Reflectance of the surface of a material is its effectiveness in reflecting radiant energy. It is the fraction of incident electromagnetic power that is reflected at an interface. The reflectance spectrum or spectral reflectance curve is the plot of the reflectance as a function of wavelength.
Contents
Mathematical definitions
Hemispherical reflectance
The hemispherical reflectance of a surface, denoted R, is defined as^{[1]}
where
- Φ_{e}^{r} is the radiant flux reflected by that surface;
- Φ_{e}^{i} is the radiant flux received by that surface.
Spectral hemispherical reflectance
The spectral hemispherical reflectance in frequency and spectral hemispherical reflectance in wavelength of a surface, denoted R_{ν} and R_{λ} respectively, are defined as^{[1]}
where
- Φ_{e,ν}^{r} is the spectral radiant flux in frequency reflected by that surface;
- Φ_{e,ν}^{i} is the spectral radiant flux in frequency received by that surface;
- Φ_{e,λ}^{r} is the spectral radiant flux in wavelength reflected by that surface;
- Φ_{e,λ}^{i} is the spectral radiant flux in wavelength received by that surface.
Directional reflectance
The directional reflectance of a surface, denoted R_{Ω}, is defined as^{[1]}
where
- L_{e,Ω}^{r} is the radiance reflected by that surface;
- L_{e,Ω}^{i} is the radiance received by that surface.
Spectral directional reflectance
The spectral directional reflectance in frequency and spectral directional reflectance in wavelength of a surface, denoted R_{Ω,ν} and R_{Ω,λ} respectively, are defined as^{[1]}
where
- L_{e,Ω,ν}^{r} is the spectral radiance in frequency reflected by that surface;
- L_{e,Ω,ν}^{i} is the spectral radiance received by that surface;
- L_{e,Ω,λ}^{r} is the spectral radiance in wavelength reflected by that surface;
- L_{e,Ω,λ}^{i} is the spectral radiance in wavelength received by that surface.
Reflectivity
For homogeneous and semi-infinite (see halfspace) materials, reflectivity is the same as reflectance. Reflectivity is the square of the magnitude of the Fresnel reflection coefficient,^{[2]} which is the ratio of the reflected to incident electric field;^{[3]} as such the reflection coefficient can be expressed as a complex number as determined by the Fresnel equations for a single layer, whereas the reflectance is always a positive real number.
For layered and finite media, according to the CIE,^{[citation needed]} reflectivity is distinguished from reflectance by the fact that reflectivity is a value that applies to thick reflecting objects.^{[4]} When reflection occurs from thin layers of material, internal reflection effects can cause the reflectance to vary with surface thickness. Reflectivity is the limit value of reflectance as the sample becomes thick; it is the intrinsic reflectance of the surface, hence irrespective of other parameters such as the reflectance of the rear surface. Another way to interpret this is that the reflectance is the fraction of electromagnetic power reflected from a specific sample, while reflectivity is a property of the material itself, which would be measured on a perfect machine if the material filled half of all space.^{[5]}
Surface type
Given that reflectance is a directional property, most surfaces can be divided into those that give specular reflection and those that give diffuse reflection:
- for specular surfaces, such as glass or polished metal, reflectance will be nearly zero at all angles except at the appropriate reflected angle; that is, reflected radiation will follow a different path from incident radiation for all cases other than radiation normal to the surface;
- for diffuse surfaces, such as matte white paint, reflectance is uniform; radiation is reflected in all angles equally or near-equally. Such surfaces are said to be Lambertian.
Most real objects have some mixture of diffuse and specular reflective properties.
Water reflectance
Reflection occurs when light moves from a medium with one index of refraction into a second medium with a different index of refraction.
Specular reflection from a body of water is calculated by the Fresnel equations.^{[6]} Fresnel reflection is directional and therefore does not contribute significantly to albedo which primarily diffuses reflection.
A real water surface may be wavy. Reflectance, which assumes a flat surface as given by the Fresnel equations, can be adjusted to account for waviness.
Grating efficiency
The generalization of reflectance to a diffraction grating, which disperses light by wavelength, is called diffraction efficiency.
Applications
Reflectance is an important concept in the fields of optics, solar thermal energy, telecommunication and radar.
