fast sampling...

[RichD]

Some time back, I attended a seminar of a mathematician
at SLAC.  He discussed the information contained in phase,
and the impossibility of measuring this at optical frequencies.

To illustrate, he presented some phase diagrams.  He
played around with those, to show the information contained -
and missing.

It was misleading, as those were derived from 2-D magnitude
images; i.e. sample the magnitudes, run the digital filters,
extract the phase domain.  Those phase diagrams weren\'t
real sampled data.

Phase is proportional to time delay.  So let\'s talk time
domain circuitry and sampling. If you\'re satisfied with
90* resolution, what\'s the highest frequency one can
sample, state of the art, using interleaved techniques and
whatever cleverness?

--
Rich



--
Rich

 

[whit3rd]

On Tuesday, November 23, 2021 at 4:43:41 PM UTC-8, RichD wrote:

Some time back, I attended a seminar of a mathematician
at SLAC. He discussed the information contained in phase,
and the impossibility of measuring this at optical frequencies. ...

Phase is proportional to time delay. So let\'s talk time
domain circuitry and sampling. If you\'re satisfied with
90* resolution, what\'s the highest frequency one can
sample, state of the art, using interleaved techniques and
whatever cleverness?

Holograms are made with visible light, and encode the phase with
good accuracy. That\'s maybe 600 THz. You don\'t get the full
bandwidth up to 600 THz, just a narrow frequency band that\'s
determined by the reference beam, but... you did say \'highest
frequency\'. Expanding upward through X-rays (atom-spacing
wavelengths and below) will require more cleverness yet.

 

[Phil Hobbs]

RichD wrote:

Some time back, I attended a seminar of a mathematician
at SLAC.  He discussed the information contained in phase,
and the impossibility of measuring this at optical frequencies.

To illustrate, he presented some phase diagrams.  He
played around with those, to show the information contained -
and missing.

It was misleading, as those were derived from 2-D magnitude
images; i.e. sample the magnitudes, run the digital filters,
extract the phase domain.  Those phase diagrams weren\'t
real sampled data.

Phase is proportional to time delay.  So let\'s talk time
domain circuitry and sampling. If you\'re satisfied with
90* resolution, what\'s the highest frequency one can
sample, state of the art, using interleaved techniques and
whatever cleverness?

--
Rich

There are all sorts of things that folks might call \"optical phase\",
some of which are much harder to measure than others.

1. _Full-bandwidth instantaneous phase of thermal light from a broad
area source._ At any point on a visibly incandescent object such as the
Sun or a tungsten filament, the E field has a well-defined magnitude,
phase, and direction. (Otherwise it couldn\'t obey Maxwell\'s equations.)

Points more than a wavelength or two apart have independent phases, and
all those independent phases have variations of order unity in times of
10**15 seconds or a bit faster, so at 8 bits per sample you\'d need to
measure on the order of 10**24 bytes per second per square centimetre of
surface. There\'s no way of _storing_ all that data even if you could
measure it. In any case, the instantaneous phase and polarization can
be described very well statistically from first principles, so there\'s
nothing useful to be gained by measuring it.

2. _Narrower-band instantaneous phase of an unresolved portion of a
thermal source._ This is much easier, because we lose a factor of about
1E8 in area, times the bandwidth ratio. You can measure that phase by
interfering it with a laser beam and looking at the RF. I\'ve actually
designed an instrument like that, in cooperation with an outfit in New
Mexico called Mesa Photonics. It wss for a DARPA program looking for HF
plumes from clandestine uranium enrichment.

3. _Phase differences in laser light propagating through different
paths,_ as in ordinary interferometry and holography. This includes
Doppler lidar and other such measurements, as well as FM detectors such
as Fabry-Perots and unbalanced Mach-Zehnders used as delay discriminators.

4. _RF phase shifts between two laser beams with slightly different
optical frequencies._ This includes laser-to-laser phase locking and
heterodyne laser linewidth measurements. Beating two lasers together
gives you the phase difference, so in order to infer the line shape of
one laser you have to assume that the two are similar.

Using three lasers gives you three pairwise phase differences, so you
can get the individual lineshapes and frequency differences uniquely.
(You obviously can\'t get the instantaneous average frequency, but you
can sometimes use a frequency-locked Ti:sapphire laser to get that too.)

