Digital BW, The Print

Austin,

I'm working off your post below, but not in a counter point fashion for now.

We must keep in mind that in spite of the disjointed nature of the
discussion here there has been something of an ordered flow. However, I
believe as we digest the points of all participants in the discussion we
drop some of our convictions, and perhaps deepen others. At this point I'm
not sure of what your convictions are, so I'm not sure what from the past I
should or should not be speaking to.

For instance, at one point you were demonstrating how one could derive a
tone count from a few simple measures of a print. You were saying you could
determine how many shades of gray a print contained from an expression like
DyR of 3.7, or 25db. That condition I believe is only true if one assumes
that there are contiguous tones within the mediums range.

Remember, you had said DyR, and thus tone count, could be computed from a
measure of (dmax - dmin)/noise, and that noise could be determined from one
intermediary tone. That could give rise to a situation where a full tone
print could yield the same DyR as one which contained 4 tones. That flies in
the face of your tone count premise. Thus your interpretation of that
formula demanded linearity. What I mean by linearity here is that all tones
that could be contained within the density range ARE represented.

Let's look at the staircase. In the situation where you know the height of
the staircase (DnR), if the rise and depth of each step is the same
(linearity), you can measure just one step to determine how many steps are
present. This method is similar to your original description of the DyR
measuring method. If each step had a different rise and depth a calculation
based upon one step, which was different than all the others, could yield an
inaccurate result. Thus linearity IS required.

Furthermore, this also assumes that every step is in place. If some of the
middle steps have fallen, your calculation WILL be inaccurate!

Later, to address non-linearity you began to include the concept of
integration and calculus. For me to really understand this would take more
explanation than I deserve, but I sense you mean taking a broader sampling
of tones and noise and calculating them together. If so, fine.

But at that point I realized that by the time you've sampled the print
sufficiently to get meaningful representation across it's density range, it
would be wasteful to contract those measures into the DyR formula rather
than plot them as a curve or histogram, as has been the convention of
photography! Again, speaking not to the "could you", but "would you", of DyR
in a non-linear analog domain.

This question of relevance is one that Martin brought up days and dozens of
posts ago, and which speaks to the whole premise of why DyR is used
differently in the field of photography than audio or digital.

Perhaps if/when you summarize what you presently maintain on the issue and
what you've dropped, and/or present an explanation of how you would approach
my three print challenge, I will know what you still maintain - or perhaps
you can convince me I'm wrong. Either way, I think we're loosing sight of
context.

Todd



> Todd,
> 
> We discussed this a number of posts ago:
> 
>> You also did not speak to my premise that I think that a calculation of
>> tones from DyR is only possible if linearity is assumed, which is not
>> something I would take for granted in a silver print.
> 
> You don't need linearity at all.  Noise can be calculated using calculus,
> and integrated over the entire range of the print...  Knowing math is not
> your strong point?  I am guessing you don't know what integration is, in a
> mathematical sense?  I can explain if you like."
> 
> And between you and I:
> 
> "> It would seem to me that those
>> calculations work well for a system that produces a full and linear
>> placement of tones between your dmin and dmax,
> 
> You are correct.
> 
>> but when those
>> conditions are
>> not met it would yield an inaccurate tone count. If I'm wrong
>> please explain
>> why.
> 
> You are absolutely right, and I'm happy that you have an understanding of
> this to make such an observation!  Bravo!
> 
> This is where calculus comes into play.  It is a way of taking into account
> the variability of the noise throughout the system.  Here's the deal.  The
> noise "change" could be deterministic (possibly linear), which means it's
> predictable.  If that is true (and I believe it is), then taking some number
> of points (what ever are warranted by the type of equation that defines the
> noise over the range, and if the noise is a simple gain, as in it's linear,
> two points would do) in the "middle" will give you enough information to
> derive the dynamic range.  Let's not talk about what that "result" or
> equations would look like yet..."
> 
> Characterizing a non-linear system is just no big deal, it's done all the
> time, and I've done it a number of times my self...