Standard illuminant

Relative spectral power distributions (SPDs) of CIE illuminants A, B, and C from Template:Nowrap to Template:Nowrap.

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

CIE illuminants

The International Commission on Illumination (usually abbreviated CIE for its French name) is the body responsible for publishing all of the well-known standard illuminants. Each of these is known by a letter or by a letter-number combination.

Illuminants A, B, and C were introduced in 1931, with the intention of respectively representing average incandescent light, direct sunlight, and average daylight. Illuminants D (1967) represent variations of daylight, illuminant E is the equal-energy illuminant, while illuminants F (2004) represent fluorescent lamps of various composition.

There are instructions on how to experimentally produce light sources ("standard sources") corresponding to the older illuminants. For the relatively newer ones (such as series D), experimenters are left to measure to profiles of their sources and compare them to the published spectra: Template:Quote

Nevertheless, they do provide a measure, called the metamerism index, to assess the quality of daylight simulators. The Metamerism Index tests how well five sets of metameric samples match under the test and reference illuminant. In a manner similar to the color rendering index, the average difference between the metamers is calculated.

Illuminant A

The CIE defines illuminant A in these terms: Template:Quote

The spectral radiant exitance of a black body follows Planck's law:

$M_{e,\lambda }(\lambda ,T)=\frac{c_1{\lambda }^{-5}}{\exp \left(\frac{c_2}{\lambda T}\right)-1}.$

At the time of standardizing illuminant A, both $c_1=2\pi \cdot h\cdot c^2$ (which does not affect the relative SPD) and $c_2=h\cdot c/k$ were different. In 1968, the estimate of c₂ was revised from 0.01438 m·K to 0.014388 m·K (and before that, it was 0.01435 m·K when illuminant A was standardized). This difference shifted the Planckian locus, changing the color temperature of the illuminant from its nominal 2848 K to 2856 K:

$T_{new}=T_{old}\times \frac{1.4388}{1.435}=2848\text{K}\times 1.002648=2855.54\text{K}.$

In order to avoid further possible changes in the color temperature, the CIE now specifies the SPD directly, based on the original (1931) value of c₂:

$S_A(\lambda )=100{\left(\frac{560}{\lambda }\right)}^5\frac{\exp \frac{1.435\times 10^7}{2848\times 560}-1}{\exp \frac{1.435\times 10^7}{2848\lambda }-1}.$

The coefficients have been selected to achieve a normalized SPD of Template:Nowrap at Template:Nowrap. The tristimulus values are Template:Nowrap, and the chromaticity coordinates using the standard observer are Template:Nowrap.

Illuminants B and C

Template:AnchorTemplate:Anchor Illuminants B and C are easily achieved daylight simulations. They modify illuminant A by using liquid filters. B served as a representative of noon sunlight, with a correlated color temperature (CCT) of 4874 K, while C represented average day light with a CCT of 6774 K. Unfortunately, they are poor approximations of any phase of natural daylight, particularly in the short-wave visible and in the ultraviolet spectral ranges. Once more realistic simulations were achievable, illuminants B and C were deprecated in favor of the D series.

Template:Quote Illuminant B was not so honored in 2004.

The liquid filters, designed by Raymond Davis and Kasson S. Gibson in 1931, have a relatively high absorbance at the red end of the spectrum, effectively increasing the CCT of the incandescent lamp to daylight levels. This is similar in function to a CTB color gel that photographers and cinematographers use today, albeit much less convenient.

Each filter uses a pair of solutions, comprising specific amounts of distilled water, copper sulfate, mannite, pyridine, sulfuric acid, cobalt, and ammonium sulfate. The solutions are separated by a sheet of uncolored glass. The amounts of the ingredients are carefully chosen so that their combination yields a color temperature conversion filter; that is, the filtered light is still white.

Illuminant series D

Relative spectral power distribution of illuminant D and a black body of the same correlated color temperature (in red), normalized about Template:Nowrap.