5. _FM-to-AM measurements._ It\'s quite common to do FM derivative
spectroscopy, where you put sinusoidal FM on a diode laser. The
instantaneous optical frequency walks up and down the spectral lines,
and you can show by a bit of very pretty math that the Nth harmonic
interrogates the Nth derivative of the line shape.

Second-derivative spectroscopy produces the second derivative of the
line shape, and second-derivative spectra are widely tabulated. The big
advantage of that is that it suppresses the sloping baseline of the
spectra and enhances the sharp features, which is where most of the
interesting spectroscopy lives.

6. _\"Phase of the phase\"_ measurements. Back in the long ago when I was
a wet-behind-the-ears postdoc, I built an atomic- and magnetic-force
microscope proof-of-concept proto, which eventually became the IBM SXM
(\'scanned anything microscope\'). It used a resonant cantilever about
100 um long, made by electro-etching a tungsten wire. The point on the
end was also formed by etching and then bent mechanically into an L-shape.

The L-shaped cantilever was wiggled near its mechanical resonance using
a piezo bimorph actuator, and its motion detected using a heterodyne
interferometer.

The phase and amplitude of the cantilever\'s vibration vibration of the
cantilever depend on the tuning of the cantilever\'s resonance, just as
in every other lightly-damped second-order system. When the tip is very
near the sample, the resonance gets shifted--the gradient of the
tip-sample force (atomic, van der Waals, and/or magnetic) appears as a
change in the spring constant of the cantilever.

The microscope works by detecting the heterodyne signal with a fast
lock-in amplifier and servoing the tip-to-sample distance to keep the
lock-in signal constant.

Detecting only the amplitude of the tip vibration makes it vulnerable to
stiction--the normal adsorbed water layer makes the tip stick to the
sample, so the vibration stops. The servo thinks the tip is way, way
too close, so it pulls it back and back until it breaks loose. This of
course makes it ring strongly at its free resonance, so the servo thinks
the tip is way, way too far away, and sends the tip crashing into the
sample again--lather rinse repeat.

Moving the excitation frequency a bit further away, so that it\'s outside
the servo bandwidth, and detecting the phase of the response instead,
allows servoing stably much closer to the sample.

Those are most of the more upmarket optical phase measurements, the ones
actually associated with the phase of the electromagnetic fields in some
clear way.

8. _Phase unwrapping._ Phase is generally measured modulo 2 pi, though
PLL things can go much further in some cases. Joining a set of these
\'wrapped\' phases into a continuous function requires unwrapping the
phase, i.e. adding judiciously chosen multiples of 2 pi to each data
point to get rid of the jumps. This isn\'t too hard in 1D, but in higher
dimensions it becomes a thorny problem in general.

9. _Phase retrieval._ There are also phases associated in various ways
with the image intensity, e.g. the phase of the optical transfer
function. There are some fairly famous \"phase retrieval\" algorithms
that allow measuring things like topography from intensity-only images.

The original Fienup algorithm iteratively applies a positivity
constraint (optical intensity is never negative) and enforces compact
support in the frequency domain, because an optical system can\'t
reproduce spatial frequencies higher than 2 lambda/NA, where NA is the
numerical aperture of the received light (related to the f-number).

More recent phase retrieval algorithms use the propagation-of-intensity
equation, which is based on the paraxial Helmholtz propagator.

--------------------------------------------------------

So all in all you can do a whole lot with optical phase, and of course
this is far from an exhaustive list.

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Martin Brown]

On 24/11/2021 00:43, RichD wrote:

Some time back, I attended a seminar of a mathematician
at SLAC.  He discussed the information contained in phase,
and the impossibility of measuring this at optical frequencies.

It isn\'t quite right to say that either. You can measure the closure
phase once you have three or more measurement points in the optical.
That is how VLBI and optical aperture synthesis interferometry works.

They have to have optical bench quality mixers and incredibly thermally
stable environment for all the optical components. They tend to work in
the near IR to um bands rather than optical because it is easier.

COAST at MRAO Cambridge was the original proof of concept. The servos
that kept the white light fringe in play caused it to be christened the
\"telescope that sings\". They applied radio astronomy techniques in the
optical band and overcame very significant engineering challenges.

https://en.wikipedia.org/wiki/Cambridge_Optical_Aperture_Synthesis_Telescope

Main limitation is that it will only work for a handful of very bright
stars - but they did get some impressive results for the time.

