sRGB

sRGB defines the chromaticities of the red, green, and blue primaries, the colors where one of the three channels is nonzero and the other two are zero. The gamut of chromaticities that can be represented in sRGB is the color triangle defined by these primaries, which are set such that the range of colors inside the triangle is well within the range of colors visible to a human with normal trichromatic vision. As with any RGB color space, for non-negative values of R, G, and B it is not possible to represent colors outside this triangle.

The primaries come from HDTV (ITU-R BT.709), which are somewhat different from those for older color TV systems (ITU-R BT.601). These values were chosen to reflect the approximate color of consumer CRT phosphors at the time of its design. Since flat-panel displays at the time were generally designed to emulate CRT characteristics, the values also reflected prevailing practice for other display devices as well.^[1]

The reference display characterisation is based on the characterisation in CIE 122. The reference display is characterised by a nominal power-law gamma of 2.2, which the sRGB working group determined was representative of the CRTs used with Windows operating systems at the time.^[2] The ability to directly display sRGB images on a CRT without any lookup greatly helped sRGB's adoption.^{[citation needed]} Gamma also usefully encodes more data near the black, which reduces visible noise and quantization artifacts.

The standard also defines a opto-electronic transfer function (OETF), which defines the conversion of linear light or signal intensity to a gamma-compressed image data. It is a piecewise compound function and has an approximate ${\displaystyle \gamma }$  of 2.2, with a linear portion near zero to avoid an infinite slope which emphasizes signal (camera) noise.^[4][5] Near zero, a ${\displaystyle \gamma ^{1/2.4}}$  power law curve intercepts a straight-line section that leads to zero.

In practice, there is still debate and confusion around whether sRGB data should be displayed with pure 2.2 gamma as defined in the standard, or with the inverse of the OETF. Some display manufacturers and calibrators use the former, while some use the latter. When a power law ${\displaystyle \gamma ^{2.2}}$  is used to display data that was intended to be displayed on displays that use the piecewise function, the result is that the shadow details will be "crushed" towards hard black.^[6]

A straight line that passes through (0,0) is ${\displaystyle y={\frac {x}{\Phi }}}$ , and a gamma curve that passes through (1,1) is ${\displaystyle y=\left({\frac {x+A}{1+A}}\right)^{\Gamma }}$ 

If these are joined at the point (X,X/Φ) then:

${\displaystyle {\frac {X}{\Phi }}=\left({\frac {X+A}{1+A}}\right)^{\Gamma }}$ 

To avoid a kink where the two segments meet, the derivatives must be equal at this point:

${\displaystyle {\frac {1}{\Phi }}=\Gamma \left({\frac {X+A}{1+A}}\right)^{\Gamma -1}\left({\frac {1}{1+A}}\right)}$ 

We now have two equations. If we take the two unknowns to be X and Φ then we can solve to give

${\displaystyle X={\frac {A}{\Gamma -1}},\Phi ={\frac {(1+A)^{\Gamma }(\Gamma -1)^{\Gamma -1}}{(A^{\Gamma -1})(\Gamma ^{\Gamma })}}}$ 

The values A = 0.055 and Γ = 2.4 were chosen^[how?] so the curve closely resembled the gamma-2.2 curve. This gives X ≈ 0.0392857, Φ ≈ 12.9232102. These values, rounded to X = 0.03928, Φ = 12.92321 sometimes describe sRGB conversion.^[7]

Draft publications by sRGB's creators further rounded Φ = 12.92,^[2] resulting in a small discontinuity in the curve. Some authors adopted these incorrect values, in part because the draft paper was freely available and the official IEC standard is behind a paywall.^[8] For the standard, the rounded value of Φ was kept and X was recomputed as 0.04045 to make the curve continuous,^[a] resulting in a slope discontinuity from 1/12.92 below the intersection to 1/12.70 above.

The sRGB specification assumes a dimly lit encoding (creation) environment with an ambient correlated color temperature (CCT) of 5003 K. This differs from the CCT of the illuminant (D65). Using D50 for both would have made the white point of most photographic paper appear excessively blue.^[10][11] The other parameters, such as the luminance level, are representative of a typical CRT monitor.

