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[OM] Noise and dynamic range of the E-1

Subject: [OM] Noise and dynamic range of the E-1
From: Joe Gwinn <joegwinn@xxxxxxxxxxx>
Date: Sun, 28 Sep 2003 22:35:31 -0400
I've been looking into the likely performance of the Oly E-1, based on the 
published performance of the CCD to be used, the Kodak KAF-5101CE.  The 28-page 
datasheet (revision 1.0, issued 23 June 2003) is available from Kodak at 
<http://www.kodak.com /go/imagers>.   This is the 5-Mpix color sensor with a 
microlens at every pixel.

The dynamic range is quoted as 67 decibels, computed as follows:

The saturation level is 40,000 electrons per pixel and the total readout noise 
is 17 electrons (rms), so the dynamic range is 20*log10(40000/17)= 67.43= 67 
db.  

Said another way, log2(40000/17)= 11.2 bits, which fits in 12 bits.  In other 
words, a 12-bit analog digital converter (ADC) will extract all the information 
that's available from that CCD.  Added bits would just contain noise.  This 
will not be an accident.  The CCD was designed to match a 12-bit ADC.

But, this isn't the whole story.  Even if the CCD itself had no readout noise, 
the light comes in discrete packets called photons, which arrive randomly, so 
the resulting photo-electrons will also arrive randomly, and CCD performance 
will ultimately be limited by this randomness.  The resulting random variation 
in the number of electrons collected is called "shot noise".

Shot noise arises in all manner of situations.  Basically, all that's needed is 
that the arrival of each particle (photon, electron, raindrop, etc) be 
independent of the arrival of all other such particles.  This is a very common 
situation in practice, and the resulting noise follows Poisson statistics, so 
the standard deviation (~rms) of the error is the square root of the average 
value.

Turning to the KAF-5101CE, its maximum signal is 40,000 electrons, so shot 
noise will be Sqrt(40000)= 200 electrons (rms), or a bit more than ten times 
the readout error.

The resolution with which tone values can be told apart is limited by this 
noise.  At full scale, the noise is Sqrt(40000)/40000= 0.0050, or 0.5%, which 
is pretty good, although it may not be quite good enough to support the 
like-looking-through-an-open-window illusion, because in the shadows the noise 
will be more prominent.  

Let's assume a scene with a 6-stop scene brightness range, which is by no means 
excessive.  If the max is 40000 electrons, then in the shadows it will be 
(40000)/(2^6)= 625 electrons, and the shot noise will contribute an added 25 
electrons (rms) of noise.  Now, the readout noise becomes important, and the 
total noise will be Sqrt[17^2+25^2)= 30.2 electrons (rms).  Expressed as a 
fraction, this is 30.2/625= 0.484= 4.8%, which will be visible in flat areas as 
color noise (because the noise in the three colors is random and uncorrelated). 
 The sky has always been a problem area for noise.

This is where CCD pixel size comes in.  The pixels in the KAF-5101CE are 
square, 6.8 microns on a side.  If they were larger, they would collect more 
light and would hold more electrons, so the relative effect of shot noise would 
be reduced.  (Readout noise would be unaffected.)   Because noise is the square 
root of average number of electrons, which in turn varies with area (the square 
of pixel size), noise is inversely proportional to pixel size (edge length).  

To get the noise levels down to the ~0.1eeded to replicate Kodachrome, the 
pixels need to be five times larger, of (5)(6.8)= 34 microns at current levels 
of Quantum Efficiency (QE), or about 10 microns at QE=100% (like film).

Quantum Efficiency is simply the percentage of incoming photons that yield an 
electron.  In the KAF-5101CE it takes on average three photons to yield one 
photoelectron (the other two photons instead becoming heat), so the QE is about 
33%.

So, size does matter.  Just like film, actually.  And large format will always 
be with us, even if the absolute size of the image area is reduced.

Joe Gwinn

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