[filmscanners] Re: Dynamic range

["Julian Robinson" <jrobinso@pcug.org.au>]

At 06:18 30/08/02, Austin wrote:

>Come on, Todd, the paper CLEARLY says dynamic range is a resolution.  Why on
>earth do they say so many times that you need so many bits to represent a
>particular dynamic range?  Forget the diagrams, you are confused by them, as
>they clearly represent two different things.

I have never read whatever paper you are talking about, but I GUARANTEE you
it does not SAY that dynamic range is a resolution.  I am sure that you,
Austin, INTERPRET it to say that, but it will not actually say that.

You ask: "Why on earth do they say ...that you need so many bits to
represent a particular dynamic range?"

Because, Austin, bit numbers put a limit to the Minimum Discernable Signal
(MDS) and hence DR, that's why.

Austin, if you have a scanner with a noise level of 36dB below the max
signal (i.e. 3.6D or 1/4096), I am sure you'd agree that you need a 12 bit
downstream system to maximise the utility of this scanner. (because 12 bits
digitises to 4096 levels, and one level is then just equal to the noise
level of 1/4096 * max signal.  You won't have wasted bits being lost below
the noise, and you won't waste good information by failing to digitise the
smallest possible discernable signal)

Call this Case 0.
***The dynamic range is 36dB or 3.6D.  I say that is the RANGE of this
scanner, you say it is the RESOLUTION.  In this case it is both.
***So, resolution also = 36dB.

CASE 1
********
Now, if this same scanner only had a 10-bit downstream system (such as from
the old days when A/D's were incredibly expensive), what is the dynamic
range?  The noise level is 1/4096, and the smallest digital non-zero signal
is one bit or 1/1024.   Obviously the minimum usable or detectable signal
cannot be smaller than either of these, or in other words it is the maximum
or the two figures.  In this case it is 1024, and the MDS is determined
ONLY by the bit-size.   Noise level is 4 times smaller than this, so is
irrelevant.  So DR is 1024:1 or 30dB or D3.0.  Remember... the DR  in this
case is NOT determined here by noise level.  Please note this, it is
determined by MDS as it always is, and in this case MDS is determined by
number of bits, not noise.

***In this case DR = 30 dB
***Resolution is still 36dB if you stick with your formula = max/noise, or
30dB as it obviously is in fact, given you have a digital step size of
1/1024 or 30dB.

CASE 2
********
If this same scanner had a 14-bit downstream system, what is the DR?  It is
(yawn): max signal / MDS. This time, MDS is determined by the noise level,
because noise level is higher (4 times higher) than the bit size.  MDS =
noise level = 1/4096. So the DR of this scanner is 36dB again.  You could
have any number of bits over 12, and it would not change the dynamic range
one iota.

***In this case DR = 36dB.
***Resolution is --- 36dB by your formula = max/noise (correct this time),
or 42 dB if you just consider digital bit numbers and step size.

CRUNCHY BIT
****************
Here is the crunchy part - the dynamic range is NOT determined by the
number of bits, it is LIMITED by the number of bits.  The dynamic range is
NOT determined by the noise level, it is LIMITED by the noise level.

The dynamic range IS determined by the Minimum Detectable Signal, which may
be determined by the noise  level OR the number of bits.  Neither of your
continued assertions are true :

A) It is NOT true to say that DR = max signal / noise.  Case 1 shows this.
B) It is NOT true to say that number of bits determines DR, as you see in
Case 2.

You are continually confused by the fact that there is an OPTIMUM number of
bits for downstream processing, and it is determined by the noise
level.  No argument here. Optimum number of bits is when a single bit step
is equal to the noise level (making a few further assumptions).

BUT you continually go on from this ASSUMPTION based on good engineering to
say that both A and B are true.  They will ONLY be true for an optimally
engineered system, neither being true in the general case, and are
certainly not true as definitions.  Do you see the difference between a
DEFINITION and GOOD ENGINEERING?

In any other case, EVERY case where the number of bits is not exactly equal
to the inverse of the noise level, then either A) or B) must not be
true.  Since the number of bits is limited in practice to powers of 2, and
since manufacturers commonly put more bits into their machines than noise
justifies, then almost always the scanner will NOT be optimally engineered
and one of A) or B) will not be true.

It is important to understand this accurately, because to discuss any of
this topic properly you have to understand WHY dynamic range might or might
not be equal to either of the figures as calculated under A or B.  Or WHY
manufacturers adding extra bits does not necessarily change their scanner's
dynamic range at all.  Without an accurate understanding of the DEFINITION
of dynamic range you won't know what it is measuring and you won't be able
to properly answer questions on the topic.

Julian


----------------------------------------------------------------------------------------
Unsubscribe by mail to listserver@halftone.co.uk, with 'unsubscribe 
filmscanners'
or 'unsubscribe filmscanners_digest' (as appropriate) in the message title or 
body