The D series of illuminants are designed to represent natural daylight and lie along the daylight locus. They are difficult to produce artificially, but are easy to characterize mathematically.

By 1964, several spectral power distributions (SPDs) of daylight had been measured independently by H. W. Budde of the National Research Council of Canada in Ottawa, H. R. Condit and F. Grum of the Eastman Kodak Company in Rochester, New York, and S. T. Henderson and D. Hodgkiss of Thorn Electrical Industries in Enfield (north London), totaling among them 622 samples. Deane B. Judd, David MacAdam, and Günter Wyszecki analyzed these samples and found that the (x, y) chromaticity coordinates followed a simple, quadratic relation, later known as the daylight locus:

$y=2.870x-3.000x^2-0.275.$

Characteristic vector analysis revealed that the SPDs could be satisfactorily approximated by using the mean (S₀) and first two characteristic vectors (S₁ and S₂):

$S_D(\lambda )=S_0(\lambda )+M_1{S}_1(\lambda )+M_2{S}_2(\lambda ).$

Characteristic vectors of illuminant D; component SPDs S₀ (blue), S₁ (green), S₂ (red).

In simpler terms, the SPD of the studied daylight samples can be expressed as the linear combination of three, fixed SPDs. The first vector (S₀) is the mean of all the SPD samples, which is the best reconstituted SPD that can be formed with only a fixed vector. The second vector (S₁) corresponds to yellow–blue variation (along the locus), accounting for changes in the correlated color temperature due to proportion of indirect to direct sunlight. The third vector (S₂) corresponds to pink–green variation (across the locus) caused by the presence of water in the form of vapor and haze.

The Planckian locus is depicted on the CIE 1960 UCS, along with isotherms (lines of constant correlated color temperature) and representative illuminant coordinates

By the time the D-series was formalized by the CIE, a computation of the chromaticity $(x,y)$ for a particular isotherm was included. Judd et al. then extended the reconstituted SPDs to Template:Nowrap–Template:Nowrap and Template:Nowrap–Template:Nowrap by using Moon's spectral absorbance data of the Earth's atmosphere. The tabulated SPDs presented by the CIE today are derived by linear interpolation of the Template:Nowrap data set down to Template:Nowrap. However, there is a proposal to use spline interpolation instead.

Similar studies have been undertaken in other parts of the world, or repeating Judd et al.'s analysis with modern computational methods. In several of these studies, the daylight locus is notably closer to the Planckian locus than in Judd et al.

The CIE positions D65 as the standard daylight illuminant: Template:Quote

Daylight locus in the CIE 1960 UCS. The isotherms are perpendicular to the Planckian locus. The two sections of the daylight locus, from 4000–7000 K and 7000–25000 K, are color-coded. Note that the two loci are separated by a fairly even distance, of around ${\mathrm{\Delta }}_{uv}=0.003$.

Computation

The relative spectral power distribution (SPD) $S_D(\lambda )$ of a D series illuminant can be derived from its chromaticity coordinates in the CIE 1931 color space, $(x_D,y_D)$. First, the chromaticity coordinates must be determined:

$x_D=\{\begin{array}{cc}0.244063+0.09911\frac{10^3}{T}+2.9678\frac{10^6}{T^2}-4.6070\frac{10^9}{T^3}& 4000\mathrm{K}\le T\le 7000\mathrm{K}\\ 0.237040+0.24748\frac{10^3}{T}+1.9018\frac{10^6}{T^2}-2.0064\frac{10^9}{T^3}& 7000\mathrm{K}<T\le 25000\mathrm{K}\end{array}$

$y_D=-3.000x_D^2+2.870x_D-0.275$

where T is the illuminant's CCT. Note that the CCTs of the canonical illuminants, D₅₀, D₅₅, D₆₅, and D₇₅, differ slightly from what their names suggest. For example, D50 has a CCT of 5003 K ("horizon" light), while D65 has a CCT of 6504 K (noon light). This is because the value of the constants in Planck's law have been slightly changed since the definition of these canonical illuminants, whose SPDs are based on the original values in Planck's law. The same discrepancy applies to all illuminants in the D series—D₅₀, D₅₅, D₆₅, D₇₅—and can be "rectified" by multiplying the nominal color temperature by $\frac{c_2}{1.4380}$; for example $6500\text{K}\times \frac{1.438776877\dots }{1.4380}=6503.51\text{K}$ for D₆₅.

