Hi Austin,
Sorry, one more post.
on 8/30/02 8:28 AM, Austin Franklin at darkroom@ix.netcom.com wrote:
> Roy,
>
>> All the stuff about number of levels and resolution are artifacts of the
>> digital process and not part of the DyR concept which existed way before
>> the word digital was even coined.
>
...
> I believe the concept of resolution is inherent in the concept of dynamic
> range. Whether that "works" for you or not, at least for me, and for many
> other engineers I know, is an important understanding.
>
Fair enough. But I like to show why I believe that the "concept of
resolution" that results isn't very meaningful. See below.
>> But the SIZE of the range is ONE number -- and it can be mathematically
>> calculated with a subtraction OR with a ratio. In the dynamic range
>> case we always calculate the SIZE of the range with a ratio = max/min.
>
> I see how size can have a merit (which is a relative ratio), and range, as
> they apply to dynamic range. Size in the fact that the largest signal is N
> times larger than the smallest...and range in that you can say "all integer
> values from 1:1 to N:1". BUT...realize that "all integer values from 1:1 to
> N:1" really denotes a resolution over a particular "range" too...that you
> have N discrete values.
Yes, but I never said "integer". In the real-world i.e. analog, there no
reason why any real number couldn't be used. What's wrong with going from
1:1 to 1.01:1 to 1.02:1 ...
>
>> You don't seem to have trouble when someone says "density range" and
>> Dmax - Dmin. Why the hangup when the adjective is changed?
>
> Because dynamic range and density range are two entirely different things.
> When someone says a "density range" of 3.6D, that means from, say, .2D to
> 3.8D, or whatever. Within that range, you can discern ANY value you want at
> any resolution you want, down to .0000001D if you could...but dynamic range,
> in and of it self, has a number of "discernable" steps. Density range does
> not.
Here's why I have a problem with the "concept of resolution":
Let me go through a simple example of a (semi-idealized) scanner.
Here's the basic specs of the scanner:
Density Range: 0D to 3.6D
Bit Depth: 12 bits
Number of levels: 4096
A couple of simple observations:
The density range is also 12 photographic stops -- each stop is .3 of
density so 12*.3 = 3.6
You can chop up the density range into 12 one-stop ranges i.e.:
0 to .3, .3 to .6, .6 to .9 ... etc to 3.3 to 3.6
Photographically and human perception wise each of these one-stop
ranges are equivalent in size.
So now let's chop the density range into the 4096 levels. The
density range 3.6 divided by 4096 gives a little less than 0.001D
per level. Approximately, 300 levels for each of the 12 one-stop
range. Sounds like a great concept of resolution, doesn't it?
We get a new level every 0.001D change in density -- it sure
looks like a resolution of 0.001D.
Fine, but the trouble is: scanners don't work anywhere even remotely
close to that scenario. This is what scanners actually output
as the levels:
The first one-stop range contains 1/2 of all the levels, the next
on contain 1/2 of the remaining ones, etc. until the last one.
This is what it looks like:
0 to .3 => 2048 levels
.3 to .6 => 1024 levels
.6 to .9 => 512 levels
.9 to 1.2 => 256 levels
...
3.0 to 3.3 => 2 levels
3.3 to 3.6 => 1 level
Pretty weird, but that's the way it is. Here's a web reference that
has basically the same table -- just scroll down a ways.
Austin, don't take my word or the web's word for it. Try it yourself.
Scan a film step wedge in raw mode on your Leaf 45. I'm hoping
you have a 21 or 31 step wedge from Kodak or Stouffer. If you
look at the Histogram of the raw 16-bit file you'll see half of
the entire range used up with the number of steps in one-stop.
It's very surprising when you first see this.
So back to the concept of resolution. What is the resolution? At
the very dense end the resolution is a whole stop i.e. 0.30D units.
At the other end it's close to .3/2048 or 0.00015D units.
So, again, I can't feel the concept of resolution is very
meaningful -- its just too varied.
Roy
>
> Regards,
>
> Austin
>
Roy Harrington
roy@harrington.com
Black & White Photography Gallery
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