Digital BW, The Print

Hi Todd,

> Remember, you had said DyR, and thus tone count, could be computed from a
> measure of (dmax - dmin)/noise, and that noise could be
> determined from one
> intermediary tone.

That will give you a good idea of the dynamic range, yes.

> That could give rise to a situation where a full tone
> print could yield the same DyR as one which contained 4 tones.

That is true, even a print with one tone could have the same dynamic range
as one with a thousand tones (providing they were printed with exactly the
same system/paper etc.).  Dynamic range is a measure of what is possible
within the density range, as limited by "noise", not what only exists.

> That flies in
> the face of your tone count premise.

I don't believe so.

> Thus your interpretation of that
> formula demanded linearity. What I mean by linearity here is that
> all tones
> that could be contained within the density range ARE represented.

Not at all.

> Let's look at the staircase. In the situation where you know the height of
> the staircase (DnR), if the rise and depth of each step is the same
> (linearity), you can measure just one step to determine how many steps are
> present.

Correct.

> This method is similar to your original description of the DyR
> measuring method. If each step had a different rise and depth a
> calculation
> based upon one step, which was different than all the others,
> could yield an
> inaccurate result. Thus linearity IS required.

Not at all.  If the noise can be characterized, which it can, then it's easy
to get a very accurate result.

> Furthermore, this also assumes that every step is in place. If some of the
> middle steps have fallen, your calculation WILL be inaccurate!

Not at all.  Integration takes care of this (kind of like interpolation).
If the characteristic of the "noise" is consistent, you can derive the noise
at any point.

> Later, to address non-linearity you began to include the concept of
> integration and calculus. For me to really understand this would take more
> explanation than I deserve, but I sense you mean taking a broader sampling
> of tones and noise and calculating them together. If so, fine.

Yes.

> Perhaps if/when you summarize what you presently maintain on the issue and
> what you've dropped, and/or present an explanation of how you
> would approach
> my three print challenge...

I have actually strongly considered really writing this up, and subjecting
it to peer review.  When I have the time in a few months, and my new lab is
set-up, I'll not only have the space, but hopefully the time, to give this a
thorough write-up with 8x10 color glossy photographs with circles and arrows
on the back of each one ;-)

Regards,

Austin