Reflectance Fabrication
The modeling of surface reflectance is a key area of study within computer graphics since it is one of the main components that determines appearance. Although simple analytic reflectance models continue to be used in rendering applications, more complex and realistic material models are becoming practical with advances in measurement devices and methods, compact and accurate representations for such measured data, and flexible processing and rendering algorithms. This has created an opportunity to “close the loop” in this avenue of research, by considering the output stage. We leverage research positing that complex appearance is often determined by small-scale surface structure or microgeometry. Because these geometric features, typically called microfacets, are too small to be seen individually, the surface appearance is dictated by their aggregate distribution, in combination with the behavior of the underlying material (metal, dielectric, translucent / scattering, etc.).^{[7]}
The process of reflectance fabrication
The process of reflectance fabrication starts with defining a highlight shape. this highlight shape gives us information about the distribution and the direction of the micro facets. since we are working with discrete and finite number of micro facets we need to sample the highlight pattern. Due to feasibility of the manufacturing we need to perform optimization on our sampled pattern to make it continuous . Finally for fabricating the final product we have several options including Milling, Etching, Cutting, Minting...etc.
Applications of reflectance fabrication
- Architects and industrial and product designers could make material design, as opposed to purely material selection, part of their creative process.
- They could include milled surfaces, ranging from subtle to unusual and creative, as panels within products or as architectural elements.
- Interior designers could specify materials having particular reflectance to control the lighting within a space.
- In military applications, reflectance could be controlled as a form of camouflage, much as radar reflectance is already controlled in stealth aircraft. (“stealth” materials)
- Smaller milled surfaces could be used as a form of security marker, much as white-light holograms are used in credit cards today.
- Companies and advertising agencies may be interested in materials displaying product or corporate logos.
Market
The fact that many corporations are investing billions of dollars every year on more creative ways of advertisement can be an indication of the fact that there is a huge market in the area of reflectance manufacturing. the demand for creativity and diversity in manufacturing and architecture has made the computational manufacturing in general and reflectance fabrication as one of its important branches a very hot topic among the scientists of this field.
This technique is used by the EPFL spinoff company company Rayform. Rayform provides a unique technology for luxury brands, giving their products the ability to “sculpt” light. This enables completely new design and storytelling opportunities to create memorable experiences and guarantee products’ authenticity.
The key to this technology is a computer algorithm that generates special light shaping surfaces. By shaping the metal, glass or plastic product with this 3D structure, incoming light rays are redirected to form amazingly clear and highly detailed light images on nearby surfaces.^{[8]}
SI radiometry units
Quantity | Unit | Dimension | Notes | |||||
---|---|---|---|---|---|---|---|---|
Name | Symbol^{[nb 1]} | Name | Symbol | Symbol | ||||
Radiant energy | Q_{e}^{[nb 2]} | joule | J | M⋅L^{2}⋅T^{−2} | Energy of electromagnetic radiation. | |||
Radiant energy density | w_{e} | joule per cubic metre | J/m^{3} | M⋅L^{−1}⋅T^{−2} | Radiant energy per unit volume. | |||
Radiant flux | Φ_{e}^{[nb 2]} | watt | W = J/s | M⋅L^{2}⋅T^{−3} | Radiant energy emitted, reflected, transmitted or received, per unit time. This is sometimes also called "radiant power". | |||
Spectral flux | Φ_{e,ν}^{[nb 3]} or Φ_{e,λ}^{[nb 4]} |
watt per hertz or watt per metre |
W/Hz or W/m |
M⋅L^{2}⋅T^{−2} or M⋅L⋅T^{−3} |
Radiant flux per unit frequency or wavelength. The latter is commonly measured in W⋅nm^{−1}. | |||
Radiant intensity | I_{e,Ω}^{[nb 5]} | watt per steradian | W/sr | M⋅L^{2}⋅T^{−3} | Radiant flux emitted, reflected, transmitted or received, per unit solid angle. This is a directional quantity. | |||
