Dynamic range of digital and film: new data

wrote:

"Roger N. Clark (change username to rnclark)"
wrote:


The other improvement would be to go to 14 bit A to D conversion. That would
help the low end get even better at low iso, but not the high end, where
photon statistics dominate.


Lacking some externality (14b flash converters suddenly become cheaper
than 12b, Dumbya passes a law making 12b converters illegal(*),
whatever) adding bits to the ADC won't make sense unless one can lower
the read-out noise by, hm, 2 bits ~ 12dB. That's so large that one
would think if it was possible it would have been done at this point.
Hm. Perhaps an option to read the image at different rates from the
sensors ("slow and smooth" or "fast and furious")? Maybe Canon will
start selling Peltier cooling accessories for their cameras, with
colour-matching hybrid titanium scraping tools made by magic elves so
the Professionals can chip the ice off their digital backs, and write
entire chapters on the related "process" and "workflow"?

(*) actually considered a few years ago; they did get a "broadcast
flag" though.

The Canon 1D Mark II has about 7.5 electrons read noise, and a full well depth
of 52,300, see:
http://clarkvision.com/imagedetail/d...ignal.to.noise
If full well in a 12-bit system is 52,300, DN= 4095, then bit 1 =
52,300/4095 = 12.8 electrons, higher than the 7.5 electron read noise.
One would like a minimum of 1.5 DNs per read noise, so 7.5/1.5
= 5 electrons/DN. That requires a range of 52,300/5 = 10460.
14 bits would deliver a range 16,383, 13 bits only 8191, so a 14-bit
converter is needed now in order to digitize what the sensor is
delivering.

Roger

wrote:

"Roger N. Clark (change username to rnclark)"
wrote:


The other improvement would be to go to 14 bit A to D conversion. That would
help the low end get even better at low iso, but not the high end, where
photon statistics dominate.


Lacking some externality (14b flash converters suddenly become cheaper
than 12b, Dumbya passes a law making 12b converters illegal(*),
whatever) adding bits to the ADC won't make sense unless one can lower
the read-out noise by, hm, 2 bits ~ 12dB. That's so large that one
would think if it was possible it would have been done at this point.
Hm. Perhaps an option to read the image at different rates from the
sensors ("slow and smooth" or "fast and furious")? Maybe Canon will
start selling Peltier cooling accessories for their cameras, with
colour-matching hybrid titanium scraping tools made by magic elves so
the Professionals can chip the ice off their digital backs, and write
entire chapters on the related "process" and "workflow"?

(*) actually considered a few years ago; they did get a "broadcast
flag" though.

The Canon 1D Mark II has about 7.5 electrons read noise, and a full well depth
of 52,300, see:
http://clarkvision.com/imagedetail/d...ignal.to.noise
If full well in a 12-bit system is 52,300, DN= 4095, then bit 1 =
52,300/4095 = 12.8 electrons, higher than the 7.5 electron read noise.
One would like a minimum of 1.5 DNs per read noise, so 7.5/1.5
= 5 electrons/DN. That requires a range of 52,300/5 = 10460.
14 bits would deliver a range 16,383, 13 bits only 8191, so a 14-bit
converter is needed now in order to digitize what the sensor is
delivering.

Roger

jpc wrote:

On Sun, 07 Nov 2004 20:15:45 -0700, "Roger N. Clark (change username
to rnclark)" wrote:


bob wrote:


"Roger N. Clark (change username to rnclark)" wrote in
:



I've been running tests and have some interesting new plots
of film and digital dynamic range. This is the first of about
10 graphs on this page, but I though I would share it for comments
while I built the rest of the page. See:

http://clarkvision.com/imagedetail/dynamicrange2




I can't wait to see the rest.

It seems to indicate that there might not be a lot of room for improvement
in top end CCDs.

