Spectral power distribution

In radiometry, photometry and color science, a spectral power distribution (SPD) measurement describes the power per unit area per unit wavelength of an illumination (radiant exitance). More generally, the term spectral power distribution can refer to the concentration, as a function of wavelength, of any radiometric or photometric quantity (e.g. radiant energy, radiant flux, radiant intensity, radiance, irradiance, radiant exitance, radiosity, luminance, luminous flux, luminous intensity, illuminance, luminous emittance).[1][2][3][4]

Knowledge of the SPD is crucial for optical-sensor system applications. Optical properties such as transmittance, reflectivity, and absorbance as well as the sensor response are typically dependent on the incident wavelength.[3]

NormSPD with eye
CIE standard illuminant spectral power distribution comparisons referenced to the human visual system photopic response

Physics

Mathematically, for the spectral power distribution of a radiant exitance or irradiance one may write:

where M(λ) is the spectral irradiance (or exitance) of the light (SI units: W/m3 = kg·m−1·s−3); Φ is the radiant flux of the source (SI unit: watt, W); A is the area over which the radiant flux is integrated (SI unit: square meter, m2); and λ is the wavelength (SI unit: meter, m). (Note that it is more convenient to express the wavelength of light in terms of nanometers; spectral exitance would then be expressed in units of W·m−2·nm−1.) The approximation is valid when the area and wavelength interval are small.[5]

Relative SPD

Spectral Power Distributions
Characteristic spectral power distributions (SPDs) for an incandescent lamp (left) and a fluorescent lamp (right). The horizontal axes are in nanometers and the vertical axes show relative intensity in arbitrary units.

The ratio of spectral concentration (irradiance or exitance) at a given wavelength to the concentration of a reference wavelength provides the relative SPD.[4] This can be written as:

For instance, the luminance of lighting fixtures and other light sources are handled separately, a spectral power distribution may be normalized in some manner, often to unity at 555 or 560 nanometers, coinciding with the peak of the eye's luminosity function.[2][6]

Responsivity

The SPD can be used to determine the response of a sensor at a specified wavelength. This compares the output power of the sensor to the input power as a function of wavelength.[7] This can be generalized in the following formula:

Knowing the responsitivity is beneficial for determination of illumination, interactive material components, and optical components to optimize performance of a system's design.

Source SPD and matter

Rayleigh sunlight scattering
Figure showing the greater proportion of blue light scattered by the atmosphere relative to red light.

The spectral power distribution over the visible spectrum from a source can have varying concentrations of relative SPDs. The interactions between light and matter affect the absorption and reflectance properties of materials and subsequently produces a color that varies with source illumination.[8]

For example, the relative spectral power distribution of the sun produces a white appearance if observed directly, but when the sunlight illuminates the Earth's atmosphere the sky appears blue under normal daylight conditions. This stems from the optical phenomenon called Rayleigh scattering which produces a concentration of shorter wavelengths and hence the blue color appearance.[3]

Source SPD and color appearance

Incand-3500-5500-color-temp-comparison
Color temperature comparison of common electric lamps

The human visual response relies on trichromacy to process color appearance. While the human visual response integrates over all wavelengths, the relative spectral power distribution will provide color appearance modeling information as the concentration of wavelength band(s) will become the primary contributors to the perceived color.[8]

This becomes useful in photometry and colorimetry as the perceived color changes with source illumination and spectral distribution and coincides with metamerisms where an object's color appearance changes.[8]

The spectral makeup of the source can also coincide with color temperature producing differences in color appearance due to the source's temperature.[4]

