Digital BW, The Print

Hi Austin (is anybody else still listening?)

This discussion has gotten badly out of hand.  We seem to
be on totally different wavelengths of thought.  It certainly
hasn't been all bad, though.  No doubt, I've learned a few things
and its stimulated my thinking on the whole matter.

But:
We just barely agree what DynRange of audio is.  I'm not really sure!
We don't agree on DynRange of Imaging. (DROI)
We don't agree on whether DROI is one specify thing.
We don't agree on DROI has been used in the past.
We don't agree on DROI if used really is a misuse.
We don't agree on DROI changed from correct use to misuse
   because of the internet.
We don't agree on if there is a common use of DROI.
We don't agree on whether common use of DROI is a misuse.
etc. etc.

The dialogue seems to be bogging down in such esoteric and semantic
details that we can't see the forest from the trees.

I don't have the long history of working with the DynRange
concept you have.  But ... I've got a good math and science
background.  I have a pretty idea of the audio/hearing and
image/sight perception issues.  I'm not a super expert guru
in all this stuff, but the math is well within my experience
and the perception issues are simple enough.  For whatever its
worth my approach has been to look and research the whole
picture without an emphasis from one specific direction.

So. The only thing that makes a lot of sense to me now is to
spell out my logic.  I really don't we're in the realm of
proofs one way or the other.  I think you've said several times
that you can take DynRange of any variable you like.  Right?
If we start with "dynamic range of an image", no variable is
stated so who's to be the dictator of what the variable is?  

What follows is basically by definition just my opinion.
I've made choices based on what I think is important and
just plain: how I see it.  The whole package goes together.
There are many choices but they all relate in some way.

---------------------------------------------

There's a lot written about DynRange of audio and sound.
Most of my approach is in moving the concept from the audio
realm to the imaging realm.  I'm very influenced by the
parallelism of the physical properties, of the perception, and of
the math involved.   The parallelism is so compelling that
I place very high importance to it.  Modelling in the
abstract is used extensively in scientific research.  Here
we actually have two physical systems that can share a 
model or even model each other.

First some of the physical properties.  Both sound and
light are wavelike phenomena.  Sound is a pressure wave
moving through the air, there is an energy associated with
it the amplitude of the waveform determines the energy.
Likewise, light is an electromagnetic wave which has
an energy as well.  In both cases some source generates
the respective waves and they propagate in space.
We have ears and eyes to detect these waveforms.  A key
aspect is that both senses perceive linearly increasing
intensity when the underlying waveform has an 
exponentially increasing energy level. Or mathemtically
speaking the perception intensity is proportional to
the log of the waveform energy. This parallelism between
energy of the two waveforms and the perception of the
two waveforms is so strong that I believe it only makes
sense to apply the mathematical constructs in a similarly
parallel fashion.

In the audio realm we have:
The decibel dB is used extensively as a measure of a power ratio.

db = 10*log10(power1/power2)
If there are two power levels they differ by this many dB
given the levels power1 and power2.

There is one special dB measurement called dynamic range.
It has the same formula structure but uses two specific
power levels: the maximum power and the minimum power.

DynRange (dB) = 10 * log10 (maxpower/minpower)

It is basically a measure of the largest power ratio that
the audio system can produce.   Power is just energy
per time unit, so a power ratio is identical to an
energy ratio ( the "per time" unit whatever it is cancels
out in the ratio).  So DynRange becomes a measure of the
energy ratio in the loud sound wave vs. the quieter sound
wave.

Since sound and light have the same energy vs perception
characteristics, it makes sense to define DynRange for
light to also be a measure of the energy ratio of two
extremes -- called bright and dark. "bright" is the
max light energy and dark is the min energy. How shall
we measure light energy and what units?  Since we are
only ever interested in the ratio of two light energies,
the unit whatever they are always cancel.  Similarly,
we don't have to measure absolute values anyway -- just
get the ratio of the energies.  Well in photography
we do this all the time.  A one stop difference in light
is just a 2x difference in light energy i.e. ratio = 2.

As a photographer light ratios measured in stops is
used all the time.  But how do you get the ratio given
the number of stops?  1 stop = 2, 2 stops = 4, 3 stops  = 8.
Ratio = 2^numstops

Putting this all back into the dB formula we have:

dB = 10 * log10 (ratio)
   = 10 * log10 (2^numstops)
   = 10 * log10(2) * numstops
   = 3dB * numstops

Not surprisingly, this is the same as audio 3db = double power.

Now back to the main subject, DynRange.  With an appropriate
choice or measurement of maxlight value and minlight value,
we simply have:
DynRange (dB) = 3dB * (number of stops between min and max)

dB certainly could be the unit we do all calculations,
however in the imaging realm we have several units that are
already very well used.  We talk about stops everywhere in
photography -- making a new unit that is just 3 * stops
isn't necessary at all.  It makes sense to me that the unit
we use in imaging is the one that we already have. With
the  multitude of technologies involved in imaging, we
actually  have another unit that is very similar and thats
the density unit -- this is just 0.3 * stops.   It looks
very much like dB and if it didn't already exist already.
Looking at these three units they are all dimensionless
numbers that are the log of an energy ratio.  For historical
reasons stops are log base 2 whereas the others are log
base 10, otherwise they are all equivalent units.  Since
different imaging technologies have long used certain units, 
it makes sense to use the appropriate unit.  The conversion
is very simple anyway.

This sounds almost trivially simple but the important issue
is the choice of maxlight value and minlight value.
Conceptually, you just pick the brightest value and the
darkest value -- but there's lots of room for tweaking
the idea -- like does the value need texture or detail or
go just beyond that or what.

At this point I'm just showing a derivation that produces
a reasonable concept with an intuitive understanding and a 
potential measuring method.  It has a basic meaning that
matches the usage of the term in several existing areas.
Ansel Adams' book The Negative uses the term dynamic
range which is very similar -- the useful Zones or stops
for the Zone system.  The term in also used quite a bit
in the scanner realm and in that context the specification
"dynamic range" is stated as the range of densities that the
scanner can handle.

-----------------------------

So that's my take on dynamic range for imaging.  In my opinion
its the most natural way to define the idea.  I don't
think there are any large leaps of faith. Also, others have
used a similar concept.  I'd have to admit that there are
lots of usages that are not really technically defined.
But they seem to just mean that good dynamic range 
translates to "looks good tonally".  I can't really see
this as contradictory.

I haven't defined precise ways to define the max and min because
I think various people might want different standards for 
that -- just as the audio dynamic range equation doesn't
specify the standard for max and min.

I'd be glad to clarify anything in this discussion.  Austin,
if you would like to put your whole story together into
one package it would be very helpful to see where you stand.
I imagine this grates against you a bit, but ... I can't help it.
The discussion, as before, lost most of the semblence of
what we wanted to define.  I'd like to say I'm open minded
about the whole thing, but all the above fits so well.

-------------------

Best regards,

Roy

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