Digital BW, The Print

Roy Harrington wrote:



> Basically you increase the sensor dynamic range by either: reducing the noise
> at the low end and/or increasing the clip point at the high end.  The bits of
> the A/D have to fine enough to take advantage of the reduced noise at the
> low end and coarse enough to not get clipped at the high end.

It sounds to me as though we are approaching this from two different 
perspectives. When you say the bits have to be coarse enough to take 
advantage of reduced noise, and fine enough not to clip, it sounds to me 
as though you are saying something about the digital sampling of the 
signal being read off the sensor. And if I understand correctly you are 
dead right - there is no point to making the luminous flux density delta 
per ADU so coarse that the 100 (or whatever) highest ADU values all clip 
to white. Not only do you throw away values, but you also increase the 
chances of posterization in the resulting digital image.

You state correctly, above, that to increase sensor dynamic range, you 
can reduce noise. You also say you can increase the clip point at the 
high end. I'm familiar with using the term "clip" in reference to 
digital sampling, so it appears as though what you are saying is that to 
increase dynamic range you should take your highest ADU - 4096, say - 
and calibrate that to what is detected from a higher luminous intensity 
(luminous flux per unit solid angle) from a scene at a given EV. Maybe 
that is what you are suggesting, or maybe not - that's what I'm hearing.

Either way: Doing that won't work.

Well, I admit it will work in one special case: It will work when your 
sensor's highest ADU value represents a number of electrons that is less 
than the full well potential of the sensor. In your terms above, if the 
"bits of the A/D" are a bit beyond "fine enough," and are in fact too 
fine, then your digital image won't have the dynamic range it could have 
had if there were more bits available at the same sampling rate. By 
sampling rate, I mean electrons per ADU.

But if your highest ADU value already represents a number of electrons 
that is equal to the full well potential of the sensor, then adding bits 
at the *same* sampling rate buys you nothing. This would be too "coarse" 
sampling, as you put it, and all those added ADU values would be clipped.

Increasing the sampling rate (reducing electrons per ADU) while 
increasing bits *can* solve this clipping problem - and I'd like to have 
this in all my cameras. Unfortunately it will not result in greater 
dynamic range. The reason is that the maximum luminous intensity and the 
minimum noise recorded by the sensor are both limited at the analog stage.

The analog stage is mostly what I've been talking about. We are always, 
always, always limited by the photosite well. A well can hold between 
zero and n electrons. If you exceed n, and try to stuff n+x electrons 
into the well, an average of x electrons will be lost to other parts of 
the sensor. This is because the well achieves enough voltage to jump the 
resistant gap between it and another capacitor or some convenient path 
to ground. In either case, these electrons have overflowed their bucket, 
and are no longer present in the well when the sensor is read out.

In this situation the well is said to be "saturated." This sometimes 
results in blooming, but it does not result in clipping as I understand 
the term, because this has happened before any sampling of the well is 
made; there is no chance for the amplifier output to distort or the ADC 
to clip as these electrons never get there.

So a well can hold between 0 and n electrons. For a big well, n is a 
larger number; for a small well, n is a smaller number. Quantum 
efficiency determines how many electrons end up in the well, as a 
percentage of quanta of photons that are incident upon the photoelectric 
surface.

If the sensor QE is 50%, and 1k photons strike the sensor, then 500 
electrons (on average) are dumped into the photosite well. The number of 
photons striking the sensor is determined by the luminous intensity of 
the scene. So if we double the EV, we will have 2k photons striking the 
sensor and 1k electrons in the well. If we double it again, we'll have 
4k photons and 2k electrons.

Suppose the well capacity is 1k electrons. We've tried to stuff twice 
that many into the well. Half those electrons will find some other way 
out of the well, than through the readout amplifiers. Does adding bits 
to the sampling do anything to recover the lost 1k electrons?

The correct answer to this question is "no." The analog limitation of 
well depth is fundamental and exists because those lost electrons are 
not amplified and never affect the signal that the ADCs see.

And zero is a possible number of electrons in the well. This does not 
lend itself to useful representation with a proportion, which is 
probably one reason why dynamic range is specified on sensor spec sheets 
with luminous flux density and electrons of noise, rather than a ratio.

To increase the dynamic range of the sensor, we have to either reduce 
noise, or increase the saturation point of the well. The latter means 
increasing the number of electrons it can hold, because that correlates 
linearly with the maximum brightness in the scene that the sensor can 
usefully record.

What I originally started this discussion with, was a statement that 
photographers should beware the abuse of bit depth specifications. It 
does not always tell you anything about the ability to record the 
dynamic range of a scene, because no matter how many bits you have, the 
highest n ADUs could all be representing saturated photosite wells that 
contain no useful information about the scene you've just photographed. 
I think bit rate is going to be the next great digital camera scam, once 
everybody gets over the megapixel fetish - it already appears to be 
happening in the digital back realm.

--
Jeff Medkeff
Eagle River, Alaska