See also

References

  1. ^ Mark D. Fairchild (2005). Color Appearance Models. John Wiley and Sons. ISBN 0-470-01216-1.
  2. ^ a b Michael R. Peres (2007). The Focal Encyclopedia of Photography. Focal Press. ISBN 978-0-240-80740-9.
  3. ^ a b c William Ross McCluney (1994). Introduction to Radiometry and Photometry. Boston: Artech House. ISBN 0890066787.
  4. ^ a b c Franc C. Grum (1979). Optical Radiation Measurements (v. 1). New York: Academic Press. ISBN 0123049016.
  5. ^ Clair L. Wyatt (1987). Radiometric System Design. New York: Macmillan. ISBN 0029488001.
  6. ^ Wyszecki, Günter; Stiles, Walter Stanley (1982). Color Science: Concepts and Methods; Quantitative Data and Formulae (second ed.). New York: Wiley. ISBN 978-0-471-39918-6.
  7. ^ Robert W. Boyd (1983). Radiometry and the Detection of Optical Radiation. New York: Wiley. ISBN 047186188X.
  8. ^ a b c William David Wright (1969). The Measurement of Colour. New York: Van Nostrand Reinhold Co.

External links

Color appearance model

A color appearance model (CAM) is a mathematical model that seeks to describe the perceptual aspects of human color vision, i.e. viewing conditions under which the appearance of a color does not tally with the corresponding physical measurement of the stimulus source. (In contrast, a color model defines a coordinate space to describe colors, such as the RGB and CMYK color models.)

Color calibration

The aim of color calibration is to measure and/or adjust the color response of a device (input or output) to a known state. In International Color Consortium (ICC) terms, this is the basis for an additional color characterization of the device and later profiling. In non-ICC workflows, calibration refers sometimes to establishing a known relationship to a standard color space in one go. The device that is to be calibrated is sometimes known as a calibration source; the color space that serves as a standard is sometimes known as a calibration target. Color calibration is a requirement for all devices taking an active part of a color-managed workflow, and is used by many industries, such as television production, gaming, photography, engineering, chemistry, medicine and more.

Color rendering capacity

Color rendering capacity is a measure of how well colors are represented under artificial light. It is one of several measures of color rendering index, indicating the extent to which a wide range of colors may be distinguished under a given light source.

Color temperature

Not to be confused with warm and cool colors.

The color temperature of a light source is the temperature of an ideal black-body radiator that radiates light of a color comparable to that of the light source. Color temperature is a characteristic of visible light that has important applications in lighting, photography, videography, publishing, manufacturing, astrophysics, horticulture, and other fields. In practice, color temperature is meaningful only for light sources that do in fact correspond somewhat closely to the radiation of some black body, i.e., light in a range going from red to orange to yellow to white to blueish white; it does not make sense to speak of the color temperature of, e.g., a green or a purple light. Color temperature is conventionally expressed in kelvins, using the symbol K, a unit of measure for absolute temperature.

Color temperatures over 5000 K are called "cool colors" (bluish), while lower color temperatures (2700–3000 K) are called "warm colors" (yellowish). "Warm" in this context is an analogy to radiated heat flux of traditional incandescent lighting rather than temperature. The spectral peak of warm-coloured light is closer to infrared, and most natural warm-coloured light sources emit significant infrared radiation. The fact that "warm" lighting in this sense actually has a "cooler" color temperature often leads to confusion.

Colorimetry

Colorimetry is "the science and technology used to quantify and describe physically the human color perception."

It is similar to spectrophotometry, but is distinguished by its interest in reducing spectra to the physical correlates of color perception, most often the CIE 1931 XYZ color space tristimulus values and related quantities.

Compact fluorescent lamp

A compact fluorescent lamp (CFL), also called compact fluorescent light, energy-saving light, and compact fluorescent tube, is a fluorescent lamp designed to replace an incandescent light bulb; some types fit into light fixtures designed for incandescent bulbs. The lamps use a tube which is curved or folded to fit into the space of an incandescent bulb, and a compact electronic ballast in the base of the lamp.