Bob


Bob
Take a look at my other dynamic range page:
http://clarkvision.com/imagedetail/d...ignal.to.noise

and in particular, look at Figure 2. Figure 2 shows that the 1D Mark II
is working at the photon noise limit. The only way to improve on that is
to make larger pixels to collect more photons into a larger well
(which means less spatial resolution). The other improvement, which would
help low signals, is to lower the read noise and lower the dark current for
long exposures. But for everyday full light photography, the 1D Mark II
8-microns/pixel performance is the sweet spot that is essentially at
the theoretical best. If you make smaller pixels, and remain at the photon
noise limit, you collect less photons per pixel, so the noise goes up.
Larger chips is the other solution (lusting for the new 1Ds Mark II).
The other improvement would be to go to 14 bit A to D conversion. That would
help the low end get even better at low iso, but not the high end, where
photon statistics dominate.



Virtual all CCD cameras made today are photon noise limited over some
portion of their range. The readout noise is about 20 photo electrons
in modern cameras. If you say that photon noise dominates when it is
double the readout noise, the well depth will be 1600 photoelectrons.
Using the rule of thumb that you can collect between 800 and 1250
photoelectrons per square microns of silicon, sensor size would have
to drop down to around 2 square microns before photon noise ceased to
dominate

The Canon 1D Mark II has about 7.5 electrons read noise, and a full well depth
of 52,300. Other DSLRs have lower than 20 read noise. The Canon 10D, 300D,
and Nikon D70 all have full well capacities in the 42,000-45,000 range. See:
http://clarkvision.com/imagedetail/d...ignal.to.noise
An image sensor with a full well of only 1600 electrons would have
noise of 40, thus a maximum signal to noise of 40, getting worse with
fainter signals. The is pretty poor,
poorer than even a fast grainy film!


And a note in passing--the well depth on some individual sensors may
be much deeper than the rule of thumb predicts. Dispite a serious
effort on my part to find theoredical or experimental errors in the
numbers I get from my camera, (see some of my recent posts) I still
haven't been able to discover an error that would explain why my S/N
numbers points to a well depth 4 time greater than the rule of thumb
says it should be.

In order to get signal-to-noise of the sensor correctly, you need to
record the data in raw, linear 16-bit mode (or the native 12-bit
mode). If you record gamma-processed
data, the highest data gets compressed and posterized, making noise statistics
seem better than reality. This gets even worse if you use jpegs.

Roger

Roger N. Clark wrote:

The figure on the pages shows the transfer function of a digital camera
(a Canon 1D Mark II) compared to print file (Kodak Gold 200), slide
film (Fujichrome Velvia), and the relative response of the
Human eye (note the human eye has a much greater dynamic range).

Greater on the low end, but does the human eye give useful
response at the high end (above where the graph ends and
it goes exponential?)

What this plot shows is that the digital camera response function
is similar to print film, but even lower in contrast. The
response of both the digital camera and print film shows lower
contrast than apparent to the human eye (the steeper the rise,
the slope, the greater the contrast).

Except at low intensities, though? The slide film is virtually
flat below scene intensity of 3000, meaning it really isn't
producing anything useful. It's towards the higher end where
slide gets better. (as you point out below)

Nice science!

--
Ken Tough

Virtual all CCD cameras made today are photon noise limited over some
portion of their range. The readout noise is about 20 photo electrons
in modern cameras. If you say that photon noise dominates when it is
double the readout noise, the well depth will be 1600 photoelectrons.
Using the rule of thumb that you can collect between 800 and 1250
photoelectrons per square microns of silicon, sensor size would have
to drop down to around 2 square microns before photon noise ceased to
dominate

The Canon 1D Mark II has about 7.5 electrons read noise, and a full well depth
of 52,300. Other DSLRs have lower than 20 read noise. The Canon 10D, 300D,
and Nikon D70 all have full well capacities in the 42,000-45,000 range. See:
http://clarkvision.com/imagedetail/d...ignal.to.noise
An image sensor with a full well of only 1600 electrons would have
noise of 40, thus a maximum signal to noise of 40, getting worse with
fainter signals. The is pretty poor,
poorer than even a fast grainy film!