To determine the D-series SPD (S_D) that corresponds to those coordinates, the coefficients M₁ and M₂ of the characteristic vectors S₁ and S₂ are determined:

$S_D(\lambda )=S_0(\lambda )+M_1{S}_1(\lambda )+M_2{S}_2(\lambda ),$

$M_1=(-1.3515-1.7703x_D+5.9114y_D)/M,$

$M_2=(0.0300-31.4424x_D+30.0717y_D)/M,$

$M=0.0241+0.2562x_D-0.7341y_D$

where $S_0(\lambda ),S_1(\lambda ),S_2(\lambda )$ are the mean and first two eigenvector SPDs, depicted in figure. The characteristic vectors both have a zero at Template:Nowrap, since all the relative SPDs have been normalized about this point. In order to match all significant digits of the published data of the canonical illuminants the values of M₁ and M₂ have to be rounded to three decimal places before calculation of S_D.

D65 values

Using the standard 2° observer, the CIE 1931 color space chromaticity coordinates of D65 are

$$\begin{array}{cc}x& =0.31272\\ y& =0.32903\end{array}$$

and the XYZ tristimulus values (normalized to Template:Math), are

$$\begin{array}{ccc}X& =& 95.047\\ Y& =& 100\phantom{.000}\\ Z& =& 108.883\end{array}$$

For the supplementary 10° observer,Template:Cn

$$\begin{array}{cc}x& =0.31382\\ y& =0.33100\end{array}$$ and the corresponding XYZ tristimulus values are

$$\begin{array}{ccc}X& =& 94.811\\ Y& =& 100\phantom{.000}\\ Z& =& 107.304\end{array}$$

Since D65 represents white light, its coordinates are also a white point, corresponding to a correlated color temperature of 6504 K. Rec. 709, used in HDTV systems, truncates the CIE 1931 coordinates to x=0.3127, y=0.329.

Daylight simulator

There are no actual daylight light sources, only simulators. Constructing a practical light source that emulates a D-series illuminant is a difficult problem. The chromaticity can be replicated simply by taking a well known light source and applying filters, such as the Spectralight III, that used filtered incandescent lamps. However, the SPDs of these sources deviate from the D-series SPD, leading to bad performance on the CIE metamerism index. Better sources were achieved in the 2010s with phosphor-coated white LEDs that can easily emulate the A, D, and E illuminants with high CRI.

Illuminant E

Illuminant E is beneath the Planckian locus, and roughly at the CCT of D₅₅.

Illuminant E is an equal-energy radiator; it has a constant SPD inside the visible spectrum. It is useful as a theoretical reference; an illuminant that gives equal weight to all wavelengths. It also has equal CIE XYZ tristimulus values, thus its chromaticity coordinates are (x,y)=(1/3,1/3). This is by design; the XYZ color matching functions are normalized such that their integrals over the visible spectrum are the same.

Illuminant E is not a black body, so it does not have a color temperature, but it can be approximated by a D series illuminant with a CCT of 5455 K. (Of the canonical illuminants, D₅₅ is the closest.) Manufacturers sometimes compare light sources against illuminant E to calculate the excitation purity.

