Re: Kohler illumination question...

Gregor.Overney@xxxxxxxxx wrote: 
Now I slowly understand what you are trying to argue. You do not like
when I write "resolution beyond the diffraction limit" [1] in
connection WITH far-field imaging. And I am trying to talk about
improvements in far-field imaging that allow us to see structures at a
nanometer scale, something, which isn't commercialized yet. I am not
talking about breaking the diffraction limit and render the far-field
theory inadequate. I should have said "beyond the diffraction limit of
current implementations" since I was talking about real microscopes
(not theories). Of course, if someone finds a refractive index of 1000
he will be able to resolve more. I believe that this proofs that we are
not yet at the limit of far-field imaging since improving refractive
indices is also an improvement for this technology.

Except that "far-field imaging" is itself a limit. That is, it is a limiting case of a more general situation, just as "near-field imaging" is a limit. And to reiterate, there is nothing in any of the references you have provided that claims to exceed physical limiations of far-field iamging.

And, it's not clear that "improving refractive indices is also an improvement for this technology", as the term "improving" a refractive index is not a well defined concept. What about dispersion? What about absorptive losses? And most important, how can one go about creating (what is currently) unobtainium without having a rational basis for conducting the research? Would you have thought of using plasmons without knowing that they exist? And would we be able to manipulate and use plasmons without any theoretical framework that describes their properties?


Regarding describing something without well-defined mathematical
theory:
There are many examples. A "cookie recipe" that tells a manufacturer
how to make his great glass would be one. Such a recipe would be based
on experience rather than theory. Another one is the formation of micro
cracks in materials that cause the scope to experience mechanical
failures. This is also not exactly describable with well-defined
mathematical theories. How about the impact of an imperfect lens on
image formation? This is also beyond any well-defined mathematical
theory. The existence of a physical effect or even better a physical
mystery as described in Mark P. Silverman's nice book "More than one
mystery: Explorations in quantum interference" [2]. - With theory we
get far and because of theoretical understanding we are able to make
further progress. But progress is often ahead of what theories can
fully describe and sometimes even explain.

Again, there is a difference between stating that current theory is incomplete and claiming that some physical phenomena will forever and always be beyond the domain of a mathematical description. I challenge you (or anyone else, for that matter) to come up with a "cookie recipe" for transparent titanium or a material with a tensile strength of 1000 Tbar by blindly banging away in the lab, in analogy to the million monkeys banging away at a million typewriters.

The impact of an imperfect lens on an optical system is describable to the extent that the deviation of the test lens from a 'perfect' lens is describable.

True progress is not beyond what we can explain and describe to the level of reproducibility. The fact that quantum mechanics has many counterintuitive results is not incompatable with the existence of computer chips and hard drives (which require quantum mechanics to be reduced to practice).

--
Andrew Resnick, Ph.D.
Department of Physiology and Biophysics
Case Western Reserve University
.

Relevant Pages

  • Re: Kohler illumination question...
    ... And I am trying to talk about improvements in far-field imaging that allow us to see structures at a nanometer scale, something, which isn't commercialized yet. ... I am not talking about breaking the diffraction limit and render the far-field theory inadequate. ... I believe that this proofs that we are not yet at the limit of far-field imaging since improving refractive indices is also an improvement for this technology. ... The impact of an imperfect lens on an optical system is describable to the extent that the deviation of the test lens from a 'perfect' lens is describable. ...
    (sci.techniques.microscopy)
  • Re: Kohler illumination question...
    ... connection WITH far-field imaging. ... talking about breaking the diffraction limit and render the far-field ... The existence of a physical effect or even better a physical ... But progress is often ahead of what theories can ...
    (sci.techniques.microscopy)
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