I agree althought a few years back an ISO standards committee
classified a digital image with a S/N of 40 as excellent--something
that is still in their confusing standard on how to set a digital ISO
number. The only point I was trying to make was it isn't just the high
end camera that are partially photon noise limited, it's most of the
rest of them too.


And a note in passing--the well depth on some individual sensors may
be much deeper than the rule of thumb predicts. Dispite a serious
effort on my part to find theoredical or experimental errors in the
numbers I get from my camera, (see some of my recent posts) I still
haven't been able to discover an error that would explain why my S/N
numbers points to a well depth 4 time greater than the rule of thumb
says it should be.

In order to get signal-to-noise of the sensor correctly, you need to
record the data in raw, linear 16-bit mode (or the native 12-bit
mode).

Doing that. I shoot in raw mode, process in 16 bit photoshop and
linearize my data by shooting a uniformly illuminated background thru
a strip of 21 neutral density filter. If I adjust my exposure so so
the portion of the image where I have no attenuation is just going
into saturation, the A/D units are 4096. Then the darkest portion
where I have a 1000/1 attenuation will be at 4 A/D units.


If you record gamma-processed
data, the highest data gets compressed and posterized, making noise statistics
seem better than reality. This gets even worse if you use jpegs.

If by compress you mean a grey card with 18 percent reflectance now
shows up at 128, 128,128 in 24 bit color I agree. But I don't see how
gamma correction would effect the noise statistics except to make the
S/N worse. The only way I know of to improve photon S/N is: by signal
averaging to collect more photo electrons over time; by using larger
sensor wells; and by downsampling/filtering which is the
software/camera electronics way of creating larger but virtual sensor
wells.

jpc

jpc wrote:

I agree althought a few years back an ISO standards committee
classified a digital image with a S/N of 40 as excellent--something
that is still in their confusing standard on how to set a digital ISO
number. The only point I was trying to make was it isn't just the high
end camera that are partially photon noise limited, it's most of the
rest of them too.

After seeing some statistics, I can see that even point and shoot cameras
may be photon noise limited. Juts their read noise is probably higher,
their dark current is probably higher, and their full well is smaller,
so their maximum signal-to-noise is smaller. The part of iso classifying
a S/N of 40 as good would be quite amazing. That will be pretty
lousy in appearance.

In order to get signal-to-noise of the sensor correctly, you need to
record the data in raw, linear 16-bit mode (or the native 12-bit
mode).


Doing that. I shoot in raw mode, process in 16 bit photoshop and
linearize my data by shooting a uniformly illuminated background thru
a strip of 21 neutral density filter. If I adjust my exposure so so
the portion of the image where I have no attenuation is just going
into saturation, the A/D units are 4096. Then the darkest portion
where I have a 1000/1 attenuation will be at 4 A/D units.

By linear, I mean the raw conversion. Your raw converter software needs to
have a "linear" mode. Some softwear may show a straight line transfer
function, but that can be defined as relative to the standard gamma
correction. So be sure you are selecting "linear" conversion
in the raw converter.


If you record gamma-processed
data, the highest data gets compressed and posterized, making noise statistics
seem better than reality. This gets even worse if you use jpegs.


If by compress you mean a grey card with 18 percent reflectance now
shows up at 128, 128,128 in 24 bit color I agree. But I don't see how
gamma correction would effect the noise statistics except to make the
S/N worse. The only way I know of to improve photon S/N is: by signal
averaging to collect more photo electrons over time; by using larger
sensor wells; and by downsampling/filtering which is the
software/camera electronics way of creating larger but virtual sensor
wells.

Consider a string of numbers with noise spread about 1.0:

1.10, 0.99, 1.05, 1.07, 0.93, 0.96, 1.04, 1.06, 0.92, ...
The standard deviation is somewhere in the few tenths range.
Now convert to integers:

1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, ...
The standard deviation is now zero and the signal to noise is now infinite!

