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[filmscanners] Re: Density vs Dynamic range
Austin and Peter,
I don't know which of you wrote this quote below, but it threw a big light
bulb on above my head as to where part of the confusion comes from. If
either of you really thinks this then it must be a complicated business to
get into bed at night! ...
This post has 3 sections, headings are:
RANGE  discusses the confusion about range
DYNAMIC  discusses the confusion about what dynamic means
SCANNERS  applies dynamic range terminology and discusses the relationship
between density and dynamic range.
1) RANGE
***********
At 03:06 12/06/02, you wrote:
> > > However my point is that if you can reduce the noise level then you
> > > can
> > > increase the number of steps (by halving the step size) with real
> > > benefit, but ******without altering the range******.
> >
> > Correct, but that INCREASES the dynamic range.
The asterisks are mine to draw attention to the problem.
Here goes! Big breath...
Put some numbers to the above. Let's say max signal is 1000mV and noise
(or min signal) is 10mV at first. Then you reduce the noise level by
half. So min is now 5mV.
OK, so now use the plain English language definition of a range. In the
first case, the RANGE of the usable / measurable / instrumentable signal is
"10mV to 1000mV", or 100 to 1, or 40dB (volts remember, so 20log, not 10log).
In the second case the RANGE of the signal is "5mV to 1000mV", or 200 to 1,
or 46dB.
Do you see? The plain english RANGE of the signal you are dealing with has
changed from 40dB to 46dB. You HAVE altered the range. Why do you say in
the quote "without altering the range"? The range is NOT zero to 1000mV,
it never was, and never will be. It is 10mV to 1000mv, then 5mV to
1000mV. The range changes when you change the noise level, that is why you
would change the noise level, to increase the range.
And look! The calculation for plain english RANGE is the same as the
calculation of DYNAMIC RANGE! That is because they are the same thing
here. The DR is, as I have said many times, a RANGE. It is not something
else, it is a RANGE. Look at the definitions that you quote, it is a
range. It is usually measured as a ratio, and usually quoted in dB. It is
not a number of levels, or anything else, it is a range. It IMPLIES a
number of levels, but it is NOT a number of levels, it is a range.
The thinking that leads you to state that by changing the noise level you
don't change the range is at the heart of this problem. It does change the
range, and it must. And the definition of DR is no different from the
definition of plain english range. You seem to have laid an unnecessary
layer of additional complexity over all this, and the result is total
confusion. I can see WHY you might like to do this, but I don't see how it
is useful, and it is at variance with other usage.
Here is what you (Austin) said in another response to me:
>Surely, you can understand that you can have two exact same ranges, with
>different noise? That can't be hard to understand?
No I don't understand that because I most explicitly don't agree. By
DEFINITION of the most basic kind, the range we are discussing is from the
smallest (noise) to the largest. The RANGE we are discussing is noise to
max signal. Change the noise and you change the range. Zero does not
exist, because it is not measurable or includable and we are not discussing
it. The whole point of discussing the range is to specify the smallest
signal and largest signal, it is NOT to choose two arbitrary points inside
or outside those figures. The RANGE is the distance between the smallest
signal and the largest signal. It is NOT measured from somewhere "smaller
than smallest signal", or zero or anywhere else.
Zero by definition is not in the range of (AC) signals we are taking
about  because of noise. Noise not only always exists, it is at the
heart of what we are discussing. I repeat  zero does not exist. That is
usually the whole point of discussing signal ranges, to see how close we
can get our noise to zero. The upper limit is arbitrary and depends on
gain, but this arbitrariness is neutralised by stating the RANGE as a ratio.
Look Austin  we are discussing a situation in which we are trying to do
something intelligent with a smallest measurable signal, and a largest
measurable signal. So we use the concept of the RANGE. The range is the
difference (or ratio if you want, it doesn't matter) between these two. It
is not complicated, it is very very simple, and it is NOT ambiguous. It is
NOT something else, and it is NOT up to you to specify arbitrary end points
to some range and still expect that sodefined range to have any meaning.
If you DO specify arbitrary end points, then you have thrown away the basic
premise of your SIGNAL RANGE and you need to invent something else to get
it back again. I think you do this and you call your newly defined range
the Dynamic Range. But you DON'T need to do this. The actual range is
inherent and unambiguous. Why do you have to invent this other "range"
that goes from 0 to X volts? It means nothing, it is not used anywhere, it
is not relevant, it doesn't get into the maths, its existence is impossible
and it only means you spend your life explaining something that doesn't
need explaining and so have to invent another term to explain what we all
originally meant anyway.
What's worse, to define your "new" range you steal a term that has another
meaning entirely, and so we all end up here discussing "dynamic range" 
and hours at the keyboard defending to the hilt truth and our chosen way of
life!
2) DYNAMIC
*****(********
Dynamic. What is the point of the term dynamic? OK, another big
breath. Imagine please a receiver, quite sophisticated, sitting over there
in the corner. It happens to be a radar receiver, but that doesn't matter,
except that this is what I know for a FACT.
This receiver has an input, and an output that can go to some A/D converter
or a radar display. It also has a plate on the front with two
specifications from the manual inscribed on it in big letters. They read:
"Receiver dynamic range: 60 dB"
and
"Receiver input range: 90dB"
What's this? How can it handle 90 dB with a dynamic range of only
60dB? Well that depends on what Dynamic Range is defined to be, and here
is the purpose of having the term Dynamic Range. Dynamic range is the
range from noise to max signal that the receiver can handle (output) at one
particular time  that is, without changing receiver parameters. Yep,
there it is, just "max / noise" or "max / min", as we have discussed a
million times.