To illustrate, he presented some phase diagrams.  He
played around with those, to show the information contained -
and missing.

It was misleading, as those were derived from 2-D magnitude
images; i.e. sample the magnitudes, run the digital filters,
extract the phase domain.  Those phase diagrams weren\'t
real sampled data.

Sometimes you can back solve the 2D intensity image to obtain a self
consistent 3D solution. It depends how complex the target is. They have
become increasingly good at making suitable heuristic assumptions and so
obtaining 3D structures that will produce a given 2D interference
pattern. It just requires a lot of data at different cunningly chosen
angles. Sometimes the structure remains ambiguous with multiple targets
able to reproduce exactly the same set of diffraction spots.

Phase is proportional to time delay.  So let\'s talk time
domain circuitry and sampling. If you\'re satisfied with
90* resolution, what\'s the highest frequency one can
sample, state of the art, using interleaved techniques and
whatever cleverness?

This is the current state of the art near optical interferometer:

https://en.wikipedia.org/wiki/Navy_Precision_Optical_Interferometer

It is very tough to do since they have to correlate all of the baselines
at once which means a hell of a lot of pass compensators and beam
splitters. It has a tiny working field of view and needs bright compact
objects to stand any chance of working at all.

The ALMA Atacama desert mm wave interferometer is another closure phase
aperture synthesis imaging system in the same vein.

https://en.wikipedia.org/wiki/Atacama_Large_Millimeter_Array


--
Regards,
Martin Brown

 

[server]

On Tue, 23 Nov 2021 16:43:38 -0800 (PST), RichD
<r_delaney2001@yahoo.com> wrote:

Some time back, I attended a seminar of a mathematician
at SLAC.  He discussed the information contained in phase,
and the impossibility of measuring this at optical frequencies.

To illustrate, he presented some phase diagrams.  He
played around with those, to show the information contained -
and missing.

It was misleading, as those were derived from 2-D magnitude
images; i.e. sample the magnitudes, run the digital filters,
extract the phase domain.  Those phase diagrams weren\'t
real sampled data.

Phase is proportional to time delay.  So let\'s talk time
domain circuitry and sampling. If you\'re satisfied with
90* resolution, what\'s the highest frequency one can
sample, state of the art, using interleaved techniques and
whatever cleverness?

--
Rich

There are attosecond lasers that produce a light pulse that\'s only a
few wiggles long. Those can be used to sample another light source (in
a nonlinear medium) or have been used to sample electrical signals
using basically a very fast photoconductor.



--

Father Brown\'s figure remained quite dark and still;
but in that instant he had lost his head. His head was
always most valuable when he had lost it.

 

[RichD]

On November 24, Phil Hobbs wrote:

There are all sorts of things that folks might call \"optical phase\",
some of which are much harder to measure than others.

[snip seminar on advanced optics]

That\'s mostly above my pay grade.
But I\'m not complaining.

In Japan, they have a tradition, persons of noteworthy accomplishment
are declared a national resource. I\'m going to write my congressman,
to initiate that here, and add your name to the list.

Anyway, for context, at SLAC, they\'re analyzing molecular structures,
using X ray scattering. They\'ve dropped out of the particle biz, doing
more chemistry than physics, so to speak. That\'s nominal, though the
real raison d\'etre is a PhD factory.

I\'m not sure which of your recommended techniques would apply there.

--
Rich

 

[Robert Baer]

RichD wrote:

Some time back, I attended a seminar of a mathematician
at SLAC.  He discussed the information contained in phase,
and the impossibility of measuring this at optical frequencies.

To illustrate, he presented some phase diagrams.  He
played around with those, to show the information contained -
and missing.

It was misleading, as those were derived from 2-D magnitude
images; i.e. sample the magnitudes, run the digital filters,
extract the phase domain.  Those phase diagrams weren\'t
real sampled data.

Phase is proportional to time delay.  So let\'s talk time
domain circuitry and sampling. If you\'re satisfied with
90* resolution, what\'s the highest frequency one can
sample, state of the art, using interleaved techniques and
whatever cleverness?

--
Rich



--
Rich

As I remember, 1/4 wavelength optical resolution is typical.

