Does it mean that when we observe the display it will always have a brightness curve of 1/1.25? Is there any reference that introduces this part?
If you read a little closer, it says that when viewing a CRT which is gamma corrected to 2.5, so that it "reproduces physical luminance correctly," the viewer subjectively prefers a 1/1.25 gamma correction in the other direction for increased contrast; resulting in a gamma 2.0 curve as being optimal for a CRT... subjectively and situationally variable.
It goes on to explain that 2.2 is the standard and how it relates (falling in-between 2.5 and 2.0).
In terms of the visual system, a human requires a log2 (2x) change in luminance to be perceived as an equivalent change... which is why photographic exposure is logarithmic. But, of course, human vision and preference does vary by individual; which makes the whole gamma correction thing a bit arbitrary.
To me, the key phrase is
the visual system of the viewer
Because it took me many years to understand that the equations of gamma correction describe a curve fitted to values measured experimentally in experiments using human test subjects.
The equations of gamma correction are not deduced mathematically from axioms, corollaries, lemmas, or first principles.
They are tools that allow mathematical reasoning about the response of human brains to visual stimulus, but the responses of human brains have many non-linearities and dependencies because human brains are meaty wetware not metal machines or binary bits.
The math of gamma correction facilitates engineering decisions. It is not studied in university mathematics departments.
1.25 is a convenient and easy to work with number that is good enough in the vast majority of engineering applications. I suspect it is a statistical certainty that the actual response of my visual system is not 1.25 most of the time. But I could be wrong.
Photography was young in the early 1900’s. Two Scientist, Hurter and Driffield studied at length how photo film responded to light. They constructed devices to expose film with precision and measured the blackening that occurred when developed. They graphed this action.
The graph depicts 1/2 of a bell curve.
Note the straight line that sweeps upward. This curve displays the amount of blackening with density minimum on the left and density maximum on the right. The upward slope angle is found and then using trigonometry, the tan value of this angle. In this case the angle is 38 degrees tan = 0.8. This is the slope of the Stright Line we call this gamma. It tells us the contrast of this film material. If the slope angle is 45 degrees, the tan = 1 thus gamma = 1. This proved to be too contrasty for pictorial films. 0.8 gamma is typical of for pictorial films.
This graph is a black & white negative film. Its range of tones, Dmin to Dmax is about 10 f-stops. When we print this negative on photo paper, we call this a black & white print.
Now we see this print (on paper) by reflected light from an adjacent lamp. The light from the lamp plays on the print, transverse the image (metallic silver), hits the white under coat (baryta layer) and is reflected back to our eyes. The key here, the light makes two transits through the image (on paper) to get to our eye.
When printed on paper, this negative image becomes a positive image. It’s graph will be a mirror image however the steepness of the upward swing will have a gamma of 2 or greater (quite steep).
Before you cast-off this stuff – The digital image and print evolved from chemical photography as did most of the terminology. The gamma of the computer screen evolved from this science.
A image displayed by projection or on a TV or computer screen also needs contrast control. Gamma 2.2 delivers a suitable contrast scale. For some monitors, this is too contrasty, 1.8 is somewhat less contrasty. See gray scale.
When we take pictures, as a rule of thumb, your desire is to display a faithful image. The camera records and we then we display. This displayed image might be a paper print, or an image projected on a screen, or on a computer monitor / TV. In order to display a respectable image, the range of tones (scale / contrast) must be tweaked. In other words different display method require a contrast tweak. As an example, step 7 of a Kodak Gray Scale is a match of a Gray Card. This is a matte surface with an 18% reflectivity. The 18% value is about the center of the gray scale.
More than 100 years ago photo scientists learned that they could better understand photographic reproduction if they graphed the image. This is the twin science of making test materials (sensitometry) and measuring the results (densitometry). A key tool is a calibrated gray scale.
Again, looking at step 7, it has a density of 0. 75. This value is logarithmic notation base 10. Logarithmic is likely a mystery to most but scientists think it’s a marvelous way graph photographic blacking. OK 0.75 density can be converted to ordinary numbers 10^0.75 = 5.6234. The reciprocal of this is 0.18 = 18% the gray card value that we use to calibrate our instruments.
We can convert this value to RGB values. An 8-bit computer monitor can display 256 shades of gray this is the minimum that con produce a smooth gray scale. To find the RGB value for 18% we multiply 255 X 0.1778 = 45. Because of the computer monitor’s contrast, a correction must be applied to force the image to look good to our eyes. Back to the density of patch 7 = 0.75. Let’s apply a correction factor of 2.2. Thus 0.75 ÷ 2.2 = 0.3409. This is a log number. Now converting to standard notation 10^0.3509 = 2.1923. We can compute the RGB value for 2.1923 thus 255 ÷ 2.1923 = 116
Note on the calibrated Kodak Gray Scale, step 7 using 2.2 gamma correction = 116, this is RGB value for step 7. This gobbledygook forces step 7 to look like middle gray on a computer monitor. Note different display devices will require a different correction factor based on their characteristics.
Most photo films have a gamma of 0.8. Most digital cameras have a gamma of 1. In this case we are applying a fudge factor of 2.2 for a typical computer monitor.