Dynamic Range
(or Lies, Damned lies, Statistics and Scanner Specs - with apologies to Benjamin Disreali) by Bob Atkins, 2003
One of the most discussed, most important but least understood parameters
which describe the performance of a scanner "dynamic range". If you read the
manufacturer's spec sheets you'll see numbers like "a dynamic range of 3.6" or "a
dynamic range of 4.8". So what exactly does "dynamic range" mean, and why is it
important?
A Definition
A workable definition of dynamic range is the ratio of the highest (lightest)
signal which a scanner can record to the lowest (darkest) signal. The lightest
signal would correspond to the brightest highlights in an image, the darkest
signal to the deepest shadows. The units used for this measurement are density
units (D) and the scale is logarithmic. The formula is:
D = log (Io/I)
where Io is the intensity of the light falling on the slide (or negative)
and
I is the intensity of the
light transmitted by the slide (or negative).
So let's say light of 1000 "intensity units" is used to illuminate the slide,
and let's say in the highlights 95% of the light is transmitted (950 units),
while in the shadows only 5% of the light is transmitted (50 units).
| % of light transmitted |
Density (D) |
| 50 |
0.3 |
| 25 |
0.6 |
| 10 |
1 |
| 1 |
2 |
| 0.1 |
3 |
| 0.01 |
4 |
The density of the highlights would be log(1000/950) = 0.02D and the density
of the shadows would be log(1000/50) = 1.3. The Dmax (maximum value of D) for
this slide would be 1.3 and the Dmin (minimum value of D) would be 0.02
The ratio of logarithmic values is the difference between them (Dmax-Dmin), so
the dynamic range of this slide would be (1.3)-(0.02) = 1.28. You can also just
take the log of the ratio if you don't need (or know) the D values of the
signals, so the dynamic range is log (950/50) = 1.28.
Analog and Digital
Though we think of film scanners as digital devices, that only really applies
to their output. The actual sensor is an analog device. It sends out a voltage or
a current which is proportional to the intensity of the light that falls on it.
This analog signal is converted into a digital signal by an analog to digital
converter, also known as an A/D converter.
Digital Basics
Digital signals are made up of "1"s and "0"s. If you have 1 digit - or 1
"bit", it can have a value of 0 or 1 and that's all. Two values, not much of a
range! If you have 2 digits - or 2 "bits" you can have values of 00, 01, 10 or 11
so now you have 4 values instead of two. With 3 bits you can have 000, 001, 010,
011, 100, 101,110 or 111 that's 8 values. Obviously we can go on increasing the
number of bits and so expanding the range of values a digital number can
represent.
|
With 8 bits there are 256 possible values corresponding to decimal numbers
from 0 to 255. So with an 8 bit A/D converter you can take a range of analog
numbers and convert them into a digital number with a range from 0-255. Now let's
ask the question "what's the dynamic range of an 8 bit A/D converter?".
Well, it's the ratio of the smallest signal it can record to the largest
signal. The smallest signal is "1" and the largest signal is "255", so the
dynamic range is log(255/1) = 2.4.
Black and white images just need one signal channel (one A/D) but color images
use three channels (red, green and blue), so they use 3x the number of bits that
a B&W image does. However the dynamic range of a color signal is that of each
channel, so when you read about "24-bit" color, it's really 3 "8-bit" channels
not one "24-bit" channel and the dynamic range is determined by those 8 bits.
Here's a table which shows the maximum theoretical dynamic range an "n-bit"
signal can have, where "n" is 8, 10, 12, 14 or 16 (the most common values found
in scanners).
| Number of Bits (color) |
Maximum dynamic range |
| 8 (24) |
2.4 |
| 10 (30) |
3.0 |
| 12 (36) |
3.6 |
| 14 (42) |
4.2 |
| 16 (48) |
4.8 |
Something that's very important to note here is this is the
maximum theoretical dynamic range the A/D converters
can output, assuming perfect operation and no noise. If you feed them an analog
signal with a dynamic range of 2.0, each of them will output a digital signal
with a dynamic range of 2.0, no matter how many bits are involved. If you feed an
8-bit A/D with a signal which has a dynamic range of 3.2, all you get out is a
signal with a dynamic range of 2.4, since that's the best an 8-bit A/D can do.
However if you feed 16-bit A/D with a signal which has a dynamic range of 3.2 all
you get out is a digital signal with a dynamic range of 3.2, not
the 4.8 which the A/D is theoretically capable of.
Scanners
The dynamic range of a scanner is simply the ratio of the brightest signal it
can record to the darkest signal it can detect. Recording bright signals isn't
much of a trick. It's fairly easy to set things up so that with no slide in the
scanner it generates a signal just below the maximum possible output signal. For
an 8-bit system that would typically be around 250 (remember 8 bit signals can
have values from 0 to 255). Recording weak dark signals is more difficult. All
sensors generate noise, so if you increase the gain of an amplifier attached to
the sensor so as to try to read very low signals, you amplify both noise and
signal. Thus there is an intrinsic minimum signal level that the sensor can
measure and that's related to how much noise it generates.
