exposure and resulting luminance

[weasel_bar]

not sure if this is the right forum, but lots of knowledgeable people here, so here goes:

 

As I understand it, luminance of an image on screen varies from 0 (pure black) to 255 (pure white). If the image is color, a formula such as the one below can be used : RGB Luminance value = 0.3 R + 0.59 G + 0.11 B

Lets say im using RGB color space. Each color can take on a value 0-255

If I were to properly expose a picture of a grey card, I think it would end up as RGB (130,131,130).

 

My question is the following:

If I were to change the exposure of the gray card up or down by x number of stops, can we say what the new RGB value would be?

Is there a mathematical conversion for various shades of gray, to convert form stops of exposure to lightness?

Thanks.

[weasel_bar]

As I read my own question, it occurs to me that it cannot be answered as asked. , It depends on the idiosyncratic response curve of the sensor (film, digital, whatever). For example, some slide films will become almost pure white (luminance 255) with 3 stops of over-exposure. Some other films or sensors may have 9 stops of latitude between what is rendered as pure white vs pure black.

[digitaldog]

Correct, it can't be answered (for a number of reasons), one being, luminosity is almost never the word you want unless you are trying to describe the total radiant energy (watts/sec) of a source and is expressed in cd/m^2 (candela per meter squared). 2nd, any RGB values need a defined color space and the encoding can vary.

[rodeo_joe1]

If I were to change the exposure of the gray card up or down by x number of stops, can we say what the new RGB value would be?

With film, difficult, but not impossible, given an apparatus to expose the film to a known series of Lux-second steps, and an accurate densitometer to read the resulting steps after processing.

 

With digital, not so hard. Just make a series of exposures of a lightbox or similar evenly-lit surface. You can use ND filters laid down on the light box to reduce the number of exposures required. Then the eyedropper tool in any image editor gives you the corresponding digital level in the final image.

 

It should follow the response curve of whatever colour space you've set. E.G. 2^1/2.2 per stop for Adobe RGB, something close to that for sRGB, but not so close in the darker areas.

 

But - there's always going to be a deviation from 'perfection' caused by camera body and lens flare, plus normal tolerances on shutter speeds, aperture repeatability, integer rounding, etc. etc.

 

Theoretically, this is what 1/3rd stop (0.1Density) exposure variations should look like:

You can forget about any semblance of accuracy below a density around 2 - there just aren't enough bits to represent the tone values precisely enough, and flare is going to screw those values up further.

[weasel_bar]

I did a series of 40 test exposures on a nikon d3400.

Test conditions:

-incident and reflected metering using Gossen Luna-Pro SBC

-camera in grayscale mode

-sRGB color space

-target uniformly lit

-exposure values given in as stops over/under, with zero exposure anchored at meter reading

-mean luminance (from 0-255) of image calculated as 0.2126*R+0.7152*G+0.0722*B

Findings:

-exposure predicted by hand-held light meter (which is within 1/3 stop of the camera's meter) results in a luminance of around 155-160 (not 128, as I would have though)

-change in luminance with change in exposure is not symmetric. Increases to white much faster than decreases to black. I guess this is expected.

-Below are some paired exposure values along with luminance values

luminance (0-255) : stops over/under light meter exposure

30: -2.9 stops

60 : -1.9 stops

100: -1 stop

130: -0.5 stops

153: 0 stops

195: +0.5 stops

217: +1 stop

240: +1.8 stops

[digitaldog]

Articles on exposing for specifically and only raw:
OneZone – The Optimum Digital Exposure
ETTR
The Optimum Digital Exposure - Luminous Landscape
http://digitaldog.net/files/ExposeForRaw.pdf
The Unbearable Lightness of Mystic "Exposure" Triangle
Red Flowers Photography: Now It is Easy to See the Real Picture
Exposure for RAW vs. Exposure for JPEG
Beware the Histogram
Establishing the in-camera exposure meter calibration point is the way to extract more dynamic range from your camera

[rodeo_joe1]

All you really need to know is that 18% Lambertian (pure matt) Reflectance is 2.5 stops lower than 100% reflectance (not 3 stops, Zone fans!). And that 100% Lambertian reflectance is close to real-world objects such as: white fluffy clouds, clean and newly whitewashed paintwork, fresh powder snow, white porcelain, white copier paper, white linen, white flower petals, etc.

So if your camera histogram doesn't nearly end-stop with a +2.5 stop exposure compensation applied and a standard grey card as the subject, then either the camera metering is off, or your grey card isn't 18% reflective.

 

Any exposure analysis more refined than that really isn't worth the bother.... IMO. Because any decent camera with a14 bit A/D and RAW capture can dig out shadow detail that even your eye isn't aware of at the time of exposure.

 

JPEGs and the sRGB tone curve aren't the be-all and end-all.