Luminance of a grayscale image

eugen · Apr 17, 2012

Dear forum,
I hope this isn't too far-off as it isn't strictly a photography question but very much related and I think if anyone knows the answer, it might be here.

So, I want to present a completely uniform area of a grayscale-colour on my computer screen. The maximum luminance of my computer screen is 200 cd/m². The luminance for my area is also specified in cd/m². While there are many formulas for calculating some kind of relative luminance for a given colour-system, I couldn't find a formula telling me how to convert these to cd/m². Is it a linear relationship, for example, that when 256/256/256(in RGB) amount to 200 cd/m² then 128/128/128 amount to 100 cd/m², or is there a more complicated magic formula?

Thank you

Big Mike · Apr 17, 2012

Welcome to the forum.

Try to contact forum member 'Garbz'. He could probably give you some detailed information.

Helen B · Apr 17, 2012

Is your monitor profiled, and if so, what gamma is it set to? How accurate do you need the result to be? How consistent across the screen? How consistent with viewing angle? Do you have a camera or light meter that could be used to take relative measurements (that would be the easiest way)?

The numbers in an sRGB image will not be translated linearly to luminance because they should be in a variable gamma colour space that is more logarithmic than linear, except in the darkest values.

eugen · Apr 17, 2012

Yes, the gamma is apparently set to 2.2 right now. Desired luminances lie in the range of 20 to 45 cd/m², so the deviances should not be much larger than 1-2 cd/m², but I do not know if that is feasible, yet. The critical areas here have a size of about 1 by 3 degrees of visual angle. The viewing angle of the observer will be more or less fixed, looking centrally on these areas. I will try to acquire a light meter if possible, but it might take a while...

KmH · Apr 17, 2012

This sure isn't a Beginner's forum topic. :lmao:

eugen · Apr 17, 2012

Oh ok, it's just that I'm a complete beginner in these things myself, so I posted it there

On a related note to what was posted earler...would it make my life much easier if I just turned off gamma correction completely? Is that even easily doable?

Garbz · Apr 20, 2012

As mentioned already there's various issues including the calibration of your display the uniformity of the display (something that is actually harder than it sounds), and what colour values you follow. Then there's actually more than just the gamma of the monitor to take into account but also the expected gamma of the sRGB space.

Honestly by far the easiest way to do this would be to measure it and really it is the only way to be certain. But I assume that the reason you're here is because you can't measure it. So since the maths would have been more effort than simply doing an experiment here's some results:

My monitor is calibrated to a gamma 2.2 curve. Monitor was set to a brightness of 200cd/m^2 but CAVEAT: I did not recalibrate after I changed my brightness setting. None the less these values will give you a good idea:

Helen B · Apr 20, 2012

Those values look to be slightly under the theoretical values for a gamma of 2.2, with a difference of between about 1 cd/m^2 at the low end (ie sRGB 90) and at least 3 cd/m^2 at the high end (ie sRGB 134). If you really want an accuracy of 1 to 2 cd/m^2 then I suggest that you measure your monitor. My previous suggestion of using a camera meter might not achieve that accuracy easily. If you assume that the monitor's maximum brightness really is 200 cd/m^2 then you can easily calculate, in stops, the change in brightness between 200 cd/m^2 and whatever brightness you want. At the upper end of your required brightness you are looking for an accuracy of about 0.06 of a stop, and at the lower end about 0.14 of a stop. That's quite a tall order. How important is that level of accuracy?