Digital BW, The Print

Bob,

>... I've started working on custom curves. I'm trying to establish what an
>ideal distribution of values should be.

I have never seen a very good explanation of this issue, just factors to
take into consideration.  I've asked in the past, "What is linear?"  I don't
think there is a simple answer.

> I note that in the Hobeman instructions for "Customizing MIS Ultratone
>Curves" suggest that Grayvalue percentages (21 step) vs. RGB values (0-255)
>be in a linear relationship. However, when I measure 21 step grayscales
>printed on a 2200 (with color ink) and in Piezography, I get significantly
>different relationship (which is closer to what I get from your curves).

In general the say the human eye follows the logarithmic scale.  As such the
f-stops and log scales of the densitometers should be close.  However, it is
also the case that our ability to distinguish steps in the darker regions is
less than in the brighter or midtone sections.  

So, if you assume that the dmax on a matte paper is 1.65 and the paper white
is 0.05, 0.80 would be the arithmetic midpoint.  If, however, this is used
at the 50% density, the scale looks dark.  If I use a log scale that goes
from 0.05 to 1.65, measure the distance between the ends and divide it in
half, the midpoint on the scale is just below 0.30 -- too light (but close
to where some old Epson's put the BO midpoint).

(I'm sure some with a strong math background could do a better job here than
I, but I also think a background in the human visual system is needed --
another field I'm not formally trained in.)

What I did was work from a pragmatic perspective.  I was using the PiezoBW
system.  I wanted my files to be printable and the images to be consistent
with both systems.  So, I took a number of PiezoBW 21-step test strips and
averaged them.  The average for 50% was 0.61.  Smoothing the curves gave me
a 25% of 0.29 and the 75% of 1.03.

At the dark end, the dmax is a critical factor that needs to be considered
for, especially, what is between about 70% and 100%.  To give an idea of
what I've used just based on visual impression, for a dmax of 1.68 I use
1.53 for 95%.  If the dmax is 2.40 (like some glossy papers) I use 1.95 as
the 95% point.  The eye really has trouble seeing into those very dark
blacks in any kind of "normal" light level.  To be really consistent, I
suppose I would have to determine what that "normal" light level is.  As a
practical matter, I make judgments based on how things look in my office.

Hope this helps.

Paul
www.PaulRoark.com