance is a Photometry measure of the luminous intensity per unit area of light travelling in a given direction. It describes the amount of light that passes through or is emitted from a particular area, and falls within a given solid angle....
is isotropic. For example, unfinished wood exhibits roughly Lambertian reflectance, but wood finished with a glossy coat of polyurethane

Polyurethane

A polyurethane, commonly abbreviated PU, is any polymer consisting of a chain of organic chemistry units joined by carbamate links. Polyurethane polymers are formed by reacting a monomer containing at least two isocyanate functional groups with another monomer containing at least two alcohol groups in the presence of a catalyst....
does not (depending on the viewing angle, specular highlight

Specular highlight

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Encyclopedia

Luminance

Polyurethane

Specular highlight

A specular highlight is the bright spot of light that appears on shiny objects when illuminated . Specular highlights are important in 3D computer graphics, as they provide a strong visual cue for the shape of an object and its location with respect to light sources in the scene....
s 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

Johann Heinrich Lambert

Johann Heinrich Lambert , was a Switzerland mathematician, physicist and astronomer.He was born in M?lhausen . His father was a poor tailor, so Johann had to struggle to gain an education....
.

In computer graphics

Computer graphics

Computer graphics are graphics created by computers and, more generally, the representation and manipulation of pictorial data by a computer....
, Lambertian reflection is often used as a model for diffuse reflection

Diffuse reflection

Diffuse reflection is the reflection of light from an uneven or granular surface such that an incident ray is seemingly reflected at a number of angles....
. This technique causes all closed polygons (such as a triangle within a 3D mesh) to reflect light equally in all directions when rendered. The effect this has from the viewer's perspective is that rotating or scaling the object does not change the apparent brightness of its surface. The reflection is calculated by taking the dot product

Dot product

In mathematics, the dot product, also known as the scalar product, is an operation which takes two vector over the real numbers R and returns a real-valued scalar quantity....
of the surface's normalized normal vector, , and a normalized light-direction vector, , 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:

,

where is the intensity of the diffusely reflected light (surface brightness), is the color and is the intensity of the incoming light. Because

,

where 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 (the surface will be perpendicular to the direction of the light), and the lowest if the normal vector is perpendicular to the light vector (the surface runs parallel with the direction of the light).

Lambertian reflection is typically accompanied by specular reflection

Specular reflection

Specular reflection is the perfect, mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected into a single outgoing direction....
, where the surface luminance is highest when the observer is situated at the perfect reflection direction, and falls off sharply. This is simulated in computer graphics with various specular reflection models

Specular highlight

Phong shading

Phong shading refers to a set of techniques in 3D computer graphics. Phong shading includes a model for the reflection of light from surfaces and a compatible method of estimating pixel colors by interpolation surface normals across rasterized polygons....
, Cook-Torrance. etc.

Spectralon is a material which is designed to exhibit an almost perfect Lambertian reflectance, while Scotchlite

Scotchlite

Scotchlite is a material made by the 3M company that is made of millions of glass beads affixed to the surface. Each glass bead is covered with a metallic reflective layer on half of its surface and this, combined with the spherical nature of the glass beads gives the materials their reflective properties....
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.

Lambertian reflectance

Other waves

See also