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w Three vsearchr, by the time we can see this data, it has been gamma encoded, and we see that 50% at 255x(0.5 ^ 1/2.2) = 187 on the histogram. We see one stop underexposure to be at 187 (about 73% of 255), and not at 128 (50%).
The 18% gray card should come out at 18%, or at 117, which is about 46% of the 255 range after gamma encoding, which is near enough the midpoint that it confuses us, but the coincidental reasons are quite different. The midpoint 128 has been moved up to 187 at 73% now anyway. The ANSI standard for light meters is 12% reflectance, not 18%. Kodak says metering from their 18% gray card should be compensated with 1/2 stop more exposure (which converts it to 12%). All RGB images are gamma encoded, we never see anything else. See Adobe PDF Link. Their chart shows gamma stops as five equal steps, which is only a crude approximation. Perhaps that bypasses their need to explain that the actual stops (of underexposure, down from 255) computed for gamma 2.2 are at:
0 stop = (1.0 ^ 1/2.2) = 1, x255 = 255 100%
-1 stop = (0.5 ^ 1/2.2) = 0.73, x255 = 187 73% of 255 full scale
-2 stops = (0.25 ^ 1/2.2) = 0.54, x255 = = 137 54%
18% Gray card = (0.18 ^ 1/2.2) = 0.46, x255 = 117 46%
12% Gray card = (0.12 ^ 1/2.2) = 0.38, x255 = 97 38%
-3 stops = (0.125 ^ 1/2.2) = 0.39, x255 = 100 39%
-4 stops = (0.0625 ^ 1/2.2) = 0.29, x255 73 29%
-5 stops = (0.0312 ^ 1/2.2) = 0.21, x255 54 21%
-6 stops = (0.0156 ^ 1/2.2) = 0.15, x255 39 15%
-7 stops = (0.00781 ^ 1/2.2) = 0.11, x255 29 11%
-8 stops = (0.00390 ^ 1/2.2) = 0.08, x255 21 8%