--
This email has been checked for viruses by Avast antivirus software.
https://www.avast.com/antivirus

 

[Phil Hobbs]

RichD wrote:

On November 24, Phil Hobbs wrote:
There are all sorts of things that folks might call \"optical phase\",
some of which are much harder to measure than others.

[snip seminar on advanced optics]

That\'s mostly above my pay grade.
But I\'m not complaining.

In Japan, they have a tradition, persons of noteworthy accomplishment
are declared a national resource. I\'m going to write my congressman,
to initiate that here, and add your name to the list.a

\"National resource\" sounds bad--visions of being drained to cover up
stupid policy mistakes.

Anyway, for context, at SLAC, they\'re analyzing molecular structures,
using X ray scattering. They\'ve dropped out of the particle biz, doing
more chemistry than physics, so to speak. That\'s nominal, though the
real raison d\'etre is a PhD factory.

Phase retrieval in X-ray crystallography is an area of active research,
and AFAIK the general case hasn\'t been solved. A quick search pulled up
this math paper
<https://epubs.siam.org/doi/pdf/10.1137/20M132136X>, which indicates
that nobody knows how to do it ATM.

The usual method is to guess a structure based on the positions of the
diffraction peaks, which give the linear separations of the scattering
centres (atoms); compute the expected diffraction pattern; and
iteratively refine the model structure. (That step is where the magic
happens.)

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Martin Brown]

On 26/11/2021 19:29, Phil Hobbs wrote:

RichD wrote:
On November 24, Phil Hobbs wrote:
There are all sorts of things that folks might call \"optical phase\",
some of which are much harder to measure than others.

[snip seminar on advanced optics]

That\'s mostly above my pay grade.
But I\'m not complaining.

In Japan, they have a tradition, persons of noteworthy accomplishment
are declared a national resource.  I\'m going to write my congressman,
to initiate that here, and add your name to the list.a

\"National resource\" sounds bad--visions of being drained to cover up
stupid policy mistakes.

That is actually a bad translation into English by whoever made it.

The actual official Japanese translation is \"National Living Treasure\"
and it encompasses people in the arts and artisan skills who can make
the likes of traditional samurai swords, pottery or phenomenally complex
puzzle boxes according to the traditional ways of doing things.

https://en.wikipedia.org/wiki/Living_National_Treasure_(Japan)

It comes with a stipend of 2MY = $20k a year to help them survive.
There are just over a hundred of them in existence.

Think living history museum and you will not be too far out.

Anyway, for context, at SLAC, they\'re analyzing molecular structures,
using X ray scattering.   They\'ve dropped out of the particle biz, doing
more chemistry than physics, so to speak.  That\'s nominal, though the
real raison d\'etre is a PhD factory.

Phase retrieval in X-ray crystallography is an area of active research,
and AFAIK the general case hasn\'t been solved.  A quick search pulled up
this math paper
https://epubs.siam.org/doi/pdf/10.1137/20M132136X>, which indicates
that nobody knows how to do it ATM.

The general case is probably unsolvable. Radio astronomers worked out a
long time ago (ISTR ~1980\'s that many patterns of sky brightness could
lead to the same autocorrelation function ie. intensity).

Point scatterers is marginally more tractable but still very tough.

The usual method is to guess a structure based on the positions of the
diffraction peaks, which give the linear separations of the scattering
centres (atoms); compute the expected diffraction pattern; and
iteratively refine the model structure.  (That step is where the magic
happens.)

One trick they have up their sleeve sometimes is to substitute a heavier
atom into one of the scattering centres which breaks the degeneracy.

I met a guy a couple of years back that claimed they had a more general
solution for some reasonably important subclass of these problems but I
never got a chance to quiz him on the details. I never really was into
phaseless observations because we worked very hard to preserve phase if
we could and closure phase across as many closed loops if we couldn\'t.

Often it was a hybrid of the two. Absolute phase to determine position
on the sky and closure phase to refine what it really looks like.

--
Regards,
Martin Brown

 

[Phil Hobbs]

Martin Brown wrote:

On 26/11/2021 19:29, Phil Hobbs wrote:
RichD wrote:
On November 24, Phil Hobbs wrote:
There are all sorts of things that folks might call \"optical phase\",
some of which are much harder to measure than others.

[snip seminar on advanced optics]

That\'s mostly above my pay grade.
But I\'m not complaining.

