on 9/1/02 6:18 AM, Julian Robinson at jrobinso@pcug.org.au wrote:
> Hi Roy,
>
> I was talking about your context so we are discussing the same thing. You
> have already got a response from Vincent which puts that case in terms of
> resolution, here's my quick take from the dynamic range point of view - the
> two arguments are otherwise essentially the same.
Boy, am I getting tired of this. Yes, I read Vincent's response. He
starts with the premise:
"Dynamic range is the ability to distinguish tonal differences."
If you take that as a given, naturally you're going to directly lead
to the idea of Dynamic Range being equivalent to number of levels and
that a 12-bit file has more DyR than an 8-bit file. Simple logic.
But if the premise is false the conclusion not longer follows.
In fact if you prove the conclusion false, it directly proves that
the premise is also false.
>
> The important thing I think to remember about DyR is as always, the
> definition, and what defines the minimum signal, the MDS, in that
> definition. The DyR is the range from the max signal down to the MDS, not
> down to some "zero" figure. So in the case you are discussing, and if we
> call black the low end of the range as you have, we can establish the DyR
> as follows.
>
> We know it is max signal / MDS. What is the MDS? It is the minimum signal
> that can be detected ABOVE whatever corresponds to background or 'zero
> level'. In this case, and with all digital step limited situations, the
> MDS is step 1, not step 0. It is the first, lowest signal you have any
> chance of discerning above the zero signal level, which in this case is
> pure black.
The numbers in the 8-bit file go from 0 to 255, in the 12-bit file they go
from 0 to 4095. These numbers are NOT signal values, in no way is the
signal represented by the value 100 twice the size of the signal represented
by the value 50. And heaven forbid trying to even think about the value 1
being infinitely bigger than the value 0. They just plain AREN'T signal
values. Notice how one must avoid the value 0 like the plague -- that 0 in
the denominator is really problematic. But in the Photoshop file its a
perfectly ordinary value -- just one more gray tone.
The ONLY numbers you can put into the DyR ratio are the measurements of real
signal values. I.e. you've got to measure what the file levels translate
to on paper. Here's the audio analogy:
With an audio amplifier, you turn it on without any input signal. Measure
the output and you get noise level or MDS, its the smallest output value
you can get from the amp. It's what you put in the denominator of the
DyR function. In imagining, a piece of paper with the maximum amount of
black ink, outputs the least amount of light possible. Again that amount
of light is the MDS for that paper/ink combination. This is what goes in
the denominator. Notice that in either case there isn't any chance of
a real 0 value.
Now for the numerator, for audio you crack up the input
signal as high as possible and measure the max output without getting into
distortion. With paper, the max light output is just the white of the
paper by itself. That's all there is to dynamic range. If it comes out
to a value of 1000, in the audio world that means that the loudest signal
from the amp will has 1000 times as much power as the quietest signal. In
the print world the 1000 means that the white of the paper outputs 1000
times as much light as the blackest inked area.
>
> So in the first case, the DyR is : max/MDS = (4096 steps) / (1 step), and
> in the second 256/1. i,e, DyR 4096 vs 256.
>
> Looking at it another way, with an 8 bit file, the bottom step is the same
> level as step 16 was in the 12-bit case. So when you converted from the
> 12-bit to the 8-bit, you lost the 16 lowest steps and combined them all
> into 1, the lowest level of the 8-bit situation. In that conversion you
> lost the 16 lowest shades of gray, permanently. So all that info is gone
> and your MDS is now 16 times larger, and correspondingly your DyR has
> diminished by the same amount, 16 times.
I'm sticking with 0 in both files producing the same black and 255 or 4095
producing the same white paper. So the ratio of the amount of light from
either file will be the same.
And, Austin, yes I know in this case I'm saying density range is exactly
the same range as dynamic range with note that the max density corresponds
to the min light and the min density corresponds to the max light.
>
> If you then converted back to 12-bit, you can't regain those bottom 16
> shades, so your picture is permanently degraded. Despite the 12-bit
> digitisation which implies DyR of 4096, the actual image bottom step- the
> new minimum discernable signal above black MDS - is actually step 16 of
> your 4096 and so the DyR is now 4096/16 = 256, the same as the 8-bit
> case. This must be so because the information content is exactly the same
> in both cases.
Notice how all the calculations use the arbitrary values in the file
which are NOT measurements of real signals. The RAW data out of a
scanner was the last time the file values numerically corresponded
to real signals. As soon as Levels or Curves were applied the values
no longer correspond so they ought NOT be put into DyR formulas and ratios.
>
> Does this make sense?
>
> Julian
>
I guess all I can say is I think what I've written makes more sense.
Roy
Roy Harrington
roy@harrington.com
Black & White Photography Gallery
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