Hi all,
I am wondering how the "ideal density" is calculated for (e.g. 21) greyscale steps. I understand that the density is the log of the reciprocal of reflection...
Let's assume the following
Relative reflection density:
Paper white: 0.00D
Maximum black: 1.68D
My assumptions/calculations
This translates into a relative reflection (via 1/10^density) of:
Paper white: 100%
Maximum black: 2.09%
From what I have read "linearization" means that each step of a wedge (same spacing throughout) has the same change in (relative) reflection?
For the above example and a 21 step printout, the change in relative reflection from one patch to the next would be 4.90% (delta=(1-0.0209)/20); or ideal reflection (IR):
Step IR
0 100.00%
5 95.10%
10 90.21%
15 85.31%
20 80.42%
25 75.52%
30 70.63%
35 65.73%
40 60.84%
45 55.94%
50 51.04%
55 46.15%
60 41.25%
65 36.36%
70 31.46%
75 26.57%
80 21.67%
85 16.78%
90 11.88%
95 6.98%
100 2.09%
If I derive densities (second column, My) for all patches from the above assumption (via -LOG10(reflectance)) I end up with the following (third column, ID = stated in ideal_density.pdf that accompanies QTR). There is quite a discrepancy between my results and those given in the PDF).
Step My ID
0 0.000 0.000
5 0.022 0.048
10 0.045 0.098
15 0.069 0.150
20 0.095 0.204
25 0.122 0.260
30 0.151 0.319
35 0.182 0.381
40 0.216 0.446
45 0.252 0.514
50 0.292 0.586
55 0.336 0.662
60 0.385 0.743
65 0.439 0.830
70 0.502 0.922
75 0.576 1.021
80 0.664 1.129
85 0.775 1.247
90 0.025 1.376
95 1.156 1.519
100 1.680 1.680
Question
Where is the mistake with my thinking/calculation?
Unfortunately, none of the documents provide insight into their calculations. The same applies for the "checking your linearization" Excel-file:
BTW: The linked Excel-file shows "ideal" density values (in pink). If you copy them to the yellow cells (actual values), the actual curves deviates quite severely from the pink (ideal) curve. A mistake?
I'd highly appreciate if you could shed light on this topic.
Thanks in advance.