Digital BW, The Print

Hi Roy,

> Now the big question is "What's the signal?".

Very simply, for a photographic image, it is the density value.

> All my own
> recollections and everything I saw in the book has an audio/video
> type flavor.  I.e the diagrams show nice sinusoidal signals in
> the time domain.

But time has never been a part of the dynamic range equation at all, even in
the case of audio...it is purely voltage.

> Austin, you've made a clear choice in this mapping from the time
> domain to the space domain.

Not at all...see above.  Neither time or space have anything to do with
this.  It is purely a (any in fact) measurable quality that is required,
whether voltage or density or what ever.  It is what ever property YOU want
to figure out the dynamic range of.

> For you "signal" is difference
> between to tonal densities, i.e:
>     largest signal = dMax - dMin
>     smallest discernable signal = smallest density difference
> or maybe I can paraphrase "signal is basically contrast".
> (I hope I'm not putting words in your mouth!)

Sure, I'll fly with that.

> As far as I can tell your derivations from this and all the
> discussions are consistant and mathematically sound.  But I've
> been a little unsure of picking this mapping rather than
> something else.

I disagree with your use of the term "mapping".  Again, you pick the
property you want to figure out the dynamic range of...note the dynamic
range equation does NOT use any units for largest/smallest...they simply
have to be on the same scale, of the same unit.

> For pictures, what's the basic perception?  It seems you've picked
> contrast --  so the ratio is (highest contrast/lowest contrast).

Yes, since contrast (as in delta change) is all that distinguishes tones
from one another.

> Why not the more basic perception: darkness versus lightness?

What, exactly, do you mean by "darkness" and "lightness"?

> The ratio would be (darkest/lightest). I guess you can see
> where this is going->> it reduces the whole thing to
> Density Range.
>
> DynRange = log10 (darkest/lightest)
>          = log10 (darkest) - log10 (lightest)
>          = dMax - dMin
>          = Density Range

But you have now removed, arbitrarily from what I can tell, the smallest
discernable signal from the equation, that above, you agreed was part of the
equation.  Why?  This seems like one of those Gary Larson "and then magic
happened" on the chalk board...

> I doubt that you're ready to switch definitions but intuitively
> using "dynamic range" to means "number of tones" rather
> than some "range" of values seems weird.

Not at all, my guess is it really means dynamic OVER THE particular
range...but I do not know the history of the term.  It isn't really A range,
but it describes a property OF the given range.  Density range isn't a range
either, but it does describe the width OF the range of density.

> And by the prevalence
> of the "dynamic range" threads that go on regularly many
> others don't feel comfortable with your definition.

Yeah, but I didn't make up the definition, as you well know!  Remember, this
is a very technical issue, being described to and by and used by a lot of
lay people.  There are a LOT of misperceptions/understandings when this type
of thing happens...especially these days with the proliferation of the
Internet.  You can find "compelling" (as in decent presentations, that look
well thought out) sources for both sides of near any argument!

> Here's an interesting thought experiment, Say we a printing
> out gray swatches from an inkjet printer.  Each swatch
> is a small square of each grayscale value.  Assuming we're
> talking 8 bit files and printer drivers, we can have only
> 256 possible gray swatches.  If its all perfectly
> calibrated ideally we ought to be able to distinguish
> each swatch.  Now imagine a swatch which is a checkboard
> with two different adjacent gray values, for instance
> 137 and 138 mixed together.  What does it look like?  Is
> it appear as a checkerboard of two different grays or
> does it merge into a new and different 137.5 gray swatch?
> I think the answer is "it depends" ... i.e. how close you
> get to it, got your bifocals on? etc.

It does depend.  More so on lighting than anything else.  We actually can
distinguish a lot more than 100 gray tones, but the 100 number is in "a"
given light...but vary that light, and you increase the number of tones you
can see...and your standard photographic print may not have tones that
extend into that range, since most people don't view a photo in the dark or
extreme light, so they weren't designed TO be seen in those conditions.

> The point is "number of tones" is kind of nebulous.  This
> also adds to my dissatisfication with "dynamic range"
> meaning "number of tones".

Very interesting point, but I have an answer ;-)  You are right, in your
example, you will be able to shift the tones all by .5 of a tone, and get a
whole new set of shifted "discernable" tones...but you can STILL only
discern the same number, as well as have the same separation!  This does
fail at some point, when your number of tones is high enough (where adjacent
tones aren't discernable).  Does that make sense?

> Hopefully someone will find this useful.

Yes.

Regards,

Austin