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.
--
Wayne Watson (Nevada City, CA)

Web Page: <speckledwithStars.net

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.

"W. Watson" <wolf_tracks@invalid.com> 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.

"Salmon Egg" <SalmonEgg@sbcglobal.net> wrote

"W. Watson" <wolf_tracks@invalid.com> 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).

"Salmon Egg" <SalmonEgg@sbcglobal.net> wrote
"W. Watson" <wolf_tracks@invalid.com> 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).

Scanning Near-Field Optical Microscopes use near field optics to image
features < wave length of the illuminating light.

SERS uses near field effects to identify the presence of single molecules of
a substance

Some optical tweezers use near field effects to grab and move individual
cells and smaller particles.

Marco
________________________
Marc Reinig
UCO/Lick Observatory
Laboratory for Adaptive Optics

"Charles Manoras" <inconnu@cette.adresse> wrote in message
news:heCdnUScA-7ab0janZ2dnUVZ_vShnZ2d@comcast.com...
"Salmon Egg" <SalmonEgg@sbcglobal.net> wrote
"W. Watson" <wolf_tracks@invalid.com> 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).

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?

"Helpful person" <rrl...@yahoo.com> wrote

There is a configuration that does not limit resolution by the optical
aperture (diffraction).  In materials with negative refractive index
(the rays are refracted to the "other" side of the surface normal) it
can be shown that there is no limit to the resolution.

Although such materials do not exist in nature they have been
constructed using repetitive layers of LC (inductance, capacitance)
micro circuits.  These have been built and demonstrated using visible
light.

Yes I have read that several times and puzzled over this ever since.

Save me a Google search, any credible reference?  Thanks.

"W. Watson" <wolf_tracks@invalid.com> wrote in message
news:A1oBj.15662$Ej5.2728@newssvr29.news.prodigy.net...
It seems then that there really is no practical applications yet for this
idea, particularly not astronomy or even biology (microscopes).

Biology yes, astronomy no ;=)

By near field, it is basically meant optics used close to the object of
interest?

Sort of. It means you need to interact with the near field effects near the
object (hence the term near field). Their intensity decreases exponentially
with distance. However, the optics observing the result of the interaction
can be far away (relatively), since the interaction results in radiating
fields: light as we generally perceive it. Near field interactions must be
within ~wavelength distance (typically much less).

Marco
________________________
Marc Reinig
UCO/Lick Observatory
Laboratory for Adaptive Optics

There is a configuration that does not limit resolution by the optical
aperture (diffraction). In materials with negative refractive index
(the rays are refracted to the "other" side of the surface normal) it
can be shown that there is no limit to the resolution.

Although such materials do not exist in nature they have been
constructed using repetitive layers of LC (inductance, capacitance)
micro circuits. These have been built and demonstrated using visible
light.

Scanning Near-Field Optical Microscopes use near field optics to image
features < wave length of the illuminating light.

SERS uses near field effects to identify the presence of single molecules
of a substance

Some optical tweezers use near field effects to grab and move individual
cells and smaller particles.

Marco
________________________
Marc Reinig
UCO/Lick Observatory
Laboratory for Adaptive Optics

Oops but whar SERS stand for?

OK Surface Enhanced Raman Spectroscopy as per Wikipedia but that appears
to
me to be a rather specialized form of microscopy.

http://en.wikipedia.org/wiki/Martin_Fleischman