In Japan, they have a tradition, persons of noteworthy accomplishment
are declared a national resource.  I\'m going to write my congressman,
to initiate that here, and add your name to the list.a

\"National resource\" sounds bad--visions of being drained to cover up
stupid policy mistakes.

That is actually a bad translation into English by whoever made it.

The actual official Japanese translation is \"National Living Treasure\"
and it encompasses people in the arts and artisan skills who can make
the likes of traditional samurai swords, pottery or phenomenally complex
puzzle boxes according to the traditional ways of doing things.

https://en.wikipedia.org/wiki/Living_National_Treasure_(Japan)

It comes with a stipend of 2MY = $20k a year to help them survive.
There are just over a hundred of them in existence.

Think living history museum and you will not be too far out.

Anyway, for context, at SLAC, they\'re analyzing molecular structures,
using X ray scattering.   They\'ve dropped out of the particle biz, doing
more chemistry than physics, so to speak.  That\'s nominal, though the
real raison d\'etre is a PhD factory.

Phase retrieval in X-ray crystallography is an area of active
research, and AFAIK the general case hasn\'t been solved.  A quick
search pulled up this math paper
https://epubs.siam.org/doi/pdf/10.1137/20M132136X>, which indicates
that nobody knows how to do it ATM.

The general case is probably unsolvable. Radio astronomers worked out a
long time ago (ISTR ~1980\'s that many patterns of sky brightness could
lead to the same autocorrelation function ie. intensity).

Point scatterers is marginally more tractable but still very tough.

A big point in favour of the crystallographers vs. the astronomers is
that they can rotate their samples any way they like, so the problems
aren\'t strictly equivalent.

Cheers

Phil Hobbs


--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[whit3rd]

On Friday, November 26, 2021 at 12:01:37 PM UTC-8, Phil Hobbs wrote:

Martin Brown wrote:
On 26/11/2021 19:29, Phil Hobbs wrote:
RichD wrote:

Anyway, for context, at SLAC, they\'re analyzing molecular structures,
using X ray scattering. They\'ve dropped out of the particle biz, doing
more chemistry than physics, so to speak. That\'s nominal, though the
real raison d\'etre is a PhD factory.

Phase retrieval in X-ray crystallography is an area of active
research...
The general case is probably unsolvable. Radio astronomers worked out a
long time ago (ISTR ~1980\'s that many patterns of sky brightness could
lead to the same autocorrelation function ie. intensity).

Point scatterers is marginally more tractable but still very tough.
A big point in favour of the crystallographers vs. the astronomers is
that they can rotate their samples any way they like, so the problems
aren\'t strictly equivalent.

And a reason SLAC gets involved, is that they can produce polarized X-rays
which gives orientation info even on polycrystalline or powdered samples.
A crystal\'s X-ray absorption by photoelectric effect depends on outgoing electrons
and that outgoing electron can only go in the direction that polarization of
the X-ray permits. Some of those directions are blocked by the lattice, so
absorption probability is modulated accordingly.

Of course, now the problem is electron wavefunction phase, not electromagnetic.

 

[Okkim Atnarivik]

On 11/24/21 9:21 AM, Phil Hobbs wrote:

RichD wrote:
Some time back, I attended a seminar of a mathematician
at SLAC.  He discussed the information contained in phase,
and the impossibility of measuring this at optical frequencies.

To illustrate, he presented some phase diagrams.  He
played around with those, to show the information contained -
and missing.

It was misleading, as those were derived from 2-D magnitude
images; i.e. sample the magnitudes, run the digital filters,
extract the phase domain.  Those phase diagrams weren\'t
real sampled data.

Phase is proportional to time delay.  So let\'s talk time
domain circuitry and sampling.  If you\'re satisfied with
90* resolution, what\'s the highest frequency one can
sample, state of the art, using interleaved techniques and
whatever cleverness?

--
Rich

There are all sorts of things that folks might call \"optical phase\",
some of which are much harder to measure than others.

1.  _Full-bandwidth instantaneous phase of thermal light from a broad
area source._  At any point on a visibly incandescent object such as the
Sun or a tungsten filament, the E field has a well-defined magnitude,
phase, and direction.  (Otherwise it couldn\'t obey Maxwell\'s equations.)

