Alan Browne said:
Dynamic range is quantifiable regardless of a signal being digital or
analog. Ask an electrical engineer. Or here:
http://www.jeffrowland.com/tectalk6.htm
Of course, and the term existed before the concept of an analogue to
digital convertor was even invented.
Film is not an "analog", it is an image. ("Analog" means, "by
analogy", such as a voltage representing a temperature sensor and a
meter indicating that voltage as a temperature instead of as a voltage.).
However, Alan, by that definition (which I partially disagree with in
any case) film certain is an analogy of the scene, and thus analogue.
My disagreement with your definition becomes apparent when you consider
that the temperature can also be represented by a series of digital
numbers on a meter just as well - the numbers are an analogy of the
temperature. Thus, your definition leads to the immediate paradox that
digital is analogue - and thus, using the established "proof by
contradiction" method, your definition must be false.
In general terms, analogue means "continuous" whilst digital means
"discrete". A digital representation of the signal can only indicate
discrete values, whilst an analogue representation can indicate all
values with infinitesimal discrimination. The digital representation
can only indicate the signal to the noise floor if there are sufficient
discrete steps, however the analogue representation *always* indicates
the signal into the noise floor.
The confusion (as much mine as anyone's) is that the term Dmax for film
means maximum density, and this has a figure of 4.0. A film burned
clear would have a Dmin approaching 0 and a signal on the A/D would be
at or near maximum. Conversely, the densest area would have a signal at
the A/D approaching 0, but necessarilly would contain noise. The range
between the two can be construed as the Dynamic range of the film.
What seems to be missing in this entire thread is any consideration of
why the DRange of the scanner *MUST* be significantly higher than the
DRange of the film it is scanning. This relates to perception and gamma
as much as it does to the difference between analogue and digital.
Film reproduces the luminance changes in the shadows by increasing the
number and size of silver grains or dye clouds per unit area. This is
continuous, and thus effectively analogue - even at the quantum level it
remains analogue with the presence of atoms in a unit area being
probablistic.
If the DRange of the scanner simply matched the DRange of the film then
the Dmax on the film would represent a count of 0 from the scanner,
whilst the Dmin on the film would be represented by a number close to
(2^n)-1. The next darkest level on the scanner from this Dmin
representation would be a count of one less, which would be a virtually
indistinguishable visual change of density on the film. However the
next lightest level from Dmax which the scanner could represent would be
1, due to the discrete nature of the digital data. This would represent
DMax-0.3 on the film, and would be visibly discrete and lighter than the
Dmax. For example, film Dmax is generally around 3 - 3.6, which should
require no more than 10-12-bits, however a 1 bit change in the shadows
of such a linearly encoded digital image is clearly visible. In short,
an ADC which has a DRange equal to the film is inadequate to
discriminate the shadow information.
The problem this throws up is that the equations that both you and
Dimitris have been debating relate to *linear* representations of
signals, whilst our perception of density is very non-linear. It is
well known that your vision is more sensitive to fine changes of
luminance in the shadows than it is in the highlights of the scene,
hence the use of gamma encoding to minimise the bit depth used to
describe the image digitally. This means that the dynamic range
required to describe the shadows on the image is much higher than
dynamic range necessary to describe the highlights - however, your
equations relate to a uniform dynamic range in a linear system which, at
best, indicates an *average* dynamic range. Since perception of
discrete steps is the driver for quantisation level, your equations for
Drange should be applied in perceptual space, the space in which the
discrimination of discrete steps is equal throughout the range, ie.
perceptually linear. The results can then be transformed via the
inverse gamma space to voltage, luminance and digital linear space to
determine the Drange necessary to describe the shadows without
posterisation, and thus the minimum Drange necessary on the scanner.