Compared to general-service incandescent lamps giving the same amount of visible light, CFLs use one-fifth to one-third the electric power, and last eight to fifteen times longer. A CFL has a higher purchase price than an incandescent lamp, but can save over five times its purchase price in electricity costs over the lamp's lifetime. Like all fluorescent lamps, CFLs contain toxic mercury which complicates their disposal. In many countries, governments have banned the disposal of CFLs together with regular garbage. These countries have established special collection systems for CFLs and other hazardous waste.

The principle of operation remains the same as in other fluorescent lighting: electrons that are bound to mercury atoms are excited to states where they will radiate ultraviolet light as they return to a lower energy level; this emitted ultraviolet light is converted into visible light as it strikes the fluorescent coating (as well as into heat when absorbed by other materials such as glass).

CFLs radiate a spectral power distribution that is different from that of incandescent lamps. Improved phosphor formulations have improved the perceived color of the light emitted by CFLs, such that some sources rate the best "soft white" CFLs as subjectively similar in color to standard incandescent lamps.White LED lamps now compete with CFLs for high-efficiency lighting, and General Electric is stopping production of domestic CFL lamps in favour of LEDs.

Illuminant D65

CIE Standard Illuminant D65 (sometimes written D65) is a commonly used standard illuminant defined by the International Commission on Illumination (CIE). It is part of the D series of illuminants that try to portray standard illumination conditions at open-air in different parts of the world.

D65 corresponds roughly to the average midday light in Western Europe / Northern Europe (comprising both direct sunlight and the light diffused by a clear sky), hence it is also called a daylight illuminant. As any standard illuminant is represented as a table of averaged spectrophotometric data, any light source which statistically has the same relative spectral power distribution (SPD) can be considered a D65 light source. There are no actual D65 light sources, only simulators. The quality of a simulator can be assessed with the CIE Metamerism Index.The CIE positions D65 as the standard daylight illuminant:

[D65] is intended to represent average daylight and has a correlated colour temperature of approximately 6500 K. CIE standard illuminant D65 should be used in all colorimetric calculations requiring representative daylight, unless there are specific reasons for using a different illuminant. Variations in the relative spectral power distribution of daylight are known to occur, particularly in the ultraviolet spectral region, as a function of season, time of day, and geographic location.

Impossible color

Impossible colors or forbidden colors are supposed colors that cannot be perceived in normal seeing of light that is a combination of various intensities of the various frequencies of visible light, but are reported to be seen in special circumstances.

Luminosity function

A luminosity function or luminous efficiency function describes the average spectral sensitivity of human visual perception of brightness. It is based on subjective judgements of which of a pair of different-colored lights is brighter, to describe relative sensitivity to light of different wavelengths. It should not be considered perfectly accurate, but it is a good representation of visual sensitivity of the human eye and it is valuable as a baseline for experimental purposes. Different luminosity functions apply under different lighting condition, varying from photopic in brightly lit conditions through mesotopic to scotopic under low lighting conditions. Without qualification, the luminosity function generally refers to the photopic luminosity function.

The CIE photopic luminosity function y(λ) or V(λ) is a standard function established by the Commission Internationale de l'Éclairage (CIE) and may be used to convert radiant energy into luminous (i.e., visible) energy. It also forms the central color matching function in the CIE 1931 color space.

Metamerism

Metamerism may refer to:

Metamerism (biology), in zoology and developmental biology, the property of having repeated segments, as in annelids

Metamerism (color), in colorimetry, a perceived matching of the colors that, based on differences in spectral power distribution, do not actually match

In chemistry, the chemical property of having the same proportion of atomic components in different arrangements (obsolete, replaced with isomer). In organic chemistry, compounds having the same molecular formula but different number of carbon atoms ( alkyl groups) on either side of functional group ( i.e., -O-,-S-, -NH-, -C(=O)-) are called metamers and the phenomenon is called metamerism.

Metamerism (color)

In colorimetry, metamerism is a perceived matching of colors with different (nonmatching) spectral power distributions. Colors that match this way are called metamers.

