Gamma Calibration

一. What is gamma function?

Gamma is an important but seldom understood characteristic of virtually all digital imaging systems. It defines the relationship between a pixel's numerical value and its actual luminance.

Our eyes (a "nonlinear" relationship) do not perceive light the way cameras (a "linear" relationship) do.

Compared to a camera, we are much more sensitive to changes in dark tones than we are to similar changes in bright tones. There's a biological reason for this peculiarity: it enables our vision to operate over a broader range of luminance. Otherwise the typical range in brightness we encounter outdoors would be too overwhelming.

二. Gamma Encoding & Correction

A gamma encoded image has to have "gamma correction" applied when it is viewed — which effectively converts it back into light from the original scene. In other words, the purpose of gamma encoding is for recording the image — not for displaying the image.

三. Display Gamma

This is the gamma that you are controlling when you perform monitor calibration and adjust your contrast setting. Fortunately, the industry has converged on a standard display gamma of 2.2, so one doesn't need to worry about the pros/cons of different values. 

Recall that the display gamma compensates for the image file's gamma, and that the net result of this compensation is the system/overall gamma. For a standard gamma encoded image file (—), changing the display gamma (—) will therefore have the following overall impact (—) on an image:

CRT Monitors. Due to an odd bit of engineering luck, the native gamma of a CRT is 2.5 — almost the inverse of our eyes. Values from a gamma-encoded file could therefore be sent straight to the screen and they would automatically be corrected and appear nearly OK. However, a small gamma correction of ~1/1.1 needs to be applied to achieve an overall display gamma of 2.2. This is usually already set by the manufacturer's default settings, but can also be set during monitor calibration.

LCD Monitors. LCD monitors weren't so fortunate; ensuring an overall display gamma of 2.2 often requires substantial corrections, and they are also much less consistent than CRT's. LCDs therefore require something called a look-up table (LUT) in order to ensure that input values are depicted using the intended display gamma (amongst other things). See the tutorial on monitor calibration: look-up tables for more on this topic.

以上来自https://www.cambridgeincolour.com/tutorials/gamma-correction.htm

四. Calibration of a color monitor for visual psychophysics(DOI: 10.3758/BF03204528)

CRTs are, however, not perfect; they suffer from the effects of temporal instability, spatial variability, lack of phosphor constancy, gun interdependence, and gun nonlinearity. 

A major disadvantage of the CRT is that the maximum light output achievable is limited.

An ideal CRT should provide primaries that:

① are able to be controlled in a predictable and precise (preferably linear) manner, from zero to maximum intensity (gun linearity);

② are independent, so that each channel is not influenced by the actions of any of the others (gun independence) ; 

③ maintain a constant relative spectral distribution as intensity is varied (phosphor constancy); 

and ④ are widely separated in color space in order to provide a large gamut of visible colors.

Precise gun linearity is difficult to achieve because the channels follow a gamma function.

A stable luminance was achieved only after some 60 and 150 min following warm  (restart after 20 min off following a 3-h on period) and cold starts (offperiod> 14 h, overnight), respectively.

A more flexible approach involves the generation of compensating gamma "look-up tables." Look-Up tables (LUTs) are data tables that are called upon at one extra stage of processing in order to achieve the gamma correction.

Φ(E) is some physical measure of output (e.g., luminance), E is the applied voltage, α is the dark light of the system，β is a constant, and γ is the exponent of the power function.

There is one LUT for each gun, because each gun has its own characteristics. Because the calibration of a CRT has been shown to change over short periods of time (Cowan, 1987), it is necessary to have a procedure for maintaining accurate and up-to-date LUTs with minimal fuss. 

Once gamma compensation is applied to the LUTs, the resulting input-to-output relationship is fairly linear.