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[filmscanners] Re: Density vs Dynamic range
At risk of helping to push this discussion into the great black hole of
overly discussed topics, I want to take issue with a view that Austin is
promoting and which I believe is incorrect and greatly confusing the issue.
At Sun, 9 Jun 2002 23:14:46 0400 Austin wrote:
>Dynamic range is, in our case, (dMax  dMin) / noise. Density range is
>simply dMax  dMin. Dynamic range is the number of discernable values
>within a density range (in our case). Density range is simply the max
>density value you can get minus the minimum density value you can get.
This is a definition of dynamic range that is at variance with the normal
definition and VERY confusing. Dynamic range is a RANGE, this idea that it
is "divided by noise" is just strange. It is NOT "a number of values", it
is a RANGE, that is, a ratio. And it is nothing *necessarily* to do with
number of bits, in fact dynamic range existed for a long time before
digital processing existed. Where number of bits comes in is that for a
given dynamic range there is a particular number of bits which is capable
of coding all the possible levels in a meaningful way, without throwing
away significant information.
Dynamic range is no more or less than the range between ...
[the highest level / voltage / power (whatever you are measuring)
that you can measure or detect]
and
[the lowest level you can measure and detect].
The lowest level as has been said many times is determined by the noise
level, and the highest level is determined by the part of the system which
first starts limiting or saturating.
In my view, despite your (Austin's) statement to the contrary, the dynamic
range is PRECISELY the measurable density range, in our context.
*******aside on the word dynamic  skip if you want*********
The word "dynamic" is a bit tricky to explain. In the industry I used to
work in, it refers to the signal range that can be handled at one
particular instant. This is distinguished from the TOTAL range which
measures the highest and lowest levels that can be handled under *different
conditions/times*. For example, in a radar system, the gain of the
receiver is changed as you sweep from close ranges to far distant
ranges. A receiver with a *dynamic* range of, let's say, 50dB, will have a
greater *total* range  let's say 90dB. The latter figure is the range
between the smallest signal that can be displayed (in a radar, at distant
range) and the largest signal that can be handled and displayed without
saturation (at close range). The difference of 40dB between dynamic and
total range is the extent of gain variation ("swept gain") that is applied
before any saturating circuits. Swept gain is used at close ranges to
decrease the extremely strong signals to a level that fits within the
dynamic range of the subsequent receiver circuits, so they are not saturated.
There is a kind of analogous situation in our context. In a scanner the
DYNAMIC RANGE would be the range between the lightest part of an image that
can be scanned meaningfully and the darkest part. The TOTAL RANGE will be
higher if the exposure can be changed by the user or the machine between
different slides. The best example is Nikon filmscanners where the
exposure variation is available as a user control. You can vary exposure
by around +/ 2 stops i.e. 4 stops manually. Assuming that all of this is
available to us (i.e. doesn't saturate or get swamped in noise, which is
not true, but this only for the sake of the example), the DYNAMIC range is
about 3.5 measured in log units (i.e. about 12 stops) and the TOTAL range
would be 4 stops higher or about 16 stops or 4.5 on the log scale.
What is this in real life terms?
It means that while you would be able to scan a slide with density range of
3.5, you would also be able to scan another slide which is 2 stops darker
or lighter but itself has a density range itself of 3.5. So the total
range between the darkest piece of image you can scan meaningfully on one
slide and the lightest you can scan on another is 16 stops, in contrast to
the range between the darkest and lightest points on ONE slide which is 12
stops.
(I only used those figures as examples. I assumed the scanner had a genuine
dynamic range = density range of 3.5 which is less than that manufacturer
quotes. And the assumption that the exposure variation actually adds to
the dynamic range to make the total range is only true if the exposure
variation is done at a point in the circuitry where the signals still avoid
noise and saturation, which is not true in scanners I know of. In real
real life I think the total range is little different from the dynamic
range, by observation of the increased noise levels evident when you turn
the exposure down and the blooming when you turn exposure up).
I find it very hard to explain all this, but it is actually a very simple
concept.
**********end of aside****************
Now back to number of bits. The number of bits can be related to a given
dynamic range because, as has been said, you don't want to waste either
bits on the one hand, or resolution on the other hand. There is nothing to
stop you using more bits if you want, but it is largely wasted because
every level you are measuring / coding will be jumping up and down by about
the noise level. So you choose your coding so that the distance between
successive measurement levels (i.e one bit) is the same as the noise
level. If you use more bits, then you will get coded levels out which flip
between 2 values even when the actual input signal doesn't change, so there
is just no point. If you use less than optimum bits, you will be losing
some of your possible resolution.
(In fact noise and signals are statistical by nature and there are no
absolutes in this  even with optimal number of bits you will still get
output levels flipping from one value to another for the same actual
density, but less often).
So the optimum number of bits is decided by:
num coded levels = max level divided by optimum digital step size
= max level divided by noise level.
This gives you the number of levels. The number of bits is then determined
from that by: num bits = log (base2) num levels.
Note that num levels = max level divided by noise level = dynamic
range. This is NOT saying that num levels is the same thing as the dynamic
range. They are two totally different things. It is only saying that the
OPTIMUM number of levels is the same number as the dynamic range expressed
as a ratio.
OK I need to eat tonight so I have to stop this. To reiterate  my aim in
writing this was to point out that I don't agree with the definition that
is being used in this discussion. The problem being that this faulty
definition is partly responsible for the discussion failing to
converge. I doubt I have reduced the confusion , and guess I have
probably started yet another argument, but that was *not* my aim!
Julian

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