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| {{See also|Lambert's cosine law}}
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| {{one source|date=June 2012}}
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| '''Lambertian reflectance''' is the property that defines an ideal [[Diffuse reflection|diffusely reflecting]] surface. The apparent brightness of such a 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==
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| Unfinished wood exhibits roughly Lambertian reflectance, but wood finished with a glossy coat of [[polyurethane]] does not, since the glossy coating creates [[specular highlight]]s. Not all rough surfaces are Lambertian reflectors, but this is often a good approximation when the characteristics of the surface are unknown.
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| [[Spectralon]] is a material which is designed to exhibit an almost perfect Lambertian reflectance.
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| ==Use in computer graphics==
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| 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.<ref>{{cite book| last = Angel| first = Edward| title = Interactive Computer Graphics: A Top-Down Approach Using OpenGL| url = http://books.google.com/?id=Fsy_QgAACAAJ| edition = third| year = 2003| publisher = Addison-Wesley| isbn = 978-0-321-31252-5 }}</ref>{{Verify source|date=January 2009}} The reflection is calculated by taking the [[dot product]] of the surface's [[normal vector]], <math>\mathbf{N}</math>, and a normalized light-direction vector, <math>\mathbf{L}</math>, 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:
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| :<math>I_{D}=\mathbf{L}\cdot\mathbf{N} C I_{L}</math>,
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| where <math>I_{D}</math> is the intensity of the diffusely reflected light (surface brightness), <math>C</math> is the color and <math>I_{L}</math> is the intensity of the incoming light. Because | |
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| :<math>\mathbf{L}\cdot\mathbf{N}=|N||L|\cos{\alpha}=\cos{\alpha}</math>,
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| where <math>\alpha</math> 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 (<math>\cos{(0)}=1</math>, the surface will be perpendicular to the direction of the light), and the lowest if the normal vector is perpendicular to the light vector (<math>\cos{(\pi/2)}=0</math>, the surface runs parallel with the direction of the light).
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| Lambertian reflection from polished surfaces are typically accompanied by [[specular reflection]] ([[Gloss (material appearance)|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 highlight|specular reflection models]] such as [[Phong reflection model|Phong]], [[Cook-Torrance]]. etc.
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| ==Other waves==
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| 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.
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| ==See also==
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| * [[List of common shading algorithms]]
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| ==References==
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| {{reflist}}
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| [[Category:Radiometry]]
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| [[Category:Photometry]]
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| [[Category:Scattering, absorption and radiative transfer (optics)]]
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| [[Category:Shading]]
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