The type of detector which generates the least noise (and which can therefore
detect the weakest signals) is called a photomultiplier tube or "PMT". PMTs are
actually vacuum tubes and operate with voltages around 1000-1500v. The lowest
noise PMTs are actively cooled below room temperature to further reduce noise.
PMTs are used in scanners, but only in large, expensive, commercial drum
scanners. Such scanners may weigh 150lbs and cost $50,000.
Desktop scanners typically use solid state detectors (CCD or CMOS) which are
uncooled. They generate significantly more noise than PMTs and so they cannot
detect the weak signals which PMTs can. Weak signals come from the most optically
dense parts of the scanned image (i.e. the deepest shadows) and so desktop CCD
scanners don't "see" as much deep shadow detail as PMT based drum scanners.
Another way to say this is that PMT drum scanners have a higher dynamic range
than desktop CCD scanners - see, we're back to dynamic range at last!
The higher the dynamic range, the more information you can get from the
darkest areas of the slide, so high dynamic range is a good and desirable
property of a scanner. Below is a graphic example of what I'm talking about
The upper image represents a scale running from white to black. The lower two
images represent what you might get if you scanned the upper image with two
scanners, one with high dynamic range and high Dmax, the other with lower dynamic
range and Dmax. Neither fully record all the detail in the original image, but
the scanner with the higher Dmax and dynamic range records more. The effects here
are exaggerated for clarity
What Dmax do you need?
Well. most properly exposed, properly developed negatives of typical subjects
don't have a Dmax higher than about 1.5 and even overexposed negatives rarely go
higher than about 2.0, so a dynamic range of 2.0 would probably take care of just
about any negative you are likely to come across. This should be well within the
capabilities of most film scanners.
The same applies to scanning prints (though you'll need a flatbed scanner, not
a film scanner to do this). The Dmax of the blackest ink or photographic print is
probably somewhere around 2.0, so again this shouldn't tax the capabilities of
any decent scanner.
However slide film is a different story. Dmax of typical slide films can reach
maybe 3.5 and Velvia is said to be able to hit 4.0 in the deepest blacks. This
would tax even the best scanners.
Scanner Specs
Besides resolution, one of the parameters specified by scanner manufacturers
is dynamic range, since it's a pretty important facor in determining final image
quality for scanned slides. For example this is from the specs on the Minolta
Dimage Scan Dual III Film Scanner:
- "With 16-bit A/D conversion and a 4.8 dynamic range, the DiMAGE Scan Dual
III will reproduce the rich variations in tone and color of the original film
image. 16-bit A/D conversion is able to distinguish 65,536 tonal gradations for
each color channel. The ability to capture the depth and subtly of the original
film image is breathtaking. The scanner's dynamic range is 4.8"
What does that mean? Does it really have a dynamic range of 4.8? Well, no it
doesn't. It has a 16-bit A/D, which means that theoretically the A/D could have a
dynamic range as high as 4.8, but as I said earlier, if you feed such a D/A with
a signal that has a lower dynamic range, all you get out of the D/A is that lower
dynamic range. Since the dynamic range of solid state detectors is limited to
something like 3.4-3.6, that's all you get. The better the sensor and the better
the electronics, the better the dynamic range, so it could be anywhere from 2.8
to 3.6. You just don't know because the manufacturers don't publish measured
numbers, just "theoretical maximum" numbers based on a perfect noise free sensor
and perfect D/A converter - which of course don't exist!
- Nikon Coolscan IV ED has a 12 bit conversion (36 bit color) and claims a
dynamic range of 3.6.For the Nikon Super Coolscan8000ED the specs are 14 bit
conversion and a dynamic range of 4.2. Does all this sound familiar (see the
table above)
- Canon spec their Canoscan FS4000US with a dynamic range of 4.2 and....you
guessed it, it has a 14 bit (42 bit color) A/D converter.
Anyone else start seeing a bit of a pattern here?
The best PMT based drum scanners have a measured dynamic range of around 4.0.
That's about the limit. It's enough since few slides or negatives will come close
to a density of 4.0D so there's no real incentive to go for a larger dynamic
range. The best desktop solid state sensor scanners might possibly have a dynamic
range as high as 3.6, though I may be being a bit optimistic here. You'd want a
14 bit A/D to properly handle this since it's right on the limit of 12 bits and a
little headroom never hurts! 16 bits would be fine too, but probably not really
needed.
So the final conclusion is to ignore manufacturers claims on dynamic range.
They are just plain silly. Nothing more than marketing hype. That doesn't mean
there aren't good, better and best scanners when it comes to dynamic range, just
that you can't tell anything from reading the spec sheets with regard to dynamic
range or bit conversion depth. 16-bit isn't necessarily any better than 14 bit.
I'd much rather have a 12 bit scanner with an excellent low noise sensor than a
16 bit scanner with an average "off the shelf" sensor with significant noise. You
do need at least 12 bits though, since with less than that the A/D could be
limiting rather than the sensor.
Given marketing tricks, I wouldn't be totally amazed to see scanners with
18-bit (56 bit color) converters next year claiming a dynamic range of 5.6, if
there was any way of actually getting the info into an image (48 bits is the
limit for a tiff file) - though even that may not stop them!
All material (C) Copyright 2003
Robert M. Atkins All
Rights Reserved
Article created 2003
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