Digital BW, The Print

> your statement that density ratios must be
> integers is just plain wrong.
> I don't know where you get that from,

Well, I don't believe I said they "must be", but they are in every case I've
seen (and I don't believe it's important to the discussion if they are
integers or not, the fact that they represent ratios are what is
important)...I don't know any place that density ratio values are used that
aren't relative to 1.  Do you?

> unless perhaps you are somehow thinking of binary representations.

Correct.  A digital data file (which is the only place I see density ratio
values used) does not represent density by density value (for example, as in
a density value of 1.86, "DV"), it represents them as an integer value
[int(10**DV)], say "72".  I believe the distinction is "density ratio
value", which specifies a ratio, and, as I said, I have never seen this
ratio specified other than "to 1" (:1), vs "density value" (no ratio), which
is log10(1/R), where R is the reflectance measured.

The important issue is that density is measured relatively.  A density ratio
value of 2 is twice as dark as a density ratio value of 1, 3 is three times
as dark as 1, etc.  It has nothing to do with the ability to measure between
values (dynamic range).

You can technically have any dynamic range (number of discernable steps)
between the density values of 1 and 2, but still only have a density range
of 1...no matter what your dynamic range.

This next part is really esoteric...very much more so than the rest of the
discussion...just thought I'd warn you ;-)

You, technically, can design a digital system such that it uses fractional
values.  I've done exactly that, it's just representation.  If you have 16
bits, they could represent 12 bits to the left of the decimal point, and
four to the right...but the problem is, A/D systems aren't typically
designed that way, and in fact, it doesn't matter...since the values are all
relative anyway, and it wouldn't increase your dynamic range anyway, since
the A/D value of 1 (or greater) is going to represent the noise level of the
analog part of the system.  Now, it doesn't have to be, you could use a 24
bit A/D and really only get 16 valid bits out if it, where the lowest 8 bits
are nothing but noise...but that's typically not how it's done...as there is
no need to waste good bits doing that.  Noise does tend to creep up into the
least one or two bits anyway though...and that's a good thin in my
book...I'd rather have too many bits, then too few ;-)

Austin