When digital camera data are converted to a viewable image, a gamma
correction is applied, typically gamma=2. See Figure 5a at:
http://clarkvision.com/imagedetail/dynamicrange
which illustrated the shallow slope of the transfer
function at high signal levels.
The low slope has the effect of creating posterization
of the bits at the upper end of the camera's range, even in
16-bit data. At the low end, the gamma function is
such that the noise is well digitized. This will
all be illustrated on my new page at:
http://clarkvision.com/imagedetail/dynamicrange2
(give me a few more days).

I computed signal-to-noise on my camera data (linear output),
then on the standard curve, 16 bit tif and 8-bit jpegs. The
jpegs gave the highest signal-to-noise! But it was a false
signal-to-noise because of integer quantization (posterization).

Roger

jpc wrote:

I agree althought a few years back an ISO standards committee
classified a digital image with a S/N of 40 as excellent--something
that is still in their confusing standard on how to set a digital ISO
number. The only point I was trying to make was it isn't just the high
end camera that are partially photon noise limited, it's most of the
rest of them too.

After seeing some statistics, I can see that even point and shoot cameras
may be photon noise limited. Juts their read noise is probably higher,
their dark current is probably higher, and their full well is smaller,
so their maximum signal-to-noise is smaller. The part of iso classifying
a S/N of 40 as good would be quite amazing. That will be pretty
lousy in appearance.

In order to get signal-to-noise of the sensor correctly, you need to
record the data in raw, linear 16-bit mode (or the native 12-bit
mode).


Doing that. I shoot in raw mode, process in 16 bit photoshop and
linearize my data by shooting a uniformly illuminated background thru
a strip of 21 neutral density filter. If I adjust my exposure so so
the portion of the image where I have no attenuation is just going
into saturation, the A/D units are 4096. Then the darkest portion
where I have a 1000/1 attenuation will be at 4 A/D units.

By linear, I mean the raw conversion. Your raw converter software needs to
have a "linear" mode. Some softwear may show a straight line transfer
function, but that can be defined as relative to the standard gamma
correction. So be sure you are selecting "linear" conversion
in the raw converter.


If you record gamma-processed
data, the highest data gets compressed and posterized, making noise statistics
seem better than reality. This gets even worse if you use jpegs.


If by compress you mean a grey card with 18 percent reflectance now
shows up at 128, 128,128 in 24 bit color I agree. But I don't see how
gamma correction would effect the noise statistics except to make the
S/N worse. The only way I know of to improve photon S/N is: by signal
averaging to collect more photo electrons over time; by using larger
sensor wells; and by downsampling/filtering which is the
software/camera electronics way of creating larger but virtual sensor
wells.

Consider a string of numbers with noise spread about 1.0:

1.10, 0.99, 1.05, 1.07, 0.93, 0.96, 1.04, 1.06, 0.92, ...
The standard deviation is somewhere in the few tenths range.
Now convert to integers:

1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, 1.0, ...
The standard deviation is now zero and the signal to noise is now infinite!

When digital camera data are converted to a viewable image, a gamma
correction is applied, typically gamma=2. See Figure 5a at:
http://clarkvision.com/imagedetail/dynamicrange
which illustrated the shallow slope of the transfer
function at high signal levels.
The low slope has the effect of creating posterization
of the bits at the upper end of the camera's range, even in
16-bit data. At the low end, the gamma function is
such that the noise is well digitized. This will
all be illustrated on my new page at:
http://clarkvision.com/imagedetail/dynamicrange2
(give me a few more days).

I computed signal-to-noise on my camera data (linear output),
then on the standard curve, 16 bit tif and 8-bit jpegs. The
jpegs gave the highest signal-to-noise! But it was a false
signal-to-noise because of integer quantization (posterization).

Roger

Ken Tough wrote:

Roger N. Clark wrote:


The figure on the pages shows the transfer function of a digital camera
(a Canon 1D Mark II) compared to print file (Kodak Gold 200), slide
film (Fujichrome Velvia), and the relative response of the
Human eye (note the human eye has a much greater dynamic range).