Illuminant series FL

CIE Publication 15.2 introduced twelve new illuminants representing several fluorescent lamps and comprising series F, later renamed to series FL from CIE Publication 15:2004 onward. The original 12 standards are distributed to 3 groups:

• Standards FL1–FL6 represent "standard" fluorescent lamps consisting of two semi-broadband emissions of antimony and manganese activations in calcium halophosphate phosphor. FL4 is of particular interest since it was used for calibrating the CIE color rendering index (the CRI formula was chosen such that FL4 would have a CRI of 51).Template:Cn
• Standards FL7–FL9 represent "broadband" (full-spectrum light) fluorescent lamps with multiple phosphors, and higher CRIs.
• Standards FL10–FL12 represent narrow triband illuminants consisting of three "narrowband" emissions (caused by ternary compositions of rare-earth phosphors) in the R,G,B regions of the visible spectrum, which leads to poor CRI.

The members within a group represent different CCTs, such that the phosphor weights can be tuned to achieve the desired CCT. In each of these three groups, CIE states that FL2, FL7, and FL11 "take priority" to be representative of their respective groups.

• 
  FL1–6: Standard
• 
  FL7–9: Broadband
• 
  FL10–12: Narrowband

CIE 15:2004 also introduced fifteen new fluorescent illuminants representing different kinds of fluorescent lamps and comprising subseries FL3. These 15 standards are distributed in 5 groups:

• Standards FL3.1-FL3.3 represent standard halophosphate lamps (similar to FL1-6)
• Standards FL3.4-FL3.6 represent DeLuxe type lamps (similar to FL7-9)
• Standards FL3.7-FL3.11 represent three-band lamps (similar to FL10-12)
• Standards FL3.12-FL3.14 represent multi-band lamps
• Standard FL3.15 represents a D65 simulating fluorescent lamp

• 
  FL3.1-3.3 : standard
• 
  FL3.4-3.6 : DeLuxe
• 
  FL3.7-3.11 : three-band
• 
  FL3.12-3.14 : multi-band
• 
  FL3.15 : D65 simulator

Illuminant series HP

CIE 15:2004 introduced five new illuminants representing different kinds of high pressure discharge lamps and comprising series HP.:

• Standard HP1 for standard high-pressure sodium lamps
• Standard HP2 for color-enhanced high-pressure sodium lamps
• Standards HP3-HP5 for metal halide lamps.

• 
  HP1 and HP2
• 
  HP3 to HP5

Illuminant series LED

CIE Publication 15:2018 introduces nine new illuminants representing several white LEDs with CCTs ranging from 2700~6600 K. LED-B1 through B5 define standard LED illuminants with phosphor-converted blue light. LED-BH1 defines a blend of phosphor-converted blue and a red LED. LED-RGB1 defines the white light produced by a tricolor LED mix. LED-V1 and V2 define LEDs with phosphor-converted violet light.

• 
  LED-B1 to B5
• 
  LED-BH1 and RGB1
• 
  LED-V1 and V2

Illuminant series ID

CIE publication 184:2009 introduced two new illuminants representing natural indoor light, which were later included as series ID in CIE 15:2018. ID50 and ID65 are equivalent to their outdoor counterparts, D50 and D65, filtered through window glass, thereby removing the ultraviolet contents. The indoor CCTs are about 100K higher (cooler) relative to their outdoor counterparts.

White point

Template:Main The spectrum of a standard illuminant, like any other profile of light, can be converted into tristimulus values. The set of three tristimulus coordinates of an illuminant is called a white point. If the profile is normalized, then the white point can equivalently be expressed as a pair of chromaticity coordinates.

If an image is recorded in tristimulus coordinates (or in values which can be converted to and from them), then the white point of the illuminant used gives the maximum value of the tristimulus coordinates that will be recorded at any point in the image, in the absence of fluorescence. It is called the white point of the image.

The process of calculating the white point discards a great deal of information about the profile of the illuminant, and so although it is true that for every illuminant the exact white point can be calculated, it is not the case that knowing the white point of an image alone tells you a great deal about the illuminant that was used to record it.

External links

• Selected colorimetric tables in Excel, as published in CIE 15:2004
• Konica Minolta Sensing: Light sources & Illuminants