Digital BW, The Print

Hi Roy


> From: Roy Harrington <roy@...>
 

> 
> There are quite a few different units floating around and many mathematical
> formulas.  Just saying "linearize" is very ambiguous until you define exactly
> what you are linearizing.  Nobody wants to linearize "density" values.  That
> would put the 50 step at about 0.86 midway between 0.04 and 1.68.
> 
> I think we'd all agree that there has to be some sort of up sweeping curve
> when you plot density.  But there are numerous mathematical functions that
> exhibit this look but in fact are different when you get to the details of the
> shape.
> 
> I can think of three main physical values from color theory that are relevant:
> Density,  the Y of XYZ which is luminance, and L of Lab called luminosity or
> sometimes lightness.  The names sometimes get confused but the letters are
> always consistently defined.
> 
> Mathematically they are related:
> density = -log(Y)
> Y = ((L+16)/116)^3   for L >=8
> Y = L/903                  for L < 8
> 
> Gamma is a purely mathematical function:
> output = input ^ gamma
> 

Yes I agree completely and have noted these formula in the earlier posts.


> Dot Gain is a physical property of putting ink onto paper which
> typically gives a curved shape because the middle values are affected
> more that the end points.
> 
> A finally the pixel values of 0-255 are totally arbitrary -- they may be
> derived
> in any way we like.
> 

Well I would say they are real, ie an image is made up of pixel values and
their respective location.  These values can be measured to varying degrees
of accuracy, eg 8 bit vs 16 bit, and presented in any way we like: 0-255,
0-1 etc

> All the functions above have a sweeping curve character.  When you start
> combining them you have a unlimited number of possible shapes.
> So any spec that quotes a particular shape really needs a lot of qualification
> about what they really mean.

Agreed.

> 
> What QTR does and I advocate is linearizing in Lab values.  Lab was defined
> way
> back in the early 1900's using large studies of human perception and our eye's
> response to light intensities.  The weird function was designed to mimic the
> way we see.  

Don't doubt this and I am prepared to follow CIE's results: go LAB!

> So when QTR linearizes to Lab values it just uses the dynamic
> range
> of dMin to dMax to the "best" curve.

Here is where I think we break down and have a key difference.  While you
use LAB values, you do not achieve a result that fits LAB.  This is the crux
of the matter that we need to explore.

> 
> What has been the weak part is that we've been using the gray space of gamma
> 2.2 which has a different shape.  I'm always been a little surprised or
> annoyed that
> I calibrate my monitor with the best gear but when I look at a 21step wedge
> the
> dark shadows from 100 to 95 seem much more compressed that the rest of the
> wedge.  Getting the soft proofing working has "fixed" this in the sense that I
> can now get reasonable separation throught the 21step.

Well I agree it is kind of silly to work in one space and print in another.
When I started this thread I bundled a lot of issues into the one topic.  We
are slowly separating these.  The issues I bundled together included at
least the issue of working in gamma 2.2 and "printing in LAB" (shorthand)
and whether in fact we "printed in LAB" in LAB as intended.
> 
> This whole thread has gotten me to figure out more of this.  The problem with
> our
> scheme so far is the gamma 2.2 working space.  It just isn't geared to our
> perception.

I will take your word on the perception side of things (go LAB!) but I think
there are two problems with "our scheme so far". The lesser one is the
"perception" problem of gamma 2.2.  The bigger issue is, I believe, we don't
actually "linearize to [our target] LAB".

> It's close and if you look at Lindbloom's site about comparing Lab to gamma
> 2.2
> you can see what's going on.  Lab doesn't have a "gamma" --

Almost yes.  I noted this in an earlier post.  It has a gamma but this is
not a single number - because it is a cubic function to begin its first
derivative is not a single value.

>it has that cubic
> equation.  Bruce has just shown that gamma 2.2 is pretty close.   But if you
> look at
> the comparision though you'll notice a strange wiggle in the curve in the
> bottom
> left corner.  This is the source of the compressed 100-95 levels.

Almost agreed.  The wiggle in 100-95 levels (L= 0-5) is outside our present
printing range.  Even with RC papers we can't print L=5.  This error is not
our primary problem.

> 
> This is why I've introduced the new gray space.  Whatever the gray space is,
> is
> what gets converted to the monitor display space.  Now we have all the parts
> talking
> the same language.  I've still got some tweaking to do since this was done
> more by
> trial and error than mathematically.  But I think this may be a significant
> "new"
> way to deal with B&W printing.

Well I need to think about this a bit further and I see you replied to my
other post which I will take a look at now.

Cheers

Steve