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
In photometry, luminous intensity is a measure of the wavelength-weighted power emitted by a light source in a particular direction per unit solid angle, based on the luminosity function, a standardized model of the sensitivity of the human e ...
obeys
Lambert's cosine law
In optics, Lambert's cosine law says that the radiant intensity or luminous intensity observed from an ideal diffusely reflecting surface or ideal diffuse radiator is directly proportional to the cosine of the angle ''θ'' between the directi ...
. Lambertian reflectance is named after
Johann Heinrich Lambert
Johann Heinrich Lambert (, ''Jean-Henri Lambert'' in French; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Swiss or French, who made important contributions to the subject ...
, who introduced the concept of perfect diffusion in his 1760 book ''
Photometria
''Photometria'' is a book on the measurement of light by Johann Heinrich Lambert published in 1760.Lambert, Johann Heinrich, Photometria, sive de mensura et gradibus luminis, colorum et umbrae', Augsburg: Eberhard Klett, 1760. It established a com ...
''.
Examples
Unfinished wood exhibits roughly Lambertian reflectance, but wood finished with a glossy coat of
polyurethane
Polyurethane (; often abbreviated PUR and PU) refers to a class of polymers composed of organic units joined by carbamate (urethane) links. In contrast to other common polymers such as polyethylene and polystyrene, polyurethane is produced from ...
does not, since the glossy coating creates
specular highlight
A specular highlight is the bright spot of light that appears on shiny objects when illuminated (for example, see image on right). Specular highlights are important in 3D computer graphics, as they provide a strong visual cue for the shape of a ...
s. Though not all rough surfaces are Lambertian, this is often a good approximation, and is frequently used when the characteristics of the surface are unknown.
Spectralon
Spectralon is a fluoropolymer that has the highest diffuse reflectance of any known material or coating over the ultraviolet, visible, and near-infrared regions of the spectrum. It exhibits highly Lambertian behavior, and can be machined into a ...
is a material which is designed to exhibit an almost perfect Lambertian reflectance.
Use in computer graphics
In
computer graphics
Computer graphics deals with generating images with the aid of computers. Today, computer graphics is a core technology in digital photography, film, video games, cell phone and computer displays, and many specialized applications. A great de ...
, Lambertian reflection is often used as a model for
diffuse reflection
Diffuse reflection is the reflection of light or other waves or particles from a surface such that a ray incident on the surface is scattered at many angles rather than at just one angle as in the case of specular reflection. An ''ideal'' di ...
. 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 small flat region rotated around its
normal vector will not change the way it reflects light. However, the region will change the way it reflects light if it is tilted away from its initial normal vector because the area is illuminated by a smaller fraction of the incident radiation.
The reflection is calculated by taking the
dot product
In mathematics, the dot product or scalar productThe term ''scalar product'' means literally "product with a scalar as a result". It is also used sometimes for other symmetric bilinear forms, for example in a pseudo-Euclidean space. is an alge ...
of the surface's unit
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:
![Oswietlenie lamberta](https://upload.wikimedia.org/wikipedia/commons/c/ca/Oswietlenie_lamberta.svg)
:
,
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 directions 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 from polished surfaces are typically accompanied by
specular reflection
Specular reflection, or regular reflection, is the mirror-like reflection of waves, such as light, from a surface.
The law of reflection states that a reflected ray of light emerges from the reflecting surface at the same angle to the surf ...
(
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
Medical ultrasound includes diagnostic techniques (mainly imaging techniques) using ultrasound, as well as therapeutic applications of ultrasound. In diagnosis, it is used to create an image of internal body structures such as tendons, muscl ...
, "rough" tissues are said to exhibit Lambertian reflectance.
See also
*
List of common shading algorithms {{Short description, none
This article lists common shading algorithms used in computer graphics.
Interpolation techniques
These techniques can be combined with any illumination model:
* Flat shading
* Gouraud shading
* Phong shading
Illuminatio ...
*
Gamma correction
Gamma correction or gamma is a nonlinear operation used to encode and decode luminance or tristimulus values in video or still image systems. Gamma correction is, in the simplest cases, defined by the following power-law expression:
: V_\tex ...
References
{{reflist
Radiometry
Photometry
Scattering, absorption and radiative transfer (optics)
Shading