on 8/30/02 3:17 PM, Austin Franklin at darkroom@ix.netcom.com wrote:
>> Back to your interpretation of the DynRange definition/formula. You are
>> transforming the denominator from "smallest discernible signal" into
>> "smallest discernible signal increment".
>
> Whether it's the "increment" or not is determined by what ever the limiting
> factor is. BUT...you (typically) ONLY resolve down to noise, which is why,
> typically, noise IS the "increment". Do you believe you can resolve a
> scanner signal further than to noise, and that you get useful information
> from that?
Hi Austin and Julian,
I've tried to address this in the past. The more I think about it the
more this seems to be a crucial issue. With the way digital scanners
work I agree that there's no hope of resolving better than the quantization
noise (I prefer quantization error). But when it comes to true random
noise you can easily get much better resolution than the noise level.
Here's a small example: we have a voltage of 9.37 volts.
First the quantization situation, we have a digital volt meter that
measures to the nearest volt. The quantization error or noise is
+/- .5 volts. No matter what we do we'll always read 9 volts and be
off by .37 volts.
Second we'll try the random noise situation: to be similar to the above
let's say random noise of .5 volts is added to the 9.37 volts. So the
voltage is at least bouncing around from 8.8 to 9.9. So any particular
sample will have a value anywhere in that range. However if you make many
samples and average them the result will converge on 9.37 because the errors
due to random noise will cancel each other out.
I've been claiming a lot of stuff lately so I'm going to try to back it
up with a real demonstration. Here's a step wedge file that I based on
the 21step wedges that come with Piezography. The top part is the
standard wedge with 21 gray steps from 0% K to 100% K in 5% steps.
The bottom is a duplicate with lots of noise added. The PS command
is Add Noise> 12.5% Gaussian if you want to try it yourself. The
noise is a lot -- magnify to 400% on screen and see it, marquee a
single step and check the histogram. What was 1 grayscale value now
spans more than half the entire grayscale. Marquee and Histogram 2
steps and there no obvious steps. However, print the file out on
paper and the step wedge shows through loud and clear. Get out the
densitometer and the gray tone measurements of each step match very
well whether you measure the noise-less step or the noisy step. So
the "signal" here is the 5% wedge, the "noise" is large enough to span
many steps in the wedge, but its easy to resolve densities much
closer than the noise level.
Download this file, its a TIFF to insure there is no lossy compression.
Austin, I hope you are willing to print this out with Piezo and
measure some of the steps.
Roy
Roy Harrington
roy@harrington.com
Black & White Photography Gallery
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