Dear Aryeh
>
>What this does is put a (relatively) low noise amplifier ahead of the
>"conventional" electronics. Therefore, the noise from those electronics
>no longer contributes significantly to the overall noise figure of the
>system.


Quite right.


>I do not understand the connection between the quantum efficiency and
>the gain uncertainty. If there is such a connection, why is the
>reduction exactly 1/2? Also, they have a cascade of these avalanche
>stages, so the variation per stage should be reduced by something
>approaching the square root of the number of stages. Perhaps you can
>point me to a reference on this subject. I assume that a similar
>phenomenon is observed in PMTs, because the dynode gain is also subject
>to statistical fluctuations.


There is no real connection. It just turns out that the form of the noise
introduced , as described on the articles on the WWW page I sent out:

(http://www.marconitech.com/ccds/lllccd/technology.html   Try the third
article: Sub-Electron Read Noise at MHz Pixel Rates: University of
Cambridge · Date: Jan 2001 · Filesize: 650 kb )

just happens to add a type of noise that would have been produced if you
had counted twice the number of electrons that you actually counted.

It is not a particular simple process to describe in detail on the
email-net but I'll try:

The noise comes about because the gain-per-charge-transfer is very low
(about 1%/stage: if your charge packet was only one electron, you would
have a 1% chance that the transfer to the next well would give you two
electrons.  If you do end up with 2 electrons, these each have a 1% chance
of being doubled on the next transfer. Sounds like it wouldn't work at all
but it does work in a sort of average way (like compound interest) after
hundreds of transfers. You do get an average gain. You also get some
packets that didn't get amplified very much and fewer that got amplified a
lot (more like the stock market than a bank!!) .  This gives rise to
"multiplicative noise"  (not all input electrons are treated the same).

The noise produced by this sort of process has the same form and magnitude
as the Poisson noise applied to a charge packet of n electrons. As noise
terms are not added directly but as the sqrt of the sum of the squares,
this means that you end up with 1.41x as much noise: the same amount as if
you had counted twice as many photons as you actually counted.

Now think of signal-to-noise ratio (S/N). The only way to get the S/N that
you should have had from counting n electrons in the absence of charge
multiplication noise is to really count twice as many photons, because this
process reduces Poisson by 1.41x, exactly balancing the extra noise.  As we
can't magically increase QE by a factor of two to count the extra signal,
it is easiest to think of the detector as being noise free but having a QE
that is half what it would have been without the charge-multiplication
noise.

Multiplicative noise also occurs in the PMT because the actual number by
which a given electron multiplies at each dynode of the PMT is again
subject to Poisson statistics.

In a good PMT, multiplicative noise adds about 20% to the Poisson noise and
can only be overcome by counting 44% more photons  (1.2 x 1.2 = 1.44  = 1 +
44%).  So the effective QE of a PMT is only about 70%  (1/1.41) of what the
QE curves from the manufacturers claim. Actually, it is even worse than
this, because the published QE curves refer only to photoelectrons leaving
the photocathode per incoming photon, not photoelectrons that actually
reach the first dynode and result in charge multiplication.  About 30% of
the electrons leaving the photocathode fail to reach the first dynode and
propagate, further reducing the effective its QE.

A lot of variables effect the performance of photodetectors and it can be
hard to compare the relative impotance of these if they are not converted
into a "common currency".  In this case the "currency" with the most
straight-forward definition is the effective QE.  A more extensive
description of this process can be found in:

Pawley, J.B.
        The Sources of Noise in Three-dimensional Microscopical Data Sets.
        Three Dimensional Confocal Microscopy: Volume Investigation of
Biological Specimens,  (ed. J. Stevens), Academic Press. NY. 47-94, (1994).

Cheers,

Jim P.
Jim Pawley (at home)
Work: 1117 W. Johnson St., Madison, WI, 53706, 1-608-263-3147/ fax,
1-608-265-5315