So now you take your trusty signal generator over to this receiver and plug
it in to the input, and then you plug your equally trusty scope onto the
output. You adjust the siggen level and observe the receiver output on
the scope, and as you twiddle you soon see that the output limits or
saturates when the input is (say) +0dB, and gets lost in the noise at
60dB. You have confirmed the range  the dynamic range  of this receiver
is 60dB. And you see that the way it is set up, the smallest signal you
can see is 60dB.
BUT, the first stage of this receiver consists of an expensive preamplifier
with two important characteristics  this preamp has a huge dynamic range
of 90dB, and it has variable gain.
Suddenly, a light comes on the front panel. It says "Preamp gain now
30dB, it was 0dB before".
You twiddle your siggen knobs and you see that now you can see a usable
output on your scope with an input of 90dB. And now the signal saturates
at 30dB. The Dynamic Range is still 60dB. BUT you have managed to
measure a smallest signal on this receiver of 90dB and, previously, a
largest signal of 0dB. This is the total range that this receiver can
handle, 90dB. But not all at once, at one time it can only handle 60dB 
the Dynamic Range. You might like to call the 90dB figure the TOTAL RANGE,
INSTRUMENTED SIGNAL RANGE, CALIBRATED RANGE, NONDYNAMIC RANGE, SIGNAL
RANGE, INPUT RANGE or some such term. It is clearly different from the
Dynamic Range, and that is why we dignify the Dynamic Range with its own name.
3) SCANNERS
****************
This is not entirely irrelevant in the scanning world, and is specifically
involved in the relationship between density range and scanner dynamic range.
A scanner  a bad one  might have a dynamic range of 20dB i.e 100:1 (or a
D of 2.0 in the usual loose scanning jargon). BUT it may be able to
satisfactorily get detail in slides whose density varies from nearly
transparent to 1000 times darker than this i.e cover a range of
1000:1. How? Same as the receiver discussed above, by changing the
gain. With such a scanner you could NOT properly scan a single slide which
contained the 1000:1 range in a single pass, but you COULD set the gain and
scan the darkest parts getting all the detail in those dark parts, then
reset the gain and scan the light parts and get all the detail in the
light areas.
So your total recoverable density range might be 1000:1 although the
scanner only has a dynamic range of 100:1.
This fact can lead to some of the stupid specmanship that confuses
everybody. For the above scanner, you would say the Dmax = 3.0 (that is
the log version of 1000:1). But if you specified the dynamic range you
would have to say 2.0. Trouble is many people confuse the two terms (and
Dmax is possibly not being used correctly anyway) and assume that Dmax and
Dynamic Range are synonyms which they most definitely are not.
Despite the (accurately specified) Dmax of 3.0, you could NOT scan a slide
with a range of 3.0, but you COULD scan a slide with max density 3.0 and
range of 2.0.
I really hope this helps someone to understand what is a logical,
consistent approach to all this, which can be used to understand what is
going on and to therefore make informed scanner decisions and comparisons.
Now I stand to one side hoping to avoid the blast!
Julian R
*****PS to Austin******************************************************
AUSTIN  here's a related response to some of your post:
>Julian:
>(definition of Dynamic Range has) Nothing to do with resolution at all,
>
>Austin:
>It absolutely does have to do with resolution, and for some reason, you're
>not understanding that. The ratio is overall range to noise, fine. The
>noise IS the resolution, you can only resolve to the level of noise, that's
>plain and simple and indisputable. If you have a range of 1 and noise of
>1/4, you can only get four different steps within that range. You can NOT
>get 8 discernable values, because your tolerance is simply 1/4...which is
>the finest you can resolve to.
>...the noise is ALWAYS the resolution, whether it's the
>same as the low signal level or not.
I agree with everything you say here. BUT, noise is NOT involved in the
calculation of dynamic range in the general case. It is min signal that is
in the definition. In most cases the min signal is the same as the noise
level, but noise is NOT part of the definition.
Dynamic Range does have a lot to do with resolution, in a deterministic
sense under the circumstance when min=noise, but NOT in a definitional sense.
You can have noise OR min signal in your calculation but NOT both at
once. This is the problem, because here you start putting in this extra
parameter, either noise or another level depending on the time and
place. In relation to dynamic range there is only one bottomend
parameter, and that is the lowest detectable value. This might be noise,
or it might be something else. The dynamic range is defined as highest
value divided by the lowest detectable value. That's it. No divided by
noise, no nothing, it is the ratio of max to min.
So  dynamic range is max/min (a range). When min is the noise as is
usually the case, it becomes max/noise. Finished. It is not
(maxmin)/noise or anything else.
Example:
This system for some reason has a noise of 1V, a minimum detectable signal
of 2V and a max signal of 10V.
Dynamic Range = max/min = 10/2 = 5.
Not (maxmin)/noise =(102)/1 = 8
It is 5.
In this case, the DR is 5 and the number of levels to best quantify your
signal is 8.
DR is NOT related to noise. PLEASE read this carefully, the dynamic range
in this case has NOTHING to do with noise. It doesn't in the general case
either, except when min signal = noise, and even then only by a derived
relationship, not by definition. The fact that min signal is the same as
noise in the usual case is not a good reason for mixing the definitions up.
What exactly do you think Dynamic Range is if it is not a range?

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