Digital BW, The Print

Hi Roy,

> 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.

That's the problem!  They ARE basic concepts, but they can mean more than
one thing, there are ambiguous terms being used.  I've cited this countless
times.  Largest can mean the maximum/largest "level" of the signal related
to 0, OR it can be the that I just mentioned, minus the lowest/minimum
"level" of the signal, again, related to 0, and it is therefore a range.
Why is that so hard to understand?

> 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 diagram that I posted a picture of, was actually NOT a sine wave (there
is a sine wave to the left of it on the page, but that's not what I posted),
but a picture of a grove in an analog record ;-)

> 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.

Hum.  I didn't know a record had any voltage ;-)

> 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?

It also doesn't have a label for voltage either.  You are missing the
importance of the diagram.  It is merely an example showing what largest and
smallest are.

This is just SO simple.  Dynamic range is a concept.  It does not apply to
any particular thing, and because I, or anyone, uses an example of audio,
does not mean it only applies to audio.

All that is required for dynamic range are the variables listed in the
equation, largest signal and smallest discernable signal.  Largest meaning
the absolute value of the overall signal, and smallest discernable signal
being just what that means.

> 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.

I didn't have to interpret anything, the meaning of largest and smallest
discernable signal are clearly defined.

> The
> trouble is we've
> come up with different interpretations!!  There's nothing in the book that
> addresses or supports one interpretation over another.

But that's just not true.

> 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.

It is only obvious to me what it means, simply because I have worked with
dynamic range for over 25 years, and it has been exactly the same every
time, from the exercises in class, and professors and classmates that I've
had discussions with, for the hundreds of engineers I've work with, and for
the thousands of customers that have read my specifications, equations and
analysis.  It's a pretty sound base!

> First of all, I guess I have to convince you that we have both
> made choices.

You can't do that, because my terms are not by choice.  They are, and have
always been, clearly defined.

> If that works, we can agree to have different interpretations
> leading to two
> definitions of Dynamic Range

But any interpretation that does not match what I know dynamic range to be
is wrong.  It won't be dynamic range.  I did not make up dynamic range, nor
did I make up the definitions of the terms used in it.

> I contend that there
> isn't mathematical
> argument because both are sound, its just a difference
> (better/worse) argument.

I don't understand how claiming largest means highest level of signal and
smallest discernable signal means lowest level of signal is "sound".  If you
use those definitions, you are not describing DYNAMIC range.  Your
calculation will be in error.

Let's just talk about "smallest".  You CAN have a very high dMin, say 2, but
have the ability to distinguish .1 density, can you not?  Also some of the
definitions of dynamic range (the correct ones that is ;-) say noise is the
smallest discernable signal, and for the most part, it is.  Given that, are
you saying that dMin is simply noise?

> 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?

Yeah, but it isn't.  It's a record grove....and you can just take a single
slice out of the diagram, it is not necessary to be a wave at all.

> It seems like we both are
> going to replace
> the x-axis with spacial dimension across the paper (I think we OK so far).

No, I don't use an XY graph at all, I don't graph anything.  That
"graph"/image was solely to show an EXAMPLE of what smallest discernable
signal and largest mean.

> Now the tricky part, the large amplitude portion is the "loud"
> part in audio.

Fine...

> 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).

Well, it doesn't matter if there is a picture of a sine wave or not.  The
point of the example is to show the extents/bounds of the signal, and it
doesn't matter if it's voltage or density.  I do agree that the two bounding
limits can be equated to dMax and dMin, and the "largest" in the dynamic
range equation, when applied to an image is dMax - dMin.

> Likewise, the  small amplitude is "soft" in audio language

Do you mean the vertical distance between the top and bottom of the "signal"
(not the bounds)?  That is neither loud or soft.  Loud is if the signal is
at the top of the bounds, and soft is if the signal is at the bottom of the
bounds.  The, what I believe you are calling "small amplitude" has nothing
at all to do with loud or soft.

**** (tagged for below)
> and
> for you its two
> densities that are very close and just discernable.  How we doing so far?

See above.  I think your term "soft" may be ambiguous...see below too ;-)

> 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.

You can't RMS does not apply to dynamic range.  It does apply to SNR, but we
are not talking about SNR...

> Well maybe that wasn't so clear,

Well, you're right there ;-)

> 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.

Sorry, you lost me.  I don't believe your terms "loud section" and "soft
section" are really right...

> On the print I want it
> to be a dark section followed by light section (i.e.  paper half
> black and then
> half white).

He he, that I understand ;-)

> In audio we talk about RMS Power output and it is max in the
> "loud" section and min in the "soft" section.

As I've said, RMS etc. doesn't apply to dynamic range, but I'll see where
you're going with this anyway...  It seems you are using '"soft" section'
ambiguously.  Here it almost appears as you mean it as being a signal that
is close to the bottom bounds...but above, you say...see **** above.

> And so in the print we have
> density is max in the black section and min in the white section

Yes.

> --- and I
> want signal strength to be exactly analogous to density.

Fine.

> ---  Question: what does your paper look like?

You said above the paper was half black, then half white...so that's what
the paper looks like, right?

>  half high contrast and
>  half low contrast?  It sure doesn't "feel" analogous to my audio
>  example: half loud, half soft.

Where do you get "half" from?  You lost me here...

> The really weird thing about
> contrast is that its JUST the transition.  There's no extent, it
> can't keep going.

What do you mean by that?

>
> > > "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.

Agreed.

> Resolution is
> totally irrelevent.

To the range, of course.  I never said any differently.

> dMax and dMin define an interval (i.e. range) where any density between
> dMax and dMin is "in the range".

Yes, of course.

> There's an infinity number of possible
> densities

...you didn't finish that sentence.  If you mean within the range, yes, you
are right, there is an infinite number of POSSIBLE densities, but in
reality, the number is bounded.

> (distinguishability is also irrelevant to what a range is).

Absolutely, and I've never said differently.


> Come on now.  There's lots of references to dynamic range as it applies
> to the audio world.

Yes, because engineers design audio equipment, and because companies have to
test this gear and produce specs for it, it is a specified piece of
information.

> Where are the books about dynamic range as it
> applies to prints?

Ansel Adams did ;-)  I am sure that the companies that make paper/chemicals
etc. have information on this, and it may or may not be published.  This is
a very different field than audio.  To expect there to be the same level or
requirement of specsmanship in photographic paper/printing as there is in
audio is really asking too much.  Most people who are interested in this
type of information for prints are few and far between, but for audio it's
every college kid...it's far more "pedestrian".

I am sure that somewhere dynamic range of prints is discussed.  I have about
a dozen books on subjects that may contain some information on it...  The
one book I'd start with is a well known "bible", "The Handbook of Modern
Halftone Photography" by Ewald Fred Noemer.  It, unfortunately, has no
bloody index...but it would be my first guess for a book that might discuss
dynamic range with respect to photography.

> 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'm sure it's been discussed...and I'm sure we aren't the first.

> Have you read Adams short paragraph about it lately?

I read what was posted, but I haven't read the source material to see
exactly what he was talking about.

>
> > 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.

But Higgins shows the definition of dynamic range is...so it IS in a book!

> Dynamic range is just the generic
> term that
> can be applied to many areas of study.

I believe it is a very specific property, as defined by the dynamic range
equation.

> 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.

That's what I don't understand.  The definition you want to ascribe to it
isn't useful, as we already have a term for that...density range.  To me,
dynamic range is a very valuable property for imaging (as well as audio).

Phew!

Regards,

Austin