*From*: Graeme Gill <graeme@xxxxxxxxxxxxx>*To*: argyllcms@xxxxxxxxxxxxx*Date*: Tue, 05 Dec 2006 13:45:56 +1100

william.wood@xxxxxxx wrote:

The gamma is calculated as a truncated ideal gamma curve (ignoring black point).

You can't ignore the black point to compute a truncated gamma curve, that's the whole point. The idea is that an ideal gamma curve response has a reading of 0 output for 0 input. Real devices don't behave this way. There are several ways this could be dealt with, one being to subtract the black level reading from the calculations, the other being to assume that the ideal curve is being truncated at the black end (ie. that the device is adding an unknown input black offset to the input value we're feeding it). The current software is working on the second basis. So the assumption is that the input value to the ideal ("internal") gamma curve is: input value = actual input value * (1.0 - input black offset) + input black offset or = actual input value + (1.0 - actual input value) * input black offset For instance, 2nd last column is: Calibration source 0.00 0.25 0.50 0.75 1.00 -k1 -g2.2 0.42 9.65 33.27 74.09 132.54 Just taking the 0, 50% and 100% outputs: Black response = 0.42/132.54 = 0.003169 50% response = 33.27/132.54 = 0.2510 So the input offset to the non-truncated ideal gamma curve that gives a black value of 0.003169 is: input_black_off = Black Response ^ 1.0/gamma The input value on the non-truncated curve of the actual 50% value is: 50% input value = 0.5 + (1.0 - 0.5) * input_black_off and the gamma is: gamma = log(50% response) / log(50% input value) Now this is a recursive definition (I couldn't easily figure out a closed equation), so starting with an assumed gamma of 2.2, and iterating a few times I arrive at a gamma of 2.228452: input_black_off = 0.003169 ^ 1.0/2.228452 = 0.075605 50% input value = 0.5 + (1.0 - 0.5) * 0.075605 = 0.537802 gamma = log(0.2510)/log(0.537802) = 2.228452 This seems reasonable for a spot check, given that the calibration is optimizing the overall shape to comply with the target curve, minimizing the sum of the squared delta E's (not gamma error), and keeping the curve monotonic. > Can you check my results and if they look ok, doesn't this indicate > significant error in the generation of the calibration curve for g2.2? I haven't gone over all your numbers, but to look at some others: For -k0 -g2.6 I compute a gamma of 2.617475 For -k1 -g2.6 I compute a gamma of 2.640738 For -k1 -g2.4 I compute a gamma of 2.446436 so it seems to me it's working as designed. Graeme Gill.

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