Diffuse reflection
Overview

Diffuse reflection is the reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

from a surface such that an incident ray
Ray (optics)
In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

is reflected at many angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

s rather than at just one angle as in the case of specular reflection
Specular reflection
Specular reflection is the mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected into a single outgoing direction...

. An illuminated ideal diffuse reflecting surface will have equal luminance
Luminance
Luminance is a photometric 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. The SI unit for luminance is candela per square...

from all directions in the hemisphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

surrounding the surface (Lambertian reflectance
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...

).

A surface built from a non-absorbing powder such as plaster
Plaster
Plaster is a building material used for coating walls and ceilings. Plaster starts as a dry powder similar to mortar or cement and like those materials it is mixed with water to form a paste which liberates heat and then hardens. Unlike mortar and cement, plaster remains quite soft after setting,...

, or from fibers such as paper, or from a polycrystalline
Polycrystalline
Polycrystalline materials are solids that are composed of many crystallites of varying size and orientation. The variation in direction can be random or directed, possibly due to growth and processing conditions. Fiber texture is an example of the latter.Almost all common metals, and many ceramics...

material such as white marble
Marble
Marble is a metamorphic rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite.Geologists use the term "marble" to refer to metamorphosed limestone; however stonemasons use the term more broadly to encompass unmetamorphosed limestone.Marble is commonly used for...

, reflects light diffusely with great efficiency.
Encyclopedia
Diffuse reflection is the reflection
Reflection (physics)
Reflection is the change in direction of a wavefront at an interface between two differentmedia so that the wavefront returns into the medium from which it originated. Common examples include the reflection of light, sound and water waves...

of light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

from a surface such that an incident ray
Ray (optics)
In optics, a ray is an idealized narrow beam of light. Rays are used to model the propagation of light through an optical system, by dividing the real light field up into discrete rays that can be computationally propagated through the system by the techniques of ray tracing. This allows even very...

is reflected at many angle
Angle
In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

s rather than at just one angle as in the case of specular reflection
Specular reflection
Specular reflection is the mirror-like reflection of light from a surface, in which light from a single incoming direction is reflected into a single outgoing direction...

. An illuminated ideal diffuse reflecting surface will have equal luminance
Luminance
Luminance is a photometric 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. The SI unit for luminance is candela per square...

from all directions in the hemisphere
Sphere
A sphere is a perfectly round geometrical object in three-dimensional space, such as the shape of a round ball. Like a circle in two dimensions, a perfect sphere is completely symmetrical around its center, with all points on the surface lying the same distance r from the center point...

surrounding the surface (Lambertian reflectance
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...

).

A surface built from a non-absorbing powder such as plaster
Plaster
Plaster is a building material used for coating walls and ceilings. Plaster starts as a dry powder similar to mortar or cement and like those materials it is mixed with water to form a paste which liberates heat and then hardens. Unlike mortar and cement, plaster remains quite soft after setting,...

, or from fibers such as paper, or from a polycrystalline
Polycrystalline
Polycrystalline materials are solids that are composed of many crystallites of varying size and orientation. The variation in direction can be random or directed, possibly due to growth and processing conditions. Fiber texture is an example of the latter.Almost all common metals, and many ceramics...

material such as white marble
Marble
Marble is a metamorphic rock composed of recrystallized carbonate minerals, most commonly calcite or dolomite.Geologists use the term "marble" to refer to metamorphosed limestone; however stonemasons use the term more broadly to encompass unmetamorphosed limestone.Marble is commonly used for...

, reflects light diffusely with great efficiency. Many common materials exhibit a mixture of specular and diffuse reflection.

The visibility of objects is primarily caused by diffuse reflection of light: it is diffusely-scattered light that forms the image of the object in the observer's eye.

## Mechanism

Diffuse reflection from solids is generally not due to surface roughness. A flat surface is indeed required to give specular reflection, but it does not prevent diffuse reflection. A piece of highly polished white marble remains white; no amount of polishing will turn it into a mirror. Polishing produces some specular reflection, but the remaining light continues to be diffusely reflected.

