Gamma correction

A gamma characteristic is a power law relationship that approximates the relationship between the encoded luminance in a television system and the actual desired image brightness. Computer graphics systems that require a linear relationship between these quantities use gamma correction.

A cathode ray tube, for example, converts a video signal to light in a nonlinear way, because the electron gun it contains is a nonlinear device. The light intensity L is related to the source voltage V_S by the following formula:

L ∝ (V_S)^γ

where γ is the Greek letter gamma. For a CRT, γ is about 2.2. For simplicity, consider the example of a monochrome CRT. In this case, when a video signal of 0.5 (representing mid-grey) is fed to the display, the luminance is about 0.21 (resulting in a dark grey). Pure black (0.0) and pure white (1.0) are the only shades that are unaffected by gamma.

To compensate for this effect, the inverse transfer function (gamma correction) is sometimes applied to the video signal so that the end-to-end response is linear. In other words, the transmitted signal is deliberately distorted so that, after it has been distorted again by the display device, the viewer sees the correct brightness. The inverse of the function above is:

V_C ∝ (V_S)^(1/γ)

where V_C is the corrected voltage and V_S is the source voltage (e.g. from a camera or VCR). In our CRT example 1/γ is 1/2.2 or about 0.45.

A colour CRT receives three video signals (red, green and blue) and in general each colour has its own value of gamma, denoted γ_R, γ_G or γ_B. However, in simple display systems, a single value of γ is used for all three colours.

Other display devices have different values of gammas: for example, a Game Boy Advance display has a gamma between 3 and 4 depending on lighting conditions.

For a tutorial on gamma characteristics in computer graphics, see http://www.w3.org/TR/PNG-GammaAppendix.html .