8bit monitor theoretical contrast

Question

Imagine perfect monitor that can display pure blacks and is perfectly calibrated.

What would the contrast be between its second darkest shade of black, that is 1,1,1 values for blue green red sub pixel and brightest white with 256,256,256 values for rgb?

Please note that I mean second darkest shade of black, that means the pixel is active and light shines from it albeit very weakly. I specifically dont want people to mistake this with the darkest shade of black ( rgb 0,0,0 ) which means the pixels are completly turned off and no light exits them.

This is becose with monitors with perfect black, no matter the peak brightness value, the contrast is always infinite. So that is why I ask about second darkest black, not the total black.

I know SDR monitors have 2.2 gamma curve target and have 256 possible values of becose they are 8bit. I know 8 bit has 256-1 contrast ratio assuming the brightness change is the same between all the bit values but since the encoding of the digital 8 bit format is not linear like RAW files, I have no idea what contrast/dynamic range 8bit is supposed to have becose I dont know how much are the individual bit values spaced apart.

If this theoretical perfect SDR 8 bit monitor had peak brightness of 100 cd/m2, how bright would the second darkest shade of black be?

Answer 1

The contrast between the brightest and the second darkest shade in a 8-bit monitor can be as high as you want it to be, depending on your personal configuration and the intended color space. However, if you want to stick to sRGB then the contrast is 3294.6:1 because that's how the sRGB gamma is defined:

linear_brightness(1/255) = (1/255) / 12.92 = 1 / (255*12.92) = 1 / 3294.6

Answer 2

DEFINITIONS:

1. CONTRAST: At the most basic, contrast is a defined relationship between two stimuli. But WHAT relationship and HOW derived is a subject that can take a couple chapters in a textbook to describe. If you want more, Google Weber Contrast, Michelson Contrast, and CIELAB Difference.
2. Brightness is a perception, not a measure.
3. Human perception is nonlinear relative to light, and also to spectral intensities.
4. Luminance is a LINEAR measure of LIGHT, spectrally weighted. It is either relative Y (0-1 as in Y from CIEXYZ) or absolute L, as in 100 cd/m².
5. Perceptual Lightness is a non-linear measure of light, but is intended as "perceptually uniform" i.e. linear in regards to perception. L* (Lstar, not to be confused with L for Linear Luminance) from CIELAB (Lab*) is one such measure of perceptual lightness.
6. Gamma: A curve used to encode image information to take best advantage of a given data space, taking advantage of the non linear aspect of human perception.
7. Perfect black: there is no such thing, especially not in a monitor that is turned on. But if you want to discuss "theoretical black" then okay.

PAINT IT BLACK

In a real world environment, the actual "black" level (#000) including modest flare will typically be around 1 cd/m², at least that's a good approximation for most purposes.

But if your question is, what is the luminance of #010101 if #FFF = 100 cd/m²?

In that case, #010101 = 0.0303526983548837 cd/m^2. If you use the piecewise sRGB linearization, as discussed in this answer I posted on StackOverflow.

However, monitors more typically use a more "pure" gamma function. And it's not necessarily 2.2 - it's how you have ADJUSTED it. But we'll go with 2.2 for maths sake. In the case of a simple 2.2 gamma, and the imaginary "perfect black" then: #010101 = 0.000507705190066176 cd/m^2

The Contrasts:

Using the sRGB piecewise maths: Y_Lo=(1/255)/12.92

As this is normalized for 0-1, multiply by 100, i.e. Y_Lo=((1/255)/12.92)*100

For Y_Hi = 100.0 & Y_Lo = 0.0303526983548837 Then:

• Simple Ratio (Y_Hi / Y_Lo): 3294.6:1
• Weber Contrast ((Y_Hi - Y_Lo) / Y_Hi): 99.9696473016451%
• Michelson Contrast ((Y_Hi - Y_Lo) / (Y_Hi + Y_Lo)): 99.9393130234252%

Using the simple 2.2 gamma maths: Y_Lo=(1/255)^2.2

As this is normalized for 0-1, multiply by 100, i.e. Y_Lo=((1/255)^2.2)*100

For Y_Hi = 100.0 & Y_Lo = 0.000507705190066176 Then:

• Simple Ratio (Y_Hi / Y_Lo): 196964.699:1
• Weber Contrast ((Y_Hi - Y_Lo) / Y_Hi): 99.9994922948099%
• Michelson Contrast ((Y_Hi - Y_Lo) / (Y_Hi + Y_Lo)): 99.9989845947751%

(There's a potential rounding error difference of ~0.000000000030352698380 depending on if you use the rounded coefficients).

Answer 3

The perceived performance can be much better than 8-bits because a whole lot of dithering may be going on. All plasma panels and DLPs (digital micromirrors) are 1-bit devices, but thanks to pulse code modulation and forms of dithering a.k.a. noise shaping a.k.a. error diffusion they can produce a fairly decent greyscale (to our slow and unsharp human eyes). It's easy to make a 6-bits image look as good as 10-bits. Sometimes the noise on the original image is already enough for this. 8-bits video was specified for the amount of analog noise of that time, more bits would only reproduce more precise noise.

The silver grains of "analog" photography are binary (black on white) too, but given enough grains and a random distribution they can make a pretty analog photo too.