Points more than a wavelength or two apart have independent phases, and
all those independent phases have variations of order unity in times of
10**15 seconds or a bit faster, so at 8 bits per sample you\'d need to
measure on the order of 10**24 bytes per second per square centimetre of
surface.  There\'s no way of _storing_ all that data even if you could
measure it.  In any case, the instantaneous phase and polarization can
be described very well statistically from first principles, so there\'s
nothing useful to be gained by measuring it.

2. _Narrower-band instantaneous phase of an unresolved portion of a
thermal source._  This is much easier, because we lose a factor of about
1E8 in area, times the bandwidth ratio.  You can measure that phase by
interfering it with a laser beam and looking at the RF.  I\'ve actually
designed an instrument like that, in cooperation with an outfit in New
Mexico called Mesa Photonics.  It wss for a DARPA program looking for HF
plumes from clandestine uranium enrichment.

3. _Phase differences in laser light propagating through different
paths,_ as in ordinary interferometry and holography.  This includes
Doppler lidar and other such measurements, as well as FM detectors such
as Fabry-Perots and unbalanced Mach-Zehnders used as delay discriminators.

4. _RF phase shifts between two laser beams with slightly different
optical frequencies._  This includes laser-to-laser phase locking and
heterodyne laser linewidth measurements.  Beating two lasers together
gives you the phase difference, so in order to infer the line shape of
one laser you have to assume that the two are similar.

Using three lasers gives you three pairwise phase differences, so you
can get the individual lineshapes and frequency differences uniquely.
(You obviously can\'t get the instantaneous average frequency, but you
can sometimes use a frequency-locked Ti:sapphire laser to get that too.)

5. _FM-to-AM measurements._  It\'s quite common to do FM derivative
spectroscopy, where you put sinusoidal FM on a diode laser.  The
instantaneous optical frequency walks up and down the spectral lines,
and you can show by a bit of very pretty math that the Nth harmonic
interrogates the Nth derivative of the line shape.

Second-derivative spectroscopy produces the second derivative of the
line shape, and second-derivative spectra are widely tabulated.  The big
advantage of that is that it suppresses the sloping baseline of the
spectra and enhances the sharp features, which is where most of the
interesting spectroscopy lives.

6. _\"Phase of the phase\"_ measurements.  Back in the long ago when I was
a wet-behind-the-ears postdoc, I built an atomic- and magnetic-force
microscope proof-of-concept proto, which eventually became the IBM SXM
(\'scanned anything microscope\').  It used a resonant cantilever about
100 um long, made by electro-etching a tungsten wire.  The point on the
end was also formed by etching and then bent mechanically into an L-shape.

The L-shaped cantilever was wiggled near its mechanical resonance using
a piezo bimorph actuator, and its motion detected using a heterodyne
interferometer.

The phase and amplitude of the cantilever\'s vibration vibration of the
cantilever depend on the tuning of the cantilever\'s resonance, just as
in every other lightly-damped second-order system.  When the tip is very
near the sample, the resonance gets shifted--the gradient of the
tip-sample force (atomic, van der Waals, and/or magnetic) appears as a
change in the spring constant of the cantilever.

The microscope works by detecting the heterodyne signal with a fast
lock-in amplifier and servoing the tip-to-sample distance to keep the
lock-in signal constant.

Detecting only the amplitude of the tip vibration makes it vulnerable to
stiction--the normal adsorbed water layer makes the tip stick to the
sample, so the vibration stops.  The servo thinks the tip is way, way
too close, so it pulls it back and back until it breaks loose.  This of
course makes it ring strongly at its free resonance, so the servo thinks
the tip is way, way too far away, and sends the tip crashing into the
sample again--lather rinse repeat.

Moving the excitation frequency a bit further away, so that it\'s outside
the servo bandwidth, and detecting the phase of the response instead,
allows servoing stably much closer to the sample.

Those are most of the more upmarket optical phase measurements, the ones
actually associated with the phase of the electromagnetic fields in some
clear way.

8. _Phase unwrapping._  Phase is generally measured modulo 2 pi, though
PLL things can go much further in some cases.  Joining a set of these
\'wrapped\' phases into a continuous function requires unwrapping the
phase, i.e. adding judiciously chosen multiples of 2 pi to each data
point to get rid of the jumps.  This isn\'t too hard in 1D, but in higher
dimensions it becomes a thorny problem in general.

9.  _Phase retrieval._ There are also phases associated in various ways
with the image intensity, e.g. the phase of the optical transfer
function.  There are some fairly famous \"phase retrieval\" algorithms
that allow measuring things like topography from intensity-only images.

