QTR-Quadtone RIP

I'm struggling with the math required to come up with the percentages
of black ink relative to light black.  On page 14 of the User Guide it
says to find the black patch that matches the 100% light black patch.
  Say it's 40%.  I then measure the 45% black patch and determine that
percentage needed to produce the same density of the 100% light black
and so on.  It says it's bit of simple math to figure the percentage
but I can't get my simple mind around it.  What is that formula?

Thanks,

Tom

Tom

Here's an improved explanation that I provided to another confused curve
maker. Perhaps the math is less obvious than my User Guide suggests.

--------

The description that follows explains how to determine the relative
densities in the K3 case.

Print the Inkseparation page with limited inks.
Measure the density of 100%K (limited)
Measure the density of 100%LK (limited)
Measure the density of 100%LLK (limited) Etc.

What you're going to do next is determine the %K that equals the density of
100%LK. Since you printed in 5% steps, you have to interpolate between the
step that is lower or equal and the next higher step. It's simple math so
I'll explain it by an example:

	Suppose
		Your measurement of d 100%LK = .65
		You find d 40%K = .61
			and d 45%K = .68
	Therefore
		There are 7 (68-61) steps of d between 40 & 45%K
		And 100%LK is 4 (65-61) steps above 40%K
		Thus 100%LK corresponds to (40 + 5 x 4/7) = 43%K

Hopefully that's clear. Next you repeat the process comparing LK and LLK.
Suppose you find that 100%LLK is equivalent d to 32% LK. Then it is 14%
(32%of 43%) of K. You keep repeating this process with all the black inks.
You may also need the relative densities of the toners if they need to be
partitioned as well.

You may be wondering why not compare all the gray inks with black and be
done with it. You could, but it's a bit more accurate this way.

As a final note, which may change all of the above in your mind, several
people, more experienced than I, have told me that you don't have to be that
accurate and simply using your eyeball will suffice. Being a mathematician
by training, I'm more comfortable with numbers.

On the other hand, other people, also more experienced than I, reprint the
separation page for each K's ink limit and measure from that. I like to
measure the densities, but I only print the limited inks once.  That's
worked for me and my little old 2200.

Hope this helps

Good luck

Tom Moore

> -----Original Message-----
> From: QuadtoneRIP@yahoogroups.com [mailto:QuadtoneRIP@yahoogroups.com] On
> Behalf Of Tom Husband
> Sent: Monday, August 22, 2005 6:40 PM
> To: QuadtoneRIP@yahoogroups.com
> Subject: [QuadtoneRIP] Relative Percentage Formula
> 
> I'm struggling with the math required to come up with the percentages
> of black ink relative to light black.  On page 14 of the User Guide it
> says to find the black patch that matches the 100% light black patch.
>   Say it's 40%.  I then measure the 45% black patch and determine that
> percentage needed to produce the same density of the 100% light black
> and so on.  It says it's bit of simple math to figure the percentage
> but I can't get my simple mind around it.  What is that formula?
> 
> Thanks,
> 
> Tom
.... deleted stuff

--- In QuadtoneRIP@yahoogroups.com, "Tom Husband" <thusband@s...> wrote:
> I'm struggling with the math required to come up with the percentages
> of black ink relative to light black.  On page 14 of the User Guide it
> says to find the black patch that matches the 100% light black patch.
>   Say it's 40%.  I then measure the 45% black patch and determine that
> percentage needed to produce the same density of the 100% light black
> and so on.  It says it's bit of simple math to figure the percentage
> but I can't get my simple mind around it.  What is that formula?
> 
> Thanks,
> 
> Tom

The idea is called interpolation.  In the example:
we are looking for is what would match 1.29 (the 100% light-black)
so in the black ramp we have: patch 40 is 1.22   and patch 45 is 1.33
imagine that we had intermediate patches 41, 42, 43, 44 -- which is
most likely to match the 1.29?  

mathematically what you doing is:  5 levels (i.e 45 - 40) is a difference 
of 1.33 - 1.22 = 0.11 but we only want 1.29 - 1.22 = 0.07
so  (0.07 / 0.11) * 5 = 3.2 levels i.e. 40 + 3.2 = 43.2

Or:
   wanted-diff-levels = total-diff-levels * (wanted-diff-density / total-diff-density)
         3.2   =      5    *    (   0.07  /  0.11  )

(notice that with the L values there are some negative values).

Do a simple sanity check -- obviously we want a number between 40 and 45.
the 1.29 we want is a little closer to 45 than 40.  Just guess 43.  Since you will
linearize later this is probably close enough.

Roy

OK.  Thanks Tom and Roy.  It's clearer now.  Not crystal clear but I
get the gist of it.  I'm sure it'll make sense after I do it a few
times.  Now I just need to wait for that densitometer I bought off
e-Bay to arrive.

Thanks again,

Tom