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Your description of method 2 makes no sense.? ?

All the values are simple ratio -- darkness of one ink vs darkness of another ink.
So K vs LK and LK vs LLK -- then calculate K vs LLK.
It's just simple algebra ->>? ? (a/b)*(b/c) = (a/c)

But as you can see from Shilesh's experiment: once you linearize is fixes most anything.


On Wed, Feb? 5, 2025 at 08:41 AM, Hendrik Kuhlmann wrote:

>
> I think in his example Shilesh demonstrated the difference between the
> two approaches we are discussing.
>
> Curve 1 illustrates *method 1*: Here the printed luminosities of all
> lighter inks are referred to K (the common reference curve): To that end
> he determines the densities (for the ink setup) by those densities in
> the calibration plot at which the K-curve has the luminosities at which
> LK and LLK reach their respective minima. In his example:
>? ??? Lmin of LK was 55% step of K
>? ??? Lmin of LLK was 25% step of K
> This method 1 corresponds to using the open square for the LLK density
> in my graph.
>
> Curve 2 illustrates *method 2*: In this case one has to multiply the two
> fractions 0.55 and 0.25. This results in 0.25 * 0.55 ~ 14 for sought
> density of LLK. This method 2 corresponds to using the solid diamond for
> the LLK density in my graph.
>
> I think in the calibration guide (p.4 of calibration.pdf) both these
> methods are getting mixed. Here are the sentences which are contradictory:
>
>? ?* Method 1: "But it's necessary to have all the relative densities to
>? ? ?a common value".
>? ?* Method 2: "Mathematically this is very simple, just a multiply: LLK
>? ? ?= 38% of 32.7% of 100 ... = 12.4%"? and "... the comparison is most
>? ? ?accurate by comparing the LLK ink to the LK ink *not to the K ink*."
>
> Both method yield the same result for the required density of LLK only
> if all ink luminosities satisfy L(K) = A - b_ink*K (with A=L(K=0) the
> common luminosity of the paper and different values of b_ink by for each
> ink). This linear relation ship holds true for very small values of K.
> But for larger K all L(K) curves saturate.
>
> I hope it is clearer now.
>
> Best,
> Hendrik
>