This has been a fascinating thread. Thanks.
I will dip my oar in the water. Here are a couple of snippets.
Jacob: It was good of proto-crystallographers to invent diffraction as a
way to apply Fourier Series.
and
Ethan: So here's the brain-teaser: Why does Nature use Fourier
transforms rather than Wavelet transforms? Or does she?
Probably Jacob was joking, but I believe we should say that physicists
(and Ms. Nature) employ the Fourier transform/synthesis because this
models pretty precisely the way that we believe light rays/waves of all
energies interfere with one another.
Warm regards, Bob
On Fri, 10 Nov 2017, Keller, Jacob wrote:
My understanding is that EM people will routinely switch to diffraction mode
when they want accurate measurements. You lose the phase information but,
since EM lenses tend to have imperfections, you get better measurements of the
intensities.
Only to my knowledge in the case of crystalline samples like 2D crystals.
Of course the loss of phases is a serious problem when you don't have a model
of the object as precise as our atomic models.
From where does this precision arise, I wonder? I guess priors for atom-based
models are pretty invariant. On the other hand, who says that such priors,
albeit of many more varieties, don't exist for larger biological samples, such
as zebrafish brains and drosophila embryos/larvae? Anyway, right now, the state
of the art of modelling in these fluorescence data sets is hand-drawing circles
around things that look interesting, hoping the sample does not shift too much,
or perhaps using some tracking. But it could be so much better!
JPK
