http://www.normankoren.com/makingfineprints1A.html#Gammabox

https://en.wikipedia.org/wiki/Gamma_correction

http://www.photoscientia.co.uk/Gamma.htm

https://www.w3.org/Graphics/Color/sRGB.html

http://www.eizoglobal.com/library/basics/lcd_display_gamma/index.html

https://forum.reallusion.com/PrintTopic308094.aspx

Basically, gamma is the relationship between the brightness of a pixel as it appears on the screen, and the numerical value of that pixel. Generally Gamma is just about defining relationships.

Three main types:
– Image Gamma encoded in images
– Display Gammas encoded in hardware and/or viewing time
– System or Viewing Gamma which is the net effect of all gammas when you look back at a final image. In theory this should flatten back to 1.0 gamma.

Our eyes, different camera or video recorder devices do not correctly capture luminance. (they are not linear)
Different display devices (monitor, phone screen, TV) do not display luminance correctly neither. So, one needs to correct them, therefore the gamma correction function.

The human perception of brightness, under common illumination conditions (not pitch black nor blindingly bright), follows an approximate power function (note: no relation to the gamma function), with greater sensitivity to relative differences between darker tones than between lighter ones, consistent with the Stevens’ power law for brightness perception. If images are not gamma-encoded, they allocate too many bits or too much bandwidth to highlights that humans cannot differentiate, and too few bits or too little bandwidth to shadow values that humans are sensitive to and would require more bits/bandwidth to maintain the same visual quality.

https://blog.amerlux.com/4-things-architects-should-know-about-lumens-vs-perceived-brightness/

cones manage color receptivity, rods determine how large our pupils should be. The larger (more dilated) our pupils are, the more light enters our eyes. In dark situations, our rods dilate our pupils so we can see better. This impacts how we perceive brightness.

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

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. Fortunately this second step (the “display gamma”) is automatically performed by your monitor and video card. The following diagram illustrates how all of this fits together:

Display gamma
The display gamma can be a little confusing because this term is often used interchangeably with gamma correction, since it corrects for the file 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.

Gamma encoding of images is used to optimize the usage of bits when encoding an image, or bandwidth used to transport an image, by taking advantage of the non-linear manner in which humans perceive light and color. Human response to luminance is also biased. Especially sensible to dark areas.
Thus, the human visual system has a non-linear response to the power of the incoming light, so a fixed increase in power will not have a fixed increase in perceived brightness.
We perceive a value as half bright when it is actually 18% of the original intensity not 50%. As such, our perception is not linear.

You probably already know that a pixel can have any ‘value’ of Red, Green, and Blue between 0 and 255, and you would therefore think that a pixel value of 127 would appear as half of the maximum possible brightness, and that a value of 64 would represent one-quarter brightness, and so on. Well, that’s just not the case.

Pixar Color Management
https://renderman.pixar.com/color-management

– Why do we need linear gamma?
Because light works linearly and therefore only works properly when it lights linear values.

– Why do we need to view in sRGB?
Because the resulting linear image in not suitable for viewing, but contains all the proper data. Pixar’s IT viewer can compensate by showing the rendered image through a sRGB look up table (LUT), which is identical to what will be the final image after the sRGB gamma curve is applied in post.

This would be simple enough if every software would play by the same rules, but they don’t. In fact, the default gamma workflow for many 3D software is incorrect. This is where the knowledge of a proper imaging workflow comes in to save the day.

Cathode-ray tubes have a peculiar relationship between the voltage applied to them, and the amount of light emitted. It isn’t linear, and in fact it follows what’s called by mathematicians and other geeks, a ‘power law’ (a number raised to a power). The numerical value of that power is what we call the gamma of the monitor or system.

Thus. Gamma describes the nonlinear relationship between the pixel levels in your computer and the luminance of your monitor (the light energy it emits) or the reflectance of your prints. The equation is,

Luminance = C * value^gamma + black level

– C is set by the monitor Contrast control.

– Value is the pixel level normalized to a maximum of 1. For an 8 bit monitor with pixel levels 0 – 255, value = (pixel level)/255.