For optimal results, the ICC recommends using the encoding viewing environment (i.e., dim, diffuse lighting) rather than the less-stringent typical viewing environment.^[2]

The sRGB component values ${\displaystyle R_{\mathrm {srgb} }}$ , ${\displaystyle G_{\mathrm {srgb} }}$ , ${\displaystyle B_{\mathrm {srgb} }}$  are in the range 0 to 1. When represented digitally as 8-bit numbers, these color component values are in the range of 0 to 255, and should be divided (in a floating point representation) by 255 to convert to the range of 0 to 1.

${\displaystyle C_{\mathrm {linear} }={\begin{cases}{\dfrac {C_{\mathrm {srgb} }}{12.92}},&C_{\mathrm {srgb} }\leq 0.04045\\[5mu]\left({\dfrac {C_{\mathrm {srgb} }+0.055}{1.055}}\right)^{\!2.4},&C_{\mathrm {srgb} }>0.04045\end{cases}}}$ 

where ${\displaystyle C}$  is ${\displaystyle R}$ , ${\displaystyle G}$ , or ${\displaystyle B}$ .

These gamma-expanded values (sometimes called "linear values" or "linear-light values") are multiplied by a matrix to obtain CIE XYZ (the matrix has infinite precision, any change in its values or adding non-zeroes is not allowed):

${\displaystyle {\begin{bmatrix}X_{D65}\\Y_{D65}\\Z_{D65}\end{bmatrix}}={\begin{bmatrix}0.4124&0.3576&0.1805\\0.2126&0.7152&0.0722\\0.0193&0.1192&0.9505\end{bmatrix}}{\begin{bmatrix}R_{\text{linear}}\\G_{\text{linear}}\\B_{\text{linear}}\end{bmatrix}}}$ 

This is actually the matrix for BT.709 primaries, not just for sRGB, the second row corresponds to the BT.709-2 luma coefficients (BT.709-1 had a typo in these coefficients).

The CIE XYZ values must be scaled so that the Y of D65 ("white") is 1.0 (X = 0.9505, Y = 1.0000, Z = 1.0890). This is usually true but some color spaces use 100 or other values (such as in CIELAB, when using specified white points).

The first step in the calculation of sRGB from CIE XYZ is a linear transformation, which may be carried out by a matrix multiplication. (The numerical values below match those in the official sRGB specification,^[1][12] which corrected small rounding errors in the original publication^[2] by sRGB's creators, and assume the 2° standard colorimetric observer for CIE XYZ.^[2]) This matrix depends on the bitdepth.

${\displaystyle {\begin{bmatrix}R_{\text{linear}}\\G_{\text{linear}}\\B_{\text{linear}}\end{bmatrix}}={\begin{bmatrix}+3.2406&-1.5372&-0.4986\\-0.9689&+1.8758&+0.0415\\+0.0557&-0.2040&+1.0570\end{bmatrix}}{\begin{bmatrix}X_{D65}\\Y_{D65}\\Z_{D65}\end{bmatrix}}}$ 

These linear RGB values are not the final result; gamma correction must still be applied. The following formula transforms the linear values into sRGB:

${\displaystyle C_{\text{sRGB}}={\begin{cases}12.92C_{\text{linear}},&C_{\text{linear}}\leq 0.0031308\\[5mu]1.055(C_{\text{linear}}^{1/2.4})-0.055,&C_{\text{linear}}>0.0031308\end{cases}}}$ 

where ${\displaystyle C}$  is ${\displaystyle R}$ , ${\displaystyle G}$ , or ${\displaystyle B}$ .

These gamma-compressed values (sometimes called "non-linear values") are usually clipped to the 0 to 1 range. This clipping can be done before or after the gamma calculation, or done as part of converting to 8 bits. If values in the range 0 to 255 are required, e.g. for video display or 8-bit graphics, the usual technique is to multiply by 255 and round to an integer.

Due to the standardization of sRGB on the Internet, on computers, and on printers, many low- to medium-end consumer digital cameras and scanners use sRGB as the default (or only available) working color space. However, consumer-level CCDs are typically uncalibrated, meaning that even though the image is being labeled as sRGB, one can not conclude that the image is color-accurate sRGB.