Greater on the low end, but does the human eye give useful
response at the high end (above where the graph ends and
it goes exponential?)

Yes, but it too eventually saturates. But consider a bright cloud
in the sky and a scene with shadows. You can easily see
details in the shadows as well as detail in the bright cloud,
covering a much larger dynamic range than can be recorded
on film or a digital camera. At night, you can see
streetlights to stars, to the full moon: factors of a million
to 1 (e.g. 15 stellar magnitudes).
The eye is an amazing imaging device.


What this plot shows is that the digital camera response function
is similar to print film, but even lower in contrast. The
response of both the digital camera and print film shows lower
contrast than apparent to the human eye (the steeper the rise,
the slope, the greater the contrast).


Except at low intensities, though? The slide film is virtually
flat below scene intensity of 3000, meaning it really isn't
producing anything useful. It's towards the higher end where
slide gets better. (as you point out below)

Yes, I agree.

Nice science!


Thanks,

Roger

Ken Tough wrote:

Roger N. Clark wrote:


The figure on the pages shows the transfer function of a digital camera
(a Canon 1D Mark II) compared to print file (Kodak Gold 200), slide
film (Fujichrome Velvia), and the relative response of the
Human eye (note the human eye has a much greater dynamic range).


Greater on the low end, but does the human eye give useful
response at the high end (above where the graph ends and
it goes exponential?)

Yes, but it too eventually saturates. But consider a bright cloud
in the sky and a scene with shadows. You can easily see
details in the shadows as well as detail in the bright cloud,
covering a much larger dynamic range than can be recorded
on film or a digital camera. At night, you can see
streetlights to stars, to the full moon: factors of a million
to 1 (e.g. 15 stellar magnitudes).
The eye is an amazing imaging device.


What this plot shows is that the digital camera response function
is similar to print film, but even lower in contrast. The
response of both the digital camera and print film shows lower
contrast than apparent to the human eye (the steeper the rise,
the slope, the greater the contrast).


Except at low intensities, though? The slide film is virtually
flat below scene intensity of 3000, meaning it really isn't
producing anything useful. It's towards the higher end where
slide gets better. (as you point out below)

Yes, I agree.

Nice science!


Thanks,

Roger

Roger N. Clark (change username to rnclark) wrote:
Ken Tough wrote:

Roger N. Clark wrote:


The figure on the pages shows the transfer function of a digital camera
(a Canon 1D Mark II) compared to print file (Kodak Gold 200), slide
film (Fujichrome Velvia), and the relative response of the
Human eye (note the human eye has a much greater dynamic range).



Greater on the low end, but does the human eye give useful response at
the high end (above where the graph ends and
it goes exponential?)


Yes, but it too eventually saturates. But consider a bright cloud
in the sky and a scene with shadows. You can easily see
details in the shadows as well as detail in the bright cloud,
covering a much larger dynamic range than can be recorded
on film or a digital camera. At night, you can see
streetlights to stars, to the full moon: factors of a million
to 1 (e.g. 15 stellar magnitudes).
The eye is an amazing imaging device.


snip


Thanks,

Roger

It helps that the eye isn't viewing just one picture. It's "taking" a
whole bunch of pictures that the mind is splicing together. The human
eye only sees about 1 degree in sharp, clear focus. The rest is slightly
to very blurry.

Heck, we have a blind spot in our vision that is big enough to cover 6
full moons stacked on top of each other. We don't even see that, even
though it is in our area of "vision".

All this means that the human eye is adjusting more than it's focus as
it scans. It is also adjusting its exposure. That is a huge advantage in
capturing dynamic range.

Actually you can do the same thing with your digital camera too. Put it
on a tripod, make sure nothing moves, shoot several shots at the
extremes of exposure needed (and a few in between), then pick the parts
you want to use in the final picture. This can give you a VERY large
dynamic range. Alas, it doesn't work well for moving subjects.

Clyde