Spectral intensity | I_{e,Ω,ν}^{[nb 3]} or I_{e,Ω,λ}^{[nb 4]} |
watt per steradian per hertz or watt per steradian per metre |
W⋅sr^{−1}⋅Hz^{−1} or W⋅sr^{−1}⋅m^{−1} |
M⋅L^{2}⋅T^{−2} or M⋅L⋅T^{−3} |
Radiant intensity per unit frequency or wavelength. The latter is commonly measured in W⋅sr^{−1}⋅nm^{−1}. This is a directional quantity. | |||
Radiance | L_{e,Ω}^{[nb 5]} | watt per steradian per square metre | W⋅sr^{−1}⋅m^{−2} | M⋅T^{−3} | Radiant flux emitted, reflected, transmitted or received by a surface, per unit solid angle per unit projected area. This is a directional quantity. This is sometimes also confusingly called "intensity". | |||
Spectral radiance | L_{e,Ω,ν}^{[nb 3]} or L_{e,Ω,λ}^{[nb 4]} |
watt per steradian per square metre per hertz or watt per steradian per square metre, per metre |
W⋅sr^{−1}⋅m^{−2}⋅Hz^{−1} or W⋅sr^{−1}⋅m^{−3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
Radiance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅sr^{−1}⋅m^{−2}⋅nm^{−1}. This is a directional quantity. This is sometimes also confusingly called "spectral intensity". | |||
Irradiance Flux density |
E_{e}^{[nb 2]} | watt per square metre | W/m^{2} | M⋅T^{−3} | Radiant flux received by a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral irradiance Spectral flux density |
E_{e,ν}^{[nb 3]} or E_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
Irradiance of a surface per unit frequency or wavelength. This is sometimes also confusingly called "spectral intensity". Non-SI units of spectral flux density include jansky (1 Jy = 10^{−26} W⋅m^{−2}⋅Hz^{−1}) and solar flux unit (1 sfu = 10^{−22} W⋅m^{−2}⋅Hz^{−1} = 10^{4} Jy). | |||
Radiosity | J_{e}^{[nb 2]} | watt per square metre | W/m^{2} | M⋅T^{−3} | Radiant flux leaving (emitted, reflected and transmitted by) a surface per unit area. This is sometimes also confusingly called "intensity". | |||
Spectral radiosity | J_{e,ν}^{[nb 3]} or J_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
Radiosity of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m^{−2}⋅nm^{−1}. This is sometimes also confusingly called "spectral intensity". | |||
Radiant exitance | M_{e}^{[nb 2]} | watt per square metre | W/m^{2} | M⋅T^{−3} | Radiant flux emitted by a surface per unit area. This is the emitted component of radiosity. "Radiant emittance" is an old term for this quantity. This is sometimes also confusingly called "intensity". | |||
Spectral exitance | M_{e,ν}^{[nb 3]} or M_{e,λ}^{[nb 4]} |
watt per square metre per hertz or watt per square metre, per metre |
W⋅m^{−2}⋅Hz^{−1} or W/m^{3} |
M⋅T^{−2} or M⋅L^{−1}⋅T^{−3} |
Radiant exitance of a surface per unit frequency or wavelength. The latter is commonly measured in W⋅m^{−2}⋅nm^{−1}. "Spectral emittance" is an old term for this quantity. This is sometimes also confusingly called "spectral intensity". | |||
Radiant exposure | H_{e} | joule per square metre | J/m^{2} | M⋅T^{−2} | Radiant energy received by a surface per unit area, or equivalently irradiance of a surface integrated over time of irradiation. This is sometimes also called "radiant fluence". | |||
Spectral exposure | H_{e,ν}^{[nb 3]} or H_{e,λ}^{[nb 4]} |
joule per square metre per hertz or joule per square metre, per metre |
J⋅m^{−2}⋅Hz^{−1} or J/m^{3} |
M⋅T^{−1} or M⋅L^{−1}⋅T^{−2} |
Radiant exposure of a surface per unit frequency or wavelength. The latter is commonly measured in J⋅m^{−2}⋅nm^{−1}. This is sometimes also called "spectral fluence". | |||
Hemispherical emissivity | ε | 1 | Radiant exitance of a surface, divided by that of a black body at the same temperature as that surface. | |||||
Spectral hemispherical emissivity | ε_{ν} or ε_{λ} |
1 | Spectral exitance of a surface, divided by that of a black body at the same temperature as that surface. | |||||
Directional emissivity | ε_{Ω} | 1 | Radiance emitted by a surface, divided by that emitted by a black body at the same temperature as that surface. | |||||
Spectral directional emissivity | ε_{Ω,ν} or ε_{Ω,λ} |
1 | Spectral radiance emitted by a surface, divided by that of a black body at the same temperature as that surface. | |||||
Hemispherical absorptance | A | 1 | Radiant flux absorbed by a surface, divided by that received by that surface. This should not be confused with "absorbance". | |||||
Spectral hemispherical absorptance | A_{ν} or A_{λ} |
