RE: filmscanners: brief density math lesson...

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

>  >The integer ratio values are what your scanner gives you.  14
> bits means you
>  >can represent an integer number from 0 to 16,383.  This means if your
>  >scanner can record integer density ratio values from 1:1 (0) to 16,384:1
>  >(16,383).  16,384:1 is a D value of 4.2 (log 16,384 = 4.2).  That is why
>  >scanners that have 14 bit A/Ds claim to have a DMax of
> 4.2...all that means
>  >is they can support integer density ratio values of 1:1 to
> 16384:1, but that
>  >does not mean the scanner CCD and analog circuitry can provide
> that!  That's
>  >another topic of discussion...
>
> This is a common misconception - relating bit depth to dynamic range.

Believing this is a misconception IS a misconception!  The number of bits
DOES have in and of it self a dynamic range, that's simple math.  8 bits has
a dynamic range of 256:1, 14 bits, 16,384:1.  If you want all the
information from a 14 bit A/D, you NEED 14 bits.  If you have a CCD that has
a dynamic range of 10,000:1 you NEED 14 bits to accommodate that dynamic
range with linear mapping.  Plain and simple.

> Let's take a silly example. Suppose we have a CCD that can cover
> a 1000 to
> 1 range of light intensity. That's a DMax of 3. Provide an appropriate
> light source and some optics, and connect it to a four bit A to D
> converter
> (16 levels). Set the gain and offset so that the limits of CCD
> sensitivity
> correspond to values 0 and 15 (computer things count from zero,
> not one) of
> the A to D converter. We have a scanner with a DMax of 3, and
> four bits of
> resolution. The DMax has nothing to do with the number of bits in
> the A to
> D converter, just the range of the CCD sensor. We could use an A to D of
> any number of bits with this CCD sensor and capture its full
> range with any
> level of tonal precision we wish.

Actually, your example is wrong.  Your bits represent a RANGE of input
values, and if your CCD outputs a 4 volt swing, let's say, and you use a 4
bit A/D, that's 1/4 volt per code.  That is a system dynamic range of 16:1.
There is no way you can capture the 1000:1 dynamic range of the CCD with
only 4 bits without using some other technique, such as thresholding, for
the high and low values.

Many people try to bring up similar examples, and this "argument" has been
had probably 10000 times over the years and they make the mistake you did
above, forgetting that each value represents a range of input voltages.

You CAN technically REPRESENT ANY dynamic range you want with 2 bits and
thresholding, which is different than your example above.  You are confusing
actual dynamic range with REPRESENTATION of dynamic range.  It is also
common to confuse dynamic range with resolution.  Two completely different
issues.

In fact, quite a few manufacturers list the dynamic range of their CCDs in
number of bits!