[filmscanners] RE: scanner dmax discussion

["Austin Franklin" <austin@darkroom.com>]

Hi Tim,

In this context, dynamic range and bit depth are entirely deterministic, but
that does not mean that the scanner/film etc. are capable of providing the
full dynamic range that a particular number of bits are able to hold.

To calculate the dynamic range of N bits, it's basically 10log2**n, so for 8
bits, the DYNAMIC range (NOT the density range, that's an entirely different
story) would be 24dB (or 48dB depending on the application).

> "I thought I understood the relation of bit depth to dynamic range, but
> now I'm not sure.  In the latest issue of View Camera, George DeWolfe
> says that the maximum possible dmax for an 8 bit gray scale is 2.4 while
>   the maximum possible dmax of a 16 bit gray scale is 4.8.  I understand
> mathematically where these figures come from.
>
> log_10(2^8) = 2.41   and  log_10(2^16) = 4.82.
>
> But I don't see what this has to do with dmax.

dMax is a density value, and isn't necessarily the same as dynamic range,
but the term dynamic range and density range seem to be mistakenly used
interchangeably, and they are not the same, except for a very strict set of
criteria.

> The light detecting
> devices in scanners are physical devices capable of responding to some
> range of light intensities.  Below a certain level, say I_min, nothing
> will be recorded.

That would actually be noise, as in, you can't discern a signal smaller than
that.

> Above a certain level, say I_max, additional light
> won't produce any more output.

Right...  You may have the two reversed...dMax is dark, and dMin is
light...but in log terms, which this is in, it really doesn't matter...and
it depends on what your reference is as well.

> So it seems to me the total range of
> densities the device can handle should be log_10(I_max/I_min).  It seems
> to me that the bit depth just determines how finely that range is
> subdivided.

Ah, you have hit on the typical "contention" point ;-)  The point I've tried
to make is that (with respect to dynamic range, and density range as well,
but again, only under strict criteria) you can't discern smaller than noise,
therefore, noise is your minimum discernable "step" in this particular case.
It just means that given a value X, that the next discernable "value" is
X+noise...and therefore there are really only so many "steps" that you can
discern over a particular range...and this means that dynamic range, in
reality, gives you a "number of discernable data points".  But, density
range does not have a thing to do with discernability.

So, when converting the information to "digital data", each "step"
(increment of 1) is equal the noise level...having any more than that, you
don't get any more usable data.  having any less than that, and you lose
data...so the scanner is typically designed so that the noise in the
CCD/Analog Front End/A/D is equal to one bit.

Any number of bits can represent any density range, but it can't represent
any dynamic range, if you understand that dynamic range basically defines a
resolution, and density range doesn't.  You can represent any density range
with two bits...just assign the value 1 to below dMin, 2 to between dMin and
dMax and 3 to above dMax...and you have just represented any density range
you want...but you have no resolution, which is were dynamic range comes
into play.

> But why can't a scanner with 8 bit depth just use a
> larger step size.

It does, and you can represent ANY density range with 8 bits, just like you
can with two bits, but the number of bits limits your dynamic range, not
your density range.  That is why whether you get 8 bit data, or 16 bit data
from your scanner, you still get the same density range...just with less
"resolution".

> Let me also ask a related question.  Just what does my Epson 3200
> scanner and its software do when I use it to scan a b/w negative whose
> maximum density is about 1.4  at 16 bit depth?   Does it try to divide
> up the range from 0 to 1.4 into 65536 values...

No, more than likely not.

> ...or does it just use
> 1.4/3.4 of that range for about 27000 distinct values.

Probably a lot less than 2700, as 1.4 is 10**1.4 or 25, and 3.4 is
2511...but that all depends on how the scanner maps what to what.  You can
check this out by looking at a histogram of raw scanner data...and I hope
you get a heck of a lot more than 25, BTW.

Regards,

Austin

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