Re: Resolution Beyond the Classical Limit

It seems then that there really is no practical applications yet for this idea, particularly not astronomy or even biology (microscopes). By near field, it is basically meant optics used close to the object of interest?

Charles Manoras wrote:
"Salmon Egg" <SalmonEgg@xxxxxxxxxxxxx> wrote
"W. Watson" <wolf_tracks@xxxxxxxxxxx> wrote:

I'm browsing through Goodman's Introduction to Fourier Optics, and
noticed
the topic in the Subject above in sections 6.6, p160f, 2nd edition. The
math
is a bit above my current experience, but what devices does this apply
to?
What are the applications? A subtopic is extrapolation method based on
sampling theorem.
When it comes to questions of this nature, I often refer to electrical
analogies. Thin of an optical system as an information extraction
system. The amount of information that can be extracted, depends upon
the snr, signal-to-noise-ratio. Thus, by using slopes on point spread
functions, angles much smaller than the Rayleigh resolution limit can be
measured if the snr is high enough. It jus requires more sophisticated
signal processing.

Often, by changing something between measurements extra information can
be extracted. There is an exchange of time for resolution or spatial
bandwidth. The superheterodyne principle allows higher (resolution)
frequency signals to be detected with a receiver that does not have the
basic capability to work at that frequency. In optics, information is
carried in channels of limited spatial bandwidth. By the appropriate use
of gratings, the equivalent of optical local oscillator, successive
measurements in time can end up giving you the effect of a large
aperture. No physical law on the limitation of information transfer
through a channel is violated.

Indeed however the above applies to the one-dimensional case.

Optics is at least 2D. :-)

One would have to work at a lot of intermediate azimuths, reconstitute
the images from a lot of "scans" etc.

There was a flurry of papers in the sixties and seventies about "classical"
(i.e. as above) super resolution by such luminaries as Adolf Lohmann,
John Armitage and a few others (I quote from memory and I refer you
to the JOSA of those days).

All these papers were strong on theory but came quite short on practice.

I read them with great enthusiasm and anticipation, only to come to the
conclusion that the proposed schemes were 1D, entailed coherent laser
illumination (over a wide field) and would not be applicable to conventional
(i.e. far field) microscopy, big disappointment.

I doubt that things have changed much but would love to be proved
wrong or misinformed.

The only glimmer of hope (nice cliche) I can see is our vastly and ever
more increasing image processing power.

In the meantime laser scanning microscopy has brought great improvements
to the field but the observed apparent increase in resolution is mostly due
its inherent elimination of stray light which is the bane of high NA microscope
objectives (and not to any super rez trick).








--
Wayne Watson (Nevada City, CA)

Web Page: <speckledwithStars.net>
.

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