If the color space of an image is unknown and it is an 8 bit image format, sRGB is usually the assumed default, in part because color spaces with a larger gamut need a higher bit depth to maintain a low color error rate (∆E). An ICC profile or a lookup table may be used to convert sRGB to other color spaces. ICC profiles for sRGB are widely distributed, and the ICC distributes several variants of sRGB profiles,^[13] including variants for ICCmax, version 4, and version 2. Version 4 is generally recommended, but version 2 is still commonly used and is the most compatible with other software including browsers. Version 2 of the ICC profile specification does not officially support piecewise parametric curve encoding ("para"), though version 2 does support simple power-law functions.^[13] Nevertheless, lookup tables are more commonly used as they are computationally more efficient.^{[citation needed]} Even when parametric curves are used, software will often reduce to a run-time lookup table for efficient processing.^{[citation needed]}

As the sRGB gamut meets or exceeds the gamut of a low-end inkjet printer, an sRGB image is often regarded as satisfactory for home printing. sRGB is sometimes avoided by high-end print publishing professionals because its color gamut is not big enough, especially in the blue-green colors, to include all the colors that can be reproduced in CMYK printing. Images intended for professional printing via a fully color-managed workflow (e.g. prepress output) sometimes use another color space such as Adobe RGB (1998), which accommodates a wider gamut. Such images used on the Internet may be converted to sRGB using color management tools that are usually included with software that works in these other color spaces.

The two dominant programming interfaces for 3D graphics, OpenGL and Direct3D, have both incorporated support for the sRGB gamma curve.

OpenGL supports textures with sRGB gamma encoded color components (first introduced with EXT_texture_sRGB extension,^[14] added to the core in OpenGL 2.1) and rendering into sRGB gamma encoded framebuffers (first introduced with EXT_framebuffer_sRGB extension,^[15] added to the core in OpenGL 3.0). Correct mipmapping and interpolation of sRGB gamma textures has direct hardware support in texturing units of most modern GPUs (for example nVidia GeForce 8 performs conversion from 8-bit texture to linear values before interpolating those values), and does not have any performance penalty.^[16]

Amendment 1 to IEC 61966-2-1:1999, approved in 2003, includes the definition of a Y′Cb′Cr′ color representation called sYCC. Although the RGB color primaries are based on BT.709, the equations for transformation from sRGB to sYCC and vice versa are based on BT.601. sYCC uses 8 bits for the components resulting in a range of approximately 0–1 for Y; -0.5–0.5 for C.^[17] The amendment also contains a 10-bit-or-more encoding called bg-sRGB where 0–1 is mapped to -384⁄510...639⁄510, and bg-sYCC using the same number of bits for a range of approximately -0.75–1.25 for Y; -1–1 for C.^[17]

As this conversion can result in sRGB values outside the range 0–1, the amendment describes how to apply the gamma correction to negative values, by applying −f(−x) when x is negative (and f is the sRGB↔linear functions described above). This is also used by scRGB.

The amendment also recommends a higher-precision XYZ to sRGB matrix using seven decimal points, to more accurately invert the sRGB to XYZ matrix (which remains at the precision shown above):

${\displaystyle {\begin{bmatrix}R_{\text{linear}}\\G_{\text{linear}}\\B_{\text{linear}}\end{bmatrix}}={\begin{bmatrix}+3.2406255&-1.5372080&-0.4986286\\-0.9689307&+1.8757561&+0.0415175\\+0.0557101&-0.2040211&+1.0569959\end{bmatrix}}{\begin{bmatrix}X_{D65}\\Y_{D65}\\Z_{D65}\end{bmatrix}}}$ .^[17]

• IEC 61966-2-1:1999 is the official specification of sRGB. It provides viewing environment, encoding, and colorimetric details.
• Amendment A1:2003 to IEC 61966-2-1:1999 describes an sYCC encoding for YCbCr color spaces, an extended-gamut RGB encoding, and a CIELAB transformation.
• sRGB, Characterization Data from ICC
• The fourth working draft (4WD) for 2CD of IEC 61966-2-1 is available online (archived), but is not the complete standard.
• sRGB.com (archived 2003) created by HP — various information on the design, principles, and use of sRGB

• How to interpret the sRGB color space (specified in IEC 61966-2-1) for ICC profiles from ICC
• Conversion matrices for RGB vs. XYZ conversion by Bruce Justin Lindbloom
• Test that shows whether your display is pure 2.2 gamma or sRGB (~2.2 gamma) on Shadertoy
• Will the Real sRGB Profile Please Stand Up? by Elle Stone, which analyzes the inconsistency among sRGB ICC profiles
• Color spaces - REC.709 vs. sRGB from Image Engineering GmbH & Co. KG, with a graph comparing two transfer functions