The most general mechanism by which a surface gives diffuse reflection does not involve exactly the surface: most of the light is contributed by scattering centers beneath the surface, as illustrated in Figure 1 at right.
If one were to imagine that the figure represents snow, and that the polygons are its (transparent) ice crystallites, an impinging ray is partially reflected (a few percent) by the first particle, enters in it, is again reflected by the interface with the second particle, enters in it, impinges on the third, and so on, generating a series of "primary" scattered rays in random directions, which, in turn, through the same mechanism, generate a large number of "secondary" scattered rays, which generate "tertiary" rays.... All these rays walk through the snow crystallytes, which do not absorb light, until they arrive at the surface and exit in random directions. The result is that all the light that was sent out is returned in all directions, so that snow is seen to be white, in spite of the fact that it is made of transparent objects (ice crystals).

For simplicity, "reflections" are spoken of here, but more generally the interface between the small particles that constitute many materials is irregular on a scale comparable with light wavelength, so diffuse light is generated at each interface, rather than a single reflected ray, but the story can be told the same way.

This mechanism is very general, because almost all common materials are made of "small things" held together. Mineral materials are generally polycrystalline
Polycrystalline
Polycrystalline materials are solids that are composed of many crystallites of varying size and orientation. The variation in direction can be random or directed, possibly due to growth and processing conditions. Fiber texture is an example of the latter.Almost all common metals, and many ceramics...

: one can describe them as made of a 3-D mosaic of small, irregularly shaped defective crystals. Organic materials are usually composed of fibers or cells, with their membranes and their complex internal structure. And each interface, inhomogeneity or imperfection can deviate, reflect or scatter light, reproducing the above mechanism.

Few materials don't follow it: among them metals, which do not allow light to enter; gases, liquids; glass and transparent plastics (which have a liquid-like amorphous microscopic structure); single crystals, such as some gems or a salt crystal; and some very special materials, such as the tissues which make the cornea
Cornea
The cornea is the transparent front part of the eye that covers the iris, pupil, and anterior chamber. Together with the lens, the cornea refracts light, with the cornea accounting for approximately two-thirds of the eye's total optical power. In humans, the refractive power of the cornea is...

and the lens
Lens (anatomy)
The crystalline lens is a transparent, biconvex structure in the eye that, along with the cornea, helps to refract light to be focused on the retina. The lens, by changing shape, functions to change the focal distance of the eye so that it can focus on objects at various distances, thus allowing a...

of an eye. These materials can reflect diffusely, however, if their surface is microscopically rough, like in a frost glass (figure 2), or, of course, if their homogeneous structure deteriorates
Cataract
A cataract is a clouding that develops in the crystalline lens of the eye or in its envelope, varying in degree from slight to complete opacity and obstructing the passage of light...

, as in the eye lens.

A surface may also exhibit both specular and diffuse reflection, as is the case, for example, of glossy paint
Paint
Paint is any liquid, liquefiable, or mastic composition which after application to a substrate in a thin layer is converted to an opaque solid film. One may also consider the digital mimicry thereof...

s as used in home painting, which give also a fraction of specular reflection, while matte paints give almost exclusively diffuse reflection.

### Specular vs. diffuse reflection

Virtually all materials can give specular reflection, provided that their surface can be polished to eliminate irregularities comparable with light wavelength (a fraction of micrometer). A few materials, like liquids and glasses, lack the internal subdivisions which give the subsurface scattering mechanism described above, so they can be clear and give only specular reflection (not great, however), while, among common materials, only polished metals can reflect light specularly with great efficiency (the reflecting material of mirrors usually is aluminum or silver). All other common materials, even when perfectly polished, usually give not more than a few percent specular reflection, except in particular cases, such as grazing angle reflection by a lake, or the total reflection of a glass prism, or when structured in a complex purposely made configuration, such as the silvery skin of many fish species.

Diffuse reflection from white materials, instead, can be highly efficient in giving back all the light they receive, due to the summing up of the many subsurface reflections.

## Colored objects

Up to now white objects have been discussed, which do not absorb light. But the above scheme continues to be valid in the case that the material is absorbent. In this case, diffused rays will lose some wavelengths during their walk in the material, and will emerge colored.