A spectral power distribution describes the proportion of total light given off (emitted, transmitted, or reflected) by a color sample at each visible wavelength; it defines the complete information about the light coming from the sample. However, the human eye contains only three color receptors (three types of cone cells), which means that all colors are reduced to three sensory quantities, called the tristimulus values. Metamerism occurs because each type of cone responds to the cumulative energy from a broad range of wavelengths, so that different combinations of light across all wavelengths can produce an equivalent receptor response and the same tristimulus values or color sensation. In color science, the set of sensory spectral sensitivity curves is numerically represented by color matching functions.

Spectral G-index

The spectral G-Index is a variable that was developed to quantify the amount of short wavelength light in a visible light source relative to its visible emission (it is a measure of the amount of blue light per lumen). The smaller the G-index, the more blue, violet, or ultraviolet light a lamp emits relative to its total output. It is used in order to select outdoor lamps that minimize skyglow and ecological light pollution. The G-index was originally proposed by David Galadí Enríquez, an astrophysicist at Calar Alto Observatory.

Spectroradiometer

Spectroradiometers are devices designed to measure the spectral power distribution of a source. From the spectral power distribution, the radiometric, photometric, and colorimetric quantities of light can be determined in order to measure, characterize, and calibrate light sources for various applications.

Spectroradiometers typically take measurements of spectral irradiance and spectral radiance. This spectral data can be used to calculate CIE tristimulus values through mathematical integration. CIE chromaticity coordinates and luminosity can then be calculated, providing a complete description of the source’s color, including chromaticity, spectral power, illuminance, and luminance. Spectroradiometers are stand-alone systems that work independently without the need to be connected to a PC. This makes them highly portable while maintaining the accuracy of a spectrometer.

Spectrum

A spectrum (plural spectra or spectrums) is a condition that is not limited to a specific set of values but can vary, without steps, across a continuum. The word was first used scientifically in optics to describe the rainbow of colors in visible light after passing through a prism. As scientific understanding of light advanced, it came to apply to the entire electromagnetic spectrum.

Spectrum has since been applied by analogy to topics outside optics. Thus, one might talk about the "spectrum of political opinion", or the "spectrum of activity" of a drug, or the "autism spectrum". In these uses, values within a spectrum may not be associated with precisely quantifiable numbers or definitions. Such uses imply a broad range of conditions or behaviors grouped together and studied under a single title for ease of discussion. Nonscientific uses of the term spectrum are sometimes misleading. For instance, a single left–right spectrum of political opinion does not capture the full range of people's political beliefs. Political scientists use a variety of biaxial and multiaxial systems to more accurately characterize political opinion.

In most modern usages of spectrum there is a unifying theme between the extremes at either end. This was not always true in older usage.

Standard illuminant

A standard illuminant is a theoretical source of visible light with a profile (its spectral power distribution) which is published. Standard illuminants provide a basis for comparing images or colors recorded under different lighting.

Stray light

Stray light is light in an optical system, which was not intended in the design. The light may be from the intended source, but follow paths other than intended, or it may be from a source other than the intended source. This light will often set a working limit on the dynamic range of the system; it limits the signal-to-noise ratio or contrast ratio, by limiting how dark the system can be. Ocular straylight is stray light in the human eye.

Subtractive color

Subtractive color, or "subtractive color mixing", predicts the spectral power distribution of light after it passes through successive layers of partially absorbing media. This idealized model is the essential principle of how dyes and inks are used in color printing and photography where the perception of color is elicited after white light passes through microscopic "stacks" of partially absorbing media allowing some wavelengths of light to reach the eye and not others.

White point

A white point (often referred to as reference white or target white in technical documents) is a set of tristimulus values or chromaticity coordinates that serve to define the color "white" in image capture, encoding, or reproduction. Depending on the application, different definitions of white are needed to give acceptable results. For example, photographs taken indoors may be lit by incandescent lights, which are relatively orange compared to daylight. Defining "white" as daylight will give unacceptable results when attempting to color-correct a photograph taken with incandescent lighting.

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