gamma correction on screens

[Thierry]

Hi,

I am currently correcting an article about color mgt and I think that there
is a small mistake. I need your help.
I speak about the gamma correction in graphic cards.

There is for example a relation between luminance (X-axis) and brightness
(Y-axis) reprenseted by a logaritmic curve which slope is 0.45. This
non-linear relation means that a 50% of luminance will be seen as a
brightness of 75 %. This law seems correct.

Now most screen reproduce a gamma between 1.8 and 2.2, or say in another
words, the RGB signal is equivalent to the input sigal at power gamma. Here
is the problem.
Is it true that to reproduce the non-linear response of the eye on PC,
engineers apply a power 2.5 law where voltage is modulated vs Luminance
power 0.45 ? (cf gamma correction CIE Rec.709).
If I calculate log 2.5, I get 0.39 not 0.45. So is my sentence correct if I
use log 2.8 instead of 2.5 (to get 0.45) ?
Or both values of 2.5 and 0.45 are fixed in algorithms used in graphic cards
or by convention.?

Thanks in advance

Thierry

 

[Bob Myers]

There is for example a relation between luminance (X-axis) and brightness
(Y-axis) reprenseted by a logaritmic curve which slope is 0.45. This
non-linear relation means that a 50% of luminance will be seen as a
brightness of 75 %. This law seems correct.

I can't be certain what's going on in the particular graphics
card in question, but in general "gamma" and "gamma correction"
(which is rarely, if ever, actually a "correction") are very commonly
misunderstood subjects.

"Gamma" is the exponent of a function of the form

Y = KI^(gamma),

which is a simplified model for how the luminance (Y) of a display
varies with the input signal level (I). (This is technically a "power
function," not a logarithmic function or an exponential function - the
latter term is commonly misused here, but an exponential function
really has the form Y = e^x.) The "K" in this function is a constant
of proportionality, very often (in discussions of display "gamma")
referred to as the "gain."

CRT displays, by virtue of the physics of the tube itself, theoretically
will behave per the above function with a "gamma" value of right
around 2.5. (Measured "gamma" values rarely hit this number
exactly, in part due to the fact that this simple model assumes that
the display has exactly zero luminance at a zero input level - which
is rarely if ever the case, especially with a properly-adjusted CRT
monitor.)

By an odd coincidence, this curve is almost exactly the inverse of
the "response curve" of the human eye - the curve that relates the
perception of "brightness" to the light level. In other words, our
eyes themselves are non-linear; we perceive changes in lower light
levels (within the current range of adaptation) as being greater than
the identical (objective) change at the higher end of the adapted range.
(Which makes sense if you stop and think that we've evolved vision
that is, among other things, adapted to spotting possible threats in
the shadows!) What this combination - the "gamma" curve of the
CRT display and the curve that describes the response of the visual
system, taken together - boils down to is that linear changes in the
input signal level to a CRT display will be *perceived* as linear
changes in the "brightness." (Which does NOT mean that they result
in linear changes of *luminance*.)

If you "pre-correct" (if "correct" is the right word here) the input
signal for the response of the display, then the light output
(luminance) will increase more rapidly than it "should" (than it
would normally) at the low end, and slower at the high end, vs.
the signal level. That means that the darker shades of the image
will be effectively boosted, bringing details here "out of the
shadows." That may or may not be the most "accurate" or
"natural" thing to be doing for the image - much here depends on
just what the SOURCE of the image content is (i.e., was it
synthesized on the spot, does it come from a video camera,
etc.). But some "correction" here may be preferable to the viewer,
which is more often the goal of such things (as opposed to actually
improving the objective "accuracy" of the image).

There's a good deal more to the subject than this, but that may
do for an introduction. One other point to note is that non-CRT
displays, and especially the LCD, do not provide a CRT-like
"gamma" response naturally; matching the CRT's behavior requires
some changes to the natural response of the display device,
generally applied in the "front end" of the monitor. (LCDs, for
instance, naturally have a more "S-shaped" response - the curve
starts out somewhat like the CRTs, but then after the midpoint
starts to flatten out as the "full on" state is approached.)

Bob M.