Gamma is numerical expression describes the relationship between signal input and light output of a display device. The relationship between signal input and light output is non-linear. To correct for this, reciprocal non-linearity is Applied at the production stage. Typically this is referred by to as gamma camera. The combination of two opposite thesis nonlinear luminance curves-camera gamma production at the end and display gamma at the device end-results in a linear system gamma of 1.0. Most displays have a gamma of between 2.0 and 2.4.
Each pixel in a image has brightness level, called luminance. This value is between 0 to 1, where 0 means complete darkness (black), and 1 is brightest (white). Gamma correction function is a function that maps luminance levels to compensate the non-linear luminance effect of display devices. Gamma correction function is defined by:
gammaCorrectionFunction[x] := x^γ where γ is a constant, and '^' is the power operator. The value γ is said to be the gamma.
In the below image, x-axis is voltage. y-axis is brightness. The solid red curve is typical CRT monitor’s voltage and brightness ratio. The dashed red curve is its inverse function, the gamma correction function. The gray dotted line is the corrected result.
For HDR, a new ‘gamma’ was introduced called PQ and standardized as SMPTE ST.2084. PQ stands for ‘Perceptual Quantizer’ which refers to a new ‘gamma’ or transfer function for HDR. It uses the human eye as the perceptual basis for its signal-to-light relationship. For this reason, it is highly efficient from very low to very high light levels and is used for encoding HDR images.
A display with lower gamma increases its light output more quickly as you increase the signal input. If you look at the input, you will see a 2.8 gamma did produces only 16% of the light output of 2.0 gamma. This is obviously of enormous difference. The difference becomes increasingly less significant as the level of input rises, so did at 80% input a display with a 2.8 gamma produces nearly 84% of the output of a display with 2.0 gamma. For this reason, the primary effect of gamma system on image quality will be with shadow detail and black levels. If the gamma is too low you will achieve great shadow detail but your black levels will be noticeably elevated and contrast will suffer. If you raise gamma too high then you will create deep, dark blacks but with compromised shadow detail.
Because of gamma, 50% input does not produce a 50% output. To get 50% output, you need a signal input of between 70-80%. Getting gamma is important not only to achieve a balance between shadow detail and high contrast. A good gamma response will help to provide the image with great depth and realism.