That's all very interesting --- do you have a good ref for TDS where I
can read up on the theory/practice? My protein xtallography books say
even less than S&J about TDS. Anyway, this appears to be a problem
beyond the scope of this present discussion --- in an ideal world we'd
be modeling all the forms of TDS, and Bragg diffraction, and comparing
those predictions to the intensity pattern over the entire detector ---
not just integrating near the reciprocal lattice points. Going on what
you said above, it seems the acoustic component can't really be measured
independently of the Bragg peak, while the optic and Einstein components
can, or least can be estimated pretty well from the intensity around the
Bragg peak (which means we can treat it as "background"). In any case,
I'm going to ignore the TDS complications for now. :).
That's all true, but you can detect peaks independently of one another
on a detector, so obviously there is some minimal distance away from a
crystal where you could completely block any given reflection and
nothing else. Clearly the "reflection stop" would have to be the size of
the crystal (or at least the beam).
If Iback' and Iback" come from the same process, then one informs theother. Of course you'd have to account for statistical fluctuations.
This is exactly the same principle behind using Iback to give us
information about Iback' in French and Wilson's method.
Aw, come on --- QM is a theory, it says no such thing. The claim that
"it's meaningless to talk about something you can't observe" is a
philosophical principle, not science. There are many interpretations of
QM, some involving hidden variables, which are precisely things that
exist that you can't observe. Heck, I'd say all of science is *exactly*
about the existence of things that we only infer and cannot observe
directly. Remember, when you get the readout from a detector, you are
not directly observing photons even then --- you are formally inferring
things that you can't observe. There's a whole chain of theory and
interpretation that gets you from the electronic readout to the claim
that the readout actually represents some number of photons.
Again, this is your own personal philosophical interpretation of QM ---
QM itself says nothing of the sort. For instance, Bohm's pilot wave
interpretation of QM, which is completely consistent with observation
and QM theory and calculation, states that individual photons *do* go
through one slit or the other. But this is really off point here, I
think --- as I said, I don't want to get into a QM debate.
I disagree. Following that logic, we could not talk about the error in
our estiamte of the gravitational force on the Earth from the Moon
(because, if our theories of gravity are correct, the force exerted on
the Earth is the sum of the gravitational pull of all massive objects in
the universe, and it is physically impossible for us to, say, remove the
Sun and then independently measure the force exerted by the Moon).
I agree completley with that. My point is, however, that F&W implicitly
assumes that the background we measure (in Ib) comes from the same
process as the background under the spot (Ib'). In other words, the
underlying model is:
Ib
Is = Ib' + Ij
where we experimentally measure Is (the spot) and Ib (the background
around the spot), and we assume that both Ib' and Ib come from the same
(Poisson) distribution, and that Ij (a sample from the true spot
intensity J) comes from a Poisson as well.
If that's not the F&W model, then what is?
This is precisely the point I was trying to make, so we agree.
Ib and Is are not independent.
I agree that Is-Ib is approximately Gaussian for reasonably large Is and
Ib. The problem is P(Is-Ib | J,sdJ). Why is the mean of this Gaussian
J? Why not J^2, or J/4? How do you derive the Gaussian
P(Is-Ib |J,sdJ)? The claim that the mean of Is-Ib is J requires some
sort of justification --- otherwise I might as well claim that
the mean of Is-Ib is the number of quarters in my pocket.
We both agreed that Is and Ib are dependent, and so that necessarily
means that P(Is-Ib | J,sdJ) cannot be the whole story. Dependence means
that the distribution of Is-Ib will also be a function of B and sdB,
unless you've integrated them out somehow (and even then the form
of the marginalized distribution depends on B and sdB).
F&W assumes that P(Ij|J,sdJ) is Poisson. If you think F&W doesn't, then
explain how you get the Gaussian P(Is-Ib | J,sdJ). Again, why is the
mean of Is-Ib equal to J? I gave one derivation, based on the model
that P(Ij|J), P(Ib|B), and P(Ib'|B) are all Poisson. If you disagree,
then what is your derivation of the Gaussian P(Is-Ib | J,sdJ)?