More, diffusion affects in a substantial manner the color of objects, because it determines the average path of light in the material, and hence to which extent the various wavelengths are absorbed. Red ink looks black when it stays in its bottle. Its vivid color is only perceived when it is placed on a scattering material (e.g. paper). This is so because light's path through the paper fibers (and through the ink) is only a fraction of millimeter long. Light coming from the bottle, instead, has crossed centimeters of ink, and has been heavily absorbed, even in its red wavelengths.

And, when a colored object has both diffuse and specular reflection, usually only the diffuse component is colored. A cherry reflects diffusely red light, absorbs all other colors and has a specular reflection which is essentially white. This is quite general, because, except for metals, the reflectivity of most materials depends on their refraction index, which varies little with the wavelength (though it is this variation that causes the chromatic dispersion in a prism
Prism (optics)
In optics, a prism is a transparent optical element with flat, polished surfaces that refract light. The exact angles between the surfaces depend on the application. The traditional geometrical shape is that of a triangular prism with a triangular base and rectangular sides, and in colloquial use...

), so that all colors are reflected nearly with the same intensity. Reflections from different origin, instead, may be colored: metallic reflections, such as in gold or copper, or interferential reflections: iridescence
Iridescence
Iridescence is generally known as the property of certain surfaces which appear to change color as the angle of view or the angle of illumination changes...

s, peacock feathers, butterfly wings, beetle elytra, or the antireflection coating of a lens.

## Importance for vision

Looking at the surrounding environment, one sees that what makes the human eye to form an image of almost all things visible is the diffuse reflection from their surface. With few exceptions, such as black objects, glass, liquids, polished or smooth metals, some small reflections from glossy objects, and the objects that themselves emit light: the Sun, lamps, and, computer screens (which, however, emit diffuse light). Outdoors it is the same, with perhaps the exception of a transparent water stream or of the iridescent colors of a beetle, and with the addition of other types of scattering: blue (or, at sunset, variously colored) light from the sky molecules (Rayleigh scattering
Rayleigh scattering
Rayleigh scattering, named after the British physicist Lord Rayleigh, is the elastic scattering of light or other electromagnetic radiation by particles much smaller than the wavelength of the light. The particles may be individual atoms or molecules. It can occur when light travels through...

), white from the water droplets of clouds (Mie scattering).

Light scattering from the surfaces of objects is by far the primary mechanism by which humans physically observe.

## Interreflection

Diffuse interreflection is a process whereby light
Light
Light or visible light is electromagnetic radiation that is visible to the human eye, and is responsible for the sense of sight. Visible light has wavelength in a range from about 380 nanometres to about 740 nm, with a frequency range of about 405 THz to 790 THz...

reflected from an object strikes other objects in the surrounding area, illuminating them. Diffuse interreflection specifically describes light reflected from objects which are not shiny or specular. In real life terms what this means is that light is reflected off non-shiny surfaces such as the ground, walls, or fabric, to reach areas not directly in view of a light source. If the diffuse surface is color
Color
Color or colour is the visual perceptual property corresponding in humans to the categories called red, green, blue and others. Color derives from the spectrum of light interacting in the eye with the spectral sensitivities of the light receptors...

ed, the reflected light is also colored, resulting in similar coloration of surrounding objects.

In 3D computer graphics
3D computer graphics
3D computer graphics are graphics that use a three-dimensional representation of geometric data that is stored in the computer for the purposes of performing calculations and rendering 2D images...

, diffuse interreflection is an important component of global illumination
Global illumination
Global illumination is a general name for a group of algorithms used in 3D computer graphics that are meant to add more realistic lighting to 3D scenes...

. There are a number of ways to model diffuse interreflection when rendering a scene. Radiosity and photon mapping
Photon mapping
In computer graphics, photon mapping is a two-pass global illumination algorithm developed by Henrik Wann Jensen that solves the rendering equation. Rays from the light source and rays from the camera are traced independently until some termination criterion is met, then they are connected in a...

are two commonly used methods.