Digital BW, The Print

----- Original Message -----
From: "Austin Franklin" <darkroom@...>
To: <DigitalBlackandWhiteThePrint@yahoogroups.com>
Sent: Wednesday, March 27, 2002 5:47 PM
Subject: RE: [Digital BW] Dynamic Range Definitions and Print Tones


> > Austin,
> >
> > They are not my explanations they are the commonly accepted
> > definitions by a
> > wide range of people in many fields.
>
> Martin,
>
> Commonly accepted by whom?  Merriam Webster, magazines, etc. are hardly
good
> sources for technical definitions.  As I've said, the definitions you
cited,
> with the exception of a couple of them, require interpretation of
ambiguous
> terms.  They are NOT wrong, just open to (mis)interpretation.
Specifically
> two terms used, smallest and largest (or what ever words were used).  I
have
> shown VERY CLEARLY what is meant by smallest and largest when used with
> respect to dynamic range, as defined by a very definitive source.

Austin,

I guess I am a generalist and I like to start with a broad definition,
simple if you will, and then work my way to something more specific to the
case in front of us. If we start from the dictionary definition and try to
move to paper prints selecting the meaningful or usable min and max as seems
appropriate to that system.
>
> > I do not see the need to
> > reinvent these
> > meanings.
>
> Me either, and clarifying ambiguous terminology is hardly reinventing
> anything.  I have merely cited the clarifications from reliable sources.
> You have not attempted at all to cite any clarification to the terms that
> are in question.

For the most part I feel you are simply substituting synonyms. The point
where we collide is over "discernable." I agree with this as part of the
process of determining the min and max. You move on into the idea of
"discernable difference" over the entire tonal range and I think that this
is not covered by the general concept of dynamic. "Discernable difference"
is very important when you are talking about systems where the input and
output are changing with time and you want to discuss the ability of the
output to respond to the input. I feel that the concept of "discernable
difference" is not applicable to a paper print since it is not changing with
time but only with linear movement across the surface. With the linear
movement you can see multiple pairs simultaneously and "discernable
difference" does not seem significant.
>
> > Dynamic range is a ratio but subtracting log values is
> > mathematically the same as taking the ratio. I don't see the need to
> > reinvent the math either.
>
> Me either, and I certainly am not "reinventing" math.  Just because two
> "measurements" are expressed in log form does NOT mean they are the same.
> Dynamic range stands in and of it self as ONE log10 number.

The requirement that dynamic range be a log is not part of the general
definition or concept if you will. It seems very cleat that the dynamic
range is an expression of a ratio relationship. You need some values to
calculate that ratio. I do not see how you can directly "measure" the
dynamic range of a print. Perhaps in electronics you can.

> It is expressed
> in dB.  Density range requires TWO log10 values, dMin and dMax.  Density
> values are NOT expressed in any "scale" simply because they are relative
> unto themselves.

Well any range needs endpoints of course. Density is a log of the inverse of
a percentage, the reflectance, so it is all unitless. It would be
interesting to have the reflectance as a direct flux reading to work with.
>
> > > As has been shown, you can have a very high density range (a high
black
> > > value on a very white paper, with no intermediate tones) and that has
a
> > very
> > > LOW dynamic range, because there are no tones in-between.
> > Don't let this
> > > simple concept slip by...it's important.
> >
> > Where in the definitions was this stated?
>
> What's "this" that you are questioning?

Back to the general definition which says the dynamic range is a ratio of
the min and max. This does not seem to account for the values in between or
they assumed a continuously variable system.

> The measurement for density range
> is clear, dMax - dMin.  The measurement for dynamic range is clearly
defined
> by the dynamic range equation.  Here, I'll apply some simple numbers to
> this:
>
> dMax = 1.8
> dMin = .2
>
> Density Range (dRange) = 1.6
>
> Easy, right?
>
> What's the dynamic range?  Well, we don't know what the smallest
discernable
> signal is, now do we?  Nor do we really know the largest that the
> paper/system can attain either.  This makes for a quandary.

Not really because you are interested in the meaningful or useful values
which may simply be the only the values you do know.
>
> The dynamic range is based on the largest ATTAINABLE signal for the
medium,
> not the largest for a single print.  You certainly could just print the
> blackest black you could, and get it from that, not too tough.  Let's say
it
> was 1.8...for sake of argument.

Okay. A little high for inkjet and rather low for silver.
>
> The smallest discernable signal isn't dMin, since we could possibly be
able
> to "discern" in .01 density value steps...  and without knowing what the
> minimum discernable signal is, we don't know what the dynamic range is, by
> definition.

I agree that you may be able to discern a change of 0.01 density near Dmin.
The problem is that as you approach Dmax the density change you can discern
decreases. The discernable difference is not a constant in this system which
is why I object to using this in a dynamic range calculation for this
system.
>
> Let's say our smallest discernable signal was 0.01 density value (which is
> hardly far fetched, and actually a reasonable number).  The dynamic range
> would be 10log10((1.8-0.2)/.01) or 22dB.  Note that even in Bells, 2.2 is
> not the same as 1.6.  Of course there happens to be a value for the
smallest
> discernable signal that would make dynamic range and density range the
> same...but that's the same as saying a clock is right twice a day...it's
> purely by happenstance.

Here is the reason you cannot divide by the density value of 0.01. Assuming
as you say we can discern a density of 0.01, this means that we could
discern the difference between 0.03 and 0.04 densities. If you look at that
in terms of the reflectances that were used to calculate the density they
would be 93.3% and 91.2% so the discernable difference would be a 2.1
percentile difference. If we go to the other end of the scale and say I can
discern between tones 0.01 density values apart then I would say that I can
distinguish between 1.78 and 1.79. In terms of reflectance this would be the
difference between 1.62% and 1.66% so the discernable difference would be
0.4 percentile.

Do you see what is happening here? From your earlier diagram you indicated
that the discernable difference was constant across the entire range. That
is not the case here. The discernable difference gets larger as the tones
get darker until finally you reach a point where you eye cannot tell the
difference between a density of 2.4 and 2.8.

I think all of this would be much more easily understood if it was viewed in
terms of reflectance rather than the density log values.
>
> > Dynamic range tells you nothing
> > about the number of intermediate values.
>
> That's what you claim, and I keep telling you, you are mistaken.
>
> It really would help if YOU provide an EQUATION, with appropriate
> definitions of terms used in the equation (as I have done), NOT some
> ambiguous verbiage that is open to interpretation.

I believe I did. From the definition the dynamic range is the ratio of the
maximum divided by the minimum. Lets look at it this way, for a print:

Dynamic Range of the Reflectance = (maximum reflectance of the brightest
visually discernable white)/(minimum reflectance of the darkest visually
discernable black)

This ratio can also be expressed by raising 10 to the power of the density
range (maximum density minus minimum density).

My thought is that the dynamic range of a print may not be a particularly
useful expression for us. The simple range or knowing the lightest and
darkest shades of gray of a medium are what is of importance to us. We also
tend to overly focus on getting the deepest black where in reality you gain
more by increasing the brightness white.

Artistically range may not matter to everyone and some people will make
great prints using only a portion of the available range.

I understand that you are trying to give us an expression that says
something about the number of discernable tones that a media or system can
create but I don't think that this can be done here because I do not see
that there are a finite number of tones.

Best,
Martin