1 | Spectral flux absorbed by a surface, divided by that received by that surface. This should not be confused with "spectral absorbance". | |||||
Directional absorptance | A_{Ω} | 1 | Radiance absorbed by a surface, divided by the radiance incident onto that surface. This should not be confused with "absorbance". | |||||
Spectral directional absorptance | A_{Ω,ν} or A_{Ω,λ} |
1 | Spectral radiance absorbed by a surface, divided by the spectral radiance incident onto that surface. This should not be confused with "spectral absorbance". | |||||
Hemispherical reflectance | R | 1 | Radiant flux reflected by a surface, divided by that received by that surface. | |||||
Spectral hemispherical reflectance | R_{ν} or R_{λ} |
1 | Spectral flux reflected by a surface, divided by that received by that surface. | |||||
Directional reflectance | R_{Ω} | 1 | Radiance reflected by a surface, divided by that received by that surface. | |||||
Spectral directional reflectance | R_{Ω,ν} or R_{Ω,λ} |
1 | Spectral radiance reflected by a surface, divided by that received by that surface. | |||||
Hemispherical transmittance | T | 1 | Radiant flux transmitted by a surface, divided by that received by that surface. | |||||
Spectral hemispherical transmittance | T_{ν} or T_{λ} |
1 | Spectral flux transmitted by a surface, divided by that received by that surface. | |||||
Directional transmittance | T_{Ω} | 1 | Radiance transmitted by a surface, divided by that received by that surface. | |||||
Spectral directional transmittance | T_{Ω,ν} or T_{Ω,λ} |
1 | Spectral radiance transmitted by a surface, divided by that received by that surface. | |||||
Hemispherical attenuation coefficient | μ | reciprocal metre | m^{−1} | L^{−1} | Radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Spectral hemispherical attenuation coefficient | μ_{ν} or μ_{λ} |
reciprocal metre | m^{−1} | L^{−1} | Spectral radiant flux absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Directional attenuation coefficient | μ_{Ω} | reciprocal metre | m^{−1} | L^{−1} | Radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
Spectral directional attenuation coefficient | μ_{Ω,ν} or μ_{Ω,λ} |
reciprocal metre | m^{−1} | L^{−1} | Spectral radiance absorbed and scattered by a volume per unit length, divided by that received by that volume. | |||
See also: SI · Radiometry · Photometry |
- ^ Standards organizations recommend that radiometric quantities should be denoted with suffix "e" (for "energetic") to avoid confusion with photometric or photon quantities.
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} Alternative symbols sometimes seen: W or E for radiant energy, P or F for radiant flux, I for irradiance, W for radiant exitance.
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} Spectral quantities given per unit frequency are denoted with suffix "ν" (Greek)—not to be confused with suffix "v" (for "visual") indicating a photometric quantity.
- ^ ^{a} ^{b} ^{c} ^{d} ^{e} ^{f} ^{g} Spectral quantities given per unit wavelength are denoted with suffix "λ" (Greek).
- ^ ^{a} ^{b} Directional quantities are denoted with suffix "Ω" (Greek).
See also
- Bidirectional reflectance distribution function
- Emissivity
- Lambert's cosine law
- Transmittance
- Sun path
- Light Reflectance Value
- Albedo
References
- ^ ^{a} ^{b} ^{c} ^{d} "Thermal insulation — Heat transfer by radiation — Physical quantities and definitions". ISO 9288:1989. ISO catalogue. 1989. Retrieved 2015-03-15.
- ^ E. Hecht (2001). Optics (4th ed.). Pearson Education. ISBN 0-8053-8566-5.
- ^ IUPAC, Compendium of Chemical Terminology, 2nd ed. (the "Gold Book") (1997). Online corrected version: (2006–) "Reflectance". doi:10.1351/goldbook.R05235
- ^ CIE International Lighting Vocabulary
- ^ Palmer and Grant, The Art of Radiometry
- ^ Ottaviani, M. and Stamnes, K. and Koskulics, J. and Eide, H. and Long, S.R. and Su, W. and Wiscombe, W., 2008: 'Light Reflection from Water Waves: Suitable Setup for a Polarimetric Investigation under Controlled Laboratory Conditions. Journal of Atmospheric and Oceanic Technology, 25 (5), 715--728.
- ^ Tim Weyrich, Pieter Peers, Wojciech Matusik, and Szymon Rusinkiewicz. Fabricating Microgeometry for Custom Surface Reflectance. ACM Transactions on Graphics (Proc. SIGGRAPH) 28(3), August 2009.
- ^ "EPFL Computer Graphics and Geometry Laboratory". RAYFORM SA. Retrieved 2019-01-28.
External links
Look up reflectance in Wiktionary, the free dictionary. |