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Re: Multitones: An Exact Approach


>Not sure I fully understand your dot area formula

To this I take the liberty of quoting an earlier posting of mine (of 
Nov. 13, 1999, including a correction made the day after):


In an earlier posting I mentioned that I needed to measure Dot Area 
of printed patches for use in setting up a quadtone system, having at 
my disposal a ColorMouse with corresponding software which (at a Mac) 
allows only colorimetric measures (as XYZ, L*a*b, etc.) but not the 
measurement of density. At that time I thought that measures of 
density were needed in order to arrive at the Dot Area values to be 
inserted in Photoshop's CMYK Settings.

Fortunately there exists a simple way of deriving the Dot Area from 
the colorimetric XYZ measure. That this is the case was established 
in the following way:

1. Three checkerboard arrangements were constructed in Photoshop with 
white and black squares arranged in patterns giving 25%, 50%, and 75% 
coverage of black squares, which were printed out with a square width 
of 2 mm. These squares are sufficiently large to keep dot gain quite 
low (as evidenced by visual inspection through a loupe), while still 
sufficiently small relative to the aperture of the colorimeter (about 
4.5 mm) so that sampling each square 10 times at various points gives 
a reliable set of values for different colorimetric measures (X, Y, 
and Z of the XYZ measure; L of the L*a*b measure; and L of the HSL 

2. For each of these measures, each of which decreases with 
increasing black coverage, a prediction of dot area was computed in 
the following way: The 10 measured values were averaged; the measure 
for a 100% patch of the ink in question was subtracted; this quantity 
was divided by the difference between the measures of a 0% patch 
(i.e., the paper base) and the 100% patch; and the result multiplied 
by 100 to get a percentage.

3. This procedure was repeated with the three other inks from a set 
of MIS Archival Quadtone Inks, and the predicted measure of dot area 
for each colorimetric measure and ink was compared to the 
geometrically defined Dot Areas of the three patterns. These 
comparisons showed that X, Y, and Z resulted in predicted dot areas 
of about 26%, 55%, and 79% for the three patterns, for each of the 
four (quite different) inks, while the two L measures varied quite a 
bit with the inks, and also resulted in values quite far from the 
expected ones.

As noted above, these test were conducted with *black* inks, but I 
don't see why the same results should not obtain also with colored 

In conclusion, thus, Dot Area can be determined from the colorimetric 
XYZ measure (for instance, by averaging the three components) through 
the following formula:

	Dot Area (%) = 100 * (X0 - X) / (X0 - X100)


	X is the measured value of the given sample
	X100 is the measured value of a solid patch
	X0 is the measured value of the paper base.
	X0 is the measured value of the paper base.

>If you want another
>challenge how about seeing if you can come up with a method to set printing
>inks colors and dot area curves from a scan opened in Photoshop?  A lot of
>folks would bless you for that I think!

This would be a nice thing indeed, but I'm afraid it won't be coming from me.

>However, I think you are absolutely right in stating that even if a profile
>is available it is better to do the separations yourself -- each image
>benefits from its own unique set of separation curves while a profile can
>only provide a tonal interpretation for some mythical average image.  But
>most folks don't seem to want to go through all that effort and want a
>profile to do the job.

I would like to stress that my procedure is NOT to be repeated for 
every single image to be produced, but is performed only ONCE for 
each ink/paper combination. My point in working out the procedure has 
been to make it possible to completely specify ones image in 
Photoshop, and then be able to get this specified image down on paper.

>Anyhow, nice work on your document!
>Dan Culbertson

Strange Ross
Hvidehusvej 35
DK-3450 Alleroed
Denmark      Phone: (+45) 48 17 42 92    http://axp.psl.ku.dk/~ross/
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