Digital BW, The Print

--- In DigitalBlackandWhiteThePrint@y..., "Austin Franklin" <darkroom@i...> wrote:
> 
> > > > Now the big question is "What's the signal?".
> > >
> > > Very simply, for a photographic image, it is the density value.
> >
> > This is precisely what I'm trying to say.   Let's take the
> > original definition
> > equation and substitute "density value" for "signal".  We have:
> >
> > Dynamic Range = log10 (largest signal/smallest discernable signal)
> >             =  log10 (largest density value/smallest discernable
> > density value)
> >
> > Isn't that precisely the same as: dMax - dMin  as I derived last post?
> 
> Well, no, you're taking a "leap" here to arrive where you did.  As I've said
> a dozen times, "largest" is an ambiguous term, as well as "smallest".  It is
> open to interpretation if left undefined.  The equation for dynamic range
> clearly uses largest to mean the "absolute value of the maximum detectible
> signal", in other words, the amplitude...dMax - dMin, as opposed to just the
> single measurement for dMax...

I don't understand why you're having trouble here.   "largest", "smallest",
"maximum", "minimum"  are all pretty basic math concepts, I can't believe
you really need me to define them.

The real issue here is the "leap" of interpretation.  Let's go back to the Higgins
book -- to the pages about dynamic range.  There's the formula on one page
(using the word signal) and there's the sine wave diagram on the next page
(the same one you posted way back).   The sine wave diagram talks about
"signal" and shows a large amplitude and a small amplitude.  In the audio world
its real easy to look at it and think "voltage" oscillating back and forth over time. 
But --- we want to apply the idea to photographic prints.  Hmm!! How shall
we do this??   Density sure seems like an important concept but the diagram
certainly doesn't have any labels that say "density", so what to do?

Here's where the "leap" of interpretation HAS to occur. You've come up with
a way to put density onto the signal diagram and so have I. We both had to
"interpret" the signal diagram as it applies to density.  The trouble is we've
come up with different interpretations!!  There's nothing in the book that
addresses or supports one interpretation over another.  I think this is the
real issue here.  You have CHOSEN what you think is the most obvious
interpretation, in fact it seems so obvious to you that its hard to think of
it as a choice.   I, likewise, have chosen an interpretation but it is different from
yours.  I believe both interpretations are mathematically sound and can both
lead to lots of consistent derivations (within their own framework).

First of all, I guess I have to convince you that we have both made choices.
If that works, we can agree to have different interpretations leading to two
definitions of Dynamic Range or somehow decide which one is more appropriate
for modeling prints as human view them.  I contend that there isn't mathematical
argument because both are sound, its just a difference (better/worse) argument.

My idea is to show how you put the labels on the graph and how I put them
on the graph.  The signal diagram in the book looks like a voltage sine wave
with time along the x-axis, right?  It seems like we both are going to replace
the x-axis with spacial dimension across the paper (I think we OK so far).
Now the tricky part, the large amplitude portion is the "loud" part in audio.
You are looking at the large amplitude and putting dMin at the bottom trough
and dMax at the top of the sine wave so that "signal" means (dMax-dMin).
Likewise, the  small amplitude is "soft" in audio language and for you its two
densities that are very close and just discernable.  How we doing so far?
Now, my turn.  What I want is to use the absolute value of the amplitude
to be a measure of the density.  To be precise I'll borrow some terminology
from the audio world  -- I want density = RMS (RootMeanSquare) of the
signal amplitude.  Well maybe that wasn't so clear, let me try with a 
what the signal diagram looks like in both audio world and print world.  In
audio its: loud section followed by soft section.  On the print I want it
to be a dark section followed by light section (i.e.  paper half black and then
half white).  In audio we talk about RMS Power output and it is max in the
"loud" section and min in the "soft" section.  And so in the print we have
density is max in the black section and min in the white section --- and I
want signal strength to be exactly analogous to density.
---  Question: what does your paper look like?  half high contrast and
      half low contrast?  It sure doesn't "feel" analogous to my audio
       example: half loud, half soft.

> Contrast (in out case) simply means delta density, right?  In order to
> distinguish density, you MUST have contrast.

I don't have much problem envisioning an all black paper or an all white paper.
No contrast but I sure know which is which.  The really weird thing about
contrast is that its JUST the transition.  There's no extent, it can't keep going.


> > "Range" as commonly used in math is used to describe the set of possible
> > values.  Density range given by dMax and dMin entirely describes the
> > possible density values i.e. they all have to lie between dMax and dMin.
> 
> No, not at all.  It describes the MAXIMUM and MINIMUM value, but not the
> resolution of values in between.  Counting from 0-100, you could count by
> 10's or 5's or 1's, you have the same range, but different number of steps.

Range is a really, really basic mathematical word.  I just looked it up in my
7th grade daughter's math book, its there.   Giving a Max and a Min is by
definition a precise description of a range.  Resolution is totally irrelevent.
dMax and dMin define an interval (i.e. range) where any density between
dMax and dMin is "in the range".  There's an infinity number of possible
densities (distinguishability is also irrelevant to what a range is).


> 
> > As you say below there's lots of info about.
> > I'd like to see more supporting your  interpretation.
> 
> I don't believe this is something that people write down, it's just an
> inherent understanding.  There is no book on how to count from 2 to 3 that I
> know of, or someone substantiating that you can count trees with integer
> values....  Hum.  I'll have to think about that.

Come on now.  There's lots of references to dynamic range as it applies 
to the audio world.  Where are the books about dynamic range as it
applies to prints?  If there aren't any maybe there aren't "accepted"
ways to look at it yet.  Is that why we are having this discussion?  To
add our two cents to the issue.  

> 
> I guess if you understand the concept of dynamic range, it should be obvious
> how it can be applied to photographic prints with no problem...I mean, even
> Martin said dynamic range has been spoken about with respect to photography
> for a long time, so did Ansel Adams...so others apparently believe dynamic

Have you read Adams short paragraph about it lately?   He pretty definitely
talks about it as max and min zones i.e a range of "useful values".
Put that on a negative or paper and we have exactly a "density range".

> range applies to chemical photographic prints...  As far as interpretation
> goes, well, as I've said, I didn't make up the dynamic range equation, so
> it's not up to me to interpret it.

I think you have most definitely "interpreted" it for usage with prints.  If it's
"common amongst engineers", there's most definitely got to be a book.

  The use and definitions I've given to it
> are common amongst any engineers I know of who understand dynamic range...
> So I am on very firm ground I've gotten the equations and definitions of
> terms used in the equation correct, and others have agreed dynamic range
> applies to chemical prints...so I don't know what more I can substantiate.
> 
> Another thing is dynamic range does in fact describe a unique
> property...that is NOT defined by density range.  If dynamic range were
> simply the same thing as density range, they there probably would not be two
> distinct terms, but there are.  Density range does not describe the same
> thing that dynamic range does, and that is why dynamic range exists...

You're really stretching here.  Dynamic range is just the generic term that
can be applied to many areas of study.  It just happens that it's already
got a well-known and commonly used name is the specific area of photography.

> 
> Austin

Well, Austin, I hope we're not wasting our time, here.  I think I really understand
how you've used the technical definitions and interpreted them.  I don't
think they are "wrong" per se, but I definitely do think there are other
ways to interpret them and potentially have a more useful concept.
All using precisely the same tried-and-true technical definitions that you
and engineers at least in some industies are very familiar.

Roy