[filmscanners] RE: Density vs Dynamic range

["Austin Franklin" <darkroom@ix.netcom.com>]

Hi Julian,

I did not write it...as most all of the content is simply very mistaken and
very wrong.  I believe I did reply to it.  If you would like me to respond
more to it, or to any specific points in it, I am happy to do so...but as I
said, it's just simply wrong.

The ISO proposal coincides with my views/statements, and the below goes
completely contradictory to both ISO and my statements.

One BIG confusion the poster has is with minimum signal level and noise.  He
is confusing the two, and using them interchangeably, and that is incorrect.
If they happen to be the same, then that obviously works out...but if they
are not, you can't simply substitute one for the other, or ignore either of
them.

Also, he seems to not understand the difference between the absolute range
(max - min) and the max signal (simply max).  They aren't interchangeable.
If you have a max of 10 and a min of 3, that's an absolute range of 7, and a
max of 10...but in the DR equations, you only use the absolute range (unless
you are using max-min to derive the absolute range).  The range of 10-3 has
exactly the same range as 20-13...though the max is different, and the
important point, as far as the DR equation goes is the absolute range, not
the max.

Simple example (taken from the very bottom of this post, where he makes BOTH
these very mistakes in his "calculations"):

> This system for some reason has a noise of 1V, a minimum detectable signal
> of 2V and a max signal of 10V.

DR = ((max - min) / noise)

The absolute range is 10-2.

so... (10 - 2) / 1 or 8 is the dynamic range.

Austin

> 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.

That is wrong.  The range IS what the range is, and is NOT based on the
noise level.
The mistake is you are using noise as your divisor instead of min signal
level.  Your equations should be:

DR = 10log10(max-min)/noise)

where in case 1, range = 1-1000mV, noise 1mV so 1000-1 = 999/1 = 999,


> 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 so-defined 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 sig-gen 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 pre-amp has a huge dynamic range
> of 90dB, and it has variable gain.
>
> Suddenly, a light comes on the front panel.  It says "Pre-amp gain now
> 30dB, it was 0dB before".
>
> You twiddle your sig-gen 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, NON-DYNAMIC 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
> re-set 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 bottom-end
> 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
> (max-min)/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 (max-min)/noise  =(10-2)/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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