– Black level is set by the (misnamed) monitor Brightness control. The relationship is linear if gamma = 1. The chart illustrates the relationship for gamma = 1, 1.5, 1.8 and 2.2 with C = 1 and black level = 0.

Gamma affects middle tones; it has no effect on black or white. If gamma is set too high, middle tones appear too dark. Conversely, if it’s set too low, middle tones appear too light.

The native gamma of monitors– the relationship between grid voltage and luminance– is typically around 2.5, though it can vary considerably. This is well above any of the display standards, so you must be aware of gamma and correct it.

A display gamma of 2.2 is the de facto standard for the Windows operating system and the Internet-standard sRGB color space.

The old standard for Mcintosh and prepress file interchange is 1.8. It is now 2.2 as well.

Video cameras have gammas of approximately 0.45– the inverse of 2.2. The viewing or system gamma is the product of the gammas of all the devices in the system– the image acquisition device (film+scanner or digital camera), color lookup table (LUT), and monitor. System gamma is typically between 1.1 and 1.5. Viewing flare and other factor make images look flat at system gamma = 1.0.

Most laptop LCD screens are poorly suited for critical image editing because gamma is extremely sensitive to viewing angle.

More about screens

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

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.

About black level (brightness). Your monitor’s brightness control (which should actually be called black level) can be adjusted using the mostly black pattern on the right side of the chart. This pattern contains two dark gray vertical bars, A and B, which increase in luminance with increasing gamma. (If you can’t see them, your black level is way low.) The left bar (A) should be just above the threshold of visibility opposite your chosen gamma (2.2 or 1.8)– it should be invisible where gamma is lower by about 0.3. The right bar (B) should be distinctly visible: brighter than (A), but still very dark. This chart is only for monitors; it doesn’t work on printed media.

The 1.8 and 2.2 gray patterns at the bottom of the image represent a test of monitor quality and calibration. If your monitor is functioning properly and calibrated to gamma = 2.2 or 1.8, the corresponding pattern will appear smooth neutral gray when viewed from a distance. Any waviness, irregularity, or color banding indicates incorrect monitor calibration or poor performance.

Another test to see whether one’s computer monitor is properly hardware adjusted and can display shadow detail in sRGB images properly, they should see the left half of the circle in the large black square very faintly but the right half should be clearly visible. If not, one can adjust their monitor’s contrast and/or brightness setting. This alters the monitor’s perceived gamma. The image is best viewed against a black background.

This procedure is not suitable for calibrating or print-proofing a monitor. It can be useful for making a monitor display sRGB images approximately correctly, on systems in which profiles are not used (for example, the Firefox browser prior to version 3.0 and many others) or in systems that assume untagged source images are in the sRGB colorspace.

On some operating systems running the X Window System, one can set the gamma correction factor (applied to the existing gamma value) by issuing the command xgamma -gamma 0.9 for setting gamma correction factor to 0.9, and xgamma for querying current value of that factor (the default is 1.0). In OS X systems, the gamma and other related screen calibrations are made through the System Preference

https://www.kinematicsoup.com/news/2016/6/15/gamma-and-linear-space-what-they-are-how-they-differ

Linear color space means that numerical intensity values correspond proportionally to their perceived intensity. This means that the colors can be added and multiplied correctly. A color space without that property is called ”non-linear”. Below is an example where an intensity value is doubled in a linear and a non-linear color space. While the corresponding numerical values in linear space are correct, in the non-linear space (gamma = 0.45, more on this later) we can’t simply double the value to get the correct intensity.

The need for gamma arises for two main reasons: The first is that screens have been built with a non-linear response to intensity. The other is that the human eye can tell the difference between darker shades better than lighter shades. This means that when images are compressed to save space, we want to have greater accuracy for dark intensities at the expense of lighter intensities. Both of these problems are resolved using gamma correction, which is to say the intensity of every pixel in an image is put through a power function. Specifically, gamma is the name given to the power applied to the image.

CRT screens, simply by how they work, apply a gamma of around 2.2, and modern LCD screens are designed to mimic that behavior. A gamma of 2.2, the reciprocal of 0.45, when applied to the brightened images will darken them, leaving the original image.