Digital BW, The Print

> First off I'd like to acknowledge you and Martin for the time you've put
> into this topic. You both have gone far beyond the call of duty. Thanks.

Ha!  He's as tenacious and as verbose as you are ;-)

> > No, only two bits are needed to represent the DENSITY range.
>
> I thought one bit could give you density range: maximum measurable (max
> black), minus min measurable (paper white). Two tones, one bit.

Here's the thought, call it as you may.  You need to represent two
thresholds, and ANY value in between.  That's three numbers you need to
represent.  You need two bits to do that.

> And that it
> was the addition of the min discernable value (which I'll shorthand to
> noise), which you sampled via deviation across the test patch, which gave
> you the third component (noise) of your dynamic range equation?

No.  Bits and dynamic range are different than representing density range
with N bits.  The number of bits IS the dynamic range (of that number of
bits), as you need the intermediate tones to ALL be represented.  You do not
for density range.

> I read you to mean that you get your dynamic range (I'll
> abbreviate that to
> DyR from here on in this post) by measuring the min and max (I'm short
> handing here, you know what I mean), subtract the min from the
> max (which is
> your density range (DnR), then dividing that sum by your noise, which you
> measured from your third tone. That gives you your DyR.

Yes, that is correct.

> So you've sampled three tones, referred to as: min, max, and test (or min
> discernable, or noise). Let's assume this print was comprised of
> ONLY these
> three tones. You could calculate a very high DyR from these three tones,
> implying the print has many intermediary tones, which it does not, no?

You need to separate the dynamic range of a particular image from the
dynamic range achievable from the "system".  They are different.

> Really? First off I wasn't aware of that, when was that distinction made?

Martin said that chemical prints don't have dynamic range since you can't
measure any discernment in tones, he claims they are infinitely continuous.

> Second, so are you saying the two require different testing
> methodologies to
> determine DyR? That's the first you've said of THAT.

A single test methodology can be arrived at.

> >> A) We know a well handled glossy fiber print is capable of a
> >> greater density
> >> range than Piezo.
> >
> > Which is not really relevant to dynamic range...
>
> Okay, lets explore this.

It IS relevant in that it bounds the "largest" signal, but you can have a
lower "largest" signal, and have a higher dynamic range.  That's why I said
it isn't relevant.  Relevant really isn't the right word perhaps.

> >> B) We know the source material of a silver print (negative) is
> capapble of
> >> more tones (millions? billions?) than the source material for an inkjet
> >> print (256? 65,000?).
> >
> > I don't believe we know that.
>
> Well it's not a given in every case, but we know MOST people out here are
> Piezo printing from 8-bit, 256 shade files, and I trust you agree most
> continuous tone negative films are EASILY *capable* of containing
> more tones
> than that. Tell me you don't disagree with that!

That's negative, not print.

> >> that measuring the dynamic range of a print still
> >> doesn't tell you how many tones it contains;
> >
> > It certainly does, as defined by the equation for dynamic range ((dMax -
> > dMin) / smallest discernable value).  Note, it has an
> additional variable in
> > the equation beyond what density range does.  The dynamic range of a
> > chemical print certainly can be done as a range.  You can add
> any complexity
> > to it you want...but it doesn't change the basic concept.
>
> Okay, how many tones are in a print with a DyR of 25db? 10, 100, 1000?

25 = 10log10((dMax - dMin) / sds)

Now, I claim that ((dMax - dMin) / sds) ARE the number of tones, so it
doesn't matter what those three values are ;-)

So, 25 = 10log10X, makes X 310.

> Is it possible to measure a DyR of a print that contains less
> than that many
> tones?, Say a print with paper white with a 95% reflectance, a
> dmax of 2.2,
> a min discernable value of .1, and 10 solid shades of gray within the DnR?

You can always measure the dynamic range of one print...or the system.
Different tests though.

> > P.S.  Please keep it short if you could...
>
> I tried...

Hum ;-)

Regards,

Austin