Digital BW, The Print

The thread has been interesting and after thinking a lot and
reading about it I've got a few comments.

1) Dynamic Range Issue

At first I was very skeptical about Austin's views about
Dynamic Range.  I've got a couple of degrees in EE from way back
but its all pretty rusty since I haven't used it in a long time.
So I figured it deserved some brushing up on the subject.
Naturally, I decide to look at the book by Higgins, that Austin 
referenced for his formula.  As expected Austin's formula is
straight out of the book.

Dynamic Range (dB) = log10 (largest signal/smallest discernable signal)

Now the big question is "What's the signal?".  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.  Signals are measured by amplitude of the sine
waves.  All this is well and good, but of course for our purposes
we want to map all this into photographic prints in the spacial
domain.

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

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.

Obviously, what we are trying to do is make a mathematical
model of a human perception.  In audio, the main thing is
loudness: with dynamic range we're characterizing how much
louder the loud parts are from the soft parts.  So the ratio
inside the parentheses is (loudest/softest). Makes sense.
For pictures, what's the basic perception?  It seems you've picked
contrast --  so the ratio is (highest contrast/lowest contrast).
Why not the more basic perception: darkness versus 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

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.  And by the prevalence
of the "dynamic range" threads that go on regularly many
others don't feel comfortable with your definition.
I'm not up to trying to buck a whole industry's definition so
are there references that show this as wide spread?  I'd
love to read some.  


2) Number of Print Tones

There was some discussion about number of grays on a monitor
screen.  For current monitors they all have a maximum of 256
grays.  Every RGB monitor I know of takes 8 bits for each
color (Red,Green,Blue).  Grayscales make R=G=B i.e. the same
8 bits are sent to each color gun.  There's only 256 possibilities.

To get an interesting feel for how many grays make up a 
picture, try this.  Take a 8-bit grayscale picture small
enough to fit on the screen at 100%. Then posterize it with
128,64,32,16 levels.  Try a couple different pictures.

For both darkroom and inkjet prints, gray tones are really
just a human perception.  There is just white paper with
lots of small black specks of silver or carbon.  The
perception of grays is based on optically (eyeball) and
the brain integrating the blacks and whites over a finite
area. So its based on things other than the print itself.

I would guess that less the brain feels a need to integrate
over a larger area the sharper the image seems. But the
larger the area the more opportunity for perceiving more
different gray tones.

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.

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


Hopefully someone will find this useful.

Roy

-- 
Roy Harrington
roy@...
Black & White Photography Gallery
http://www.harrington.com