The original Fienup algorithm iteratively applies a positivity
constraint (optical intensity is never negative) and enforces compact
support in the frequency domain, because an optical system can\'t
reproduce spatial frequencies higher than 2 lambda/NA, where NA is the
numerical aperture of the received light (related to the f-number).

More recent phase retrieval algorithms use the propagation-of-intensity
equation, which is based on the paraxial Helmholtz propagator.

--------------------------------------------------------

So all in all you can do a whole lot with optical phase, and of course
this is far from an exhaustive list.

Cheers

Phil Hobbs

Wow, very ..um.. illuminating. I just attended a talk in a conference
last week which seems to be related. The topic was plenoptic imaging,
with an added twist of utilizing (Hanbury-Twiss Brown -like)
correlations somehow to determine the ray directions. The illumination
had to be either chaotic light or entangled photon pairs for the scheme
to work. I\'ll need to find time to wrap my head around the talk
contents.

Regards,
Mikko

 

[Phil Hobbs]

Okkim Atnarivik wrote:

On 11/24/21 9:21 AM, Phil Hobbs wrote:
snip


Wow, very ..um.. illuminating. I just attended a talk in a conference
last week which seems to be related. The topic was plenoptic imaging,
with an added twist of utilizing (Hanbury-Twiss Brown -like)
correlations somehow to determine the ray directions. The illumination
had to be either chaotic light or entangled photon pairs for the scheme
to work. I\'ll need to find time to wrap my head around the talk
contents.

Regards,
Mikko

Hi, Mikko,

Welcome back!

There are a lot of interesting things going on in quantum imaging, some
of which might even be useful someday. AFAIK most have theoretical SNR
advantages over the semiclassical approach, but only at very low power
levels--you almost always win big by just cranking up the power.

\'Quantum illumination\' looks like being an exception--it apparently
works even in sunlight.

I\'d be interested in what you find out about the plenoptic technique.

Cheers

Phil

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com

 

[Okkim Atnarivik]

On 11/29/21 3:44 PM, Phil Hobbs wrote:

Okkim Atnarivik wrote:
On 11/24/21 9:21 AM, Phil Hobbs wrote:
snip


   Wow, very ..um.. illuminating. I just attended a talk in a conference
last week which seems to be related. The topic was plenoptic imaging,
with an added twist of utilizing (Hanbury-Twiss Brown -like)
correlations somehow to determine the ray directions. The illumination
had to be either chaotic light or entangled photon pairs for the scheme
to work. I\'ll need to find time to wrap my head around the talk
contents.

   Regards,
           Mikko



Hi, Mikko,

Welcome back!

There are a lot of interesting things going on in quantum imaging, some
of which might even be useful someday.  AFAIK most have theoretical SNR
advantages over the semiclassical approach, but only at very low power
levels--you almost always win big by just cranking up the power.

\'Quantum illumination\' looks like being an exception--it apparently
works even in sunlight.

I\'d be interested in what you find out about the plenoptic technique.

Cheers

Phil

So Quantum Illumination still rides on? I was left under impression
that the field is declining, judging by the overview
doi:10.1109/MAES.2019.2957870 (although I have only glanced through the
paper). Interesting to hear!

Regarding the plenoptic technique, the conference organizers have not
yet made the presentation slides available. I jotted down a reference
during the talk however, doi:10.1103/PhysRevLett.116.223602 . You can
probably see at a glance whether the technique makes sense at all, for
me it\'s slower to get. ( I just downloaded the PRL, it actually seems to
containt pretty much all that was presented in the talk).

Regards,
Mikko

 

[Phil Hobbs]

Okkim Atnarivik wrote:

On 11/29/21 3:44 PM, Phil Hobbs wrote:
Okkim Atnarivik wrote:
On 11/24/21 9:21 AM, Phil Hobbs wrote:
snip


   Wow, very ..um.. illuminating. I just attended a talk in a conference
last week which seems to be related. The topic was plenoptic imaging,
with an added twist of utilizing (Hanbury-Twiss Brown -like)
correlations somehow to determine the ray directions. The illumination
had to be either chaotic light or entangled photon pairs for the scheme
to work. I\'ll need to find time to wrap my head around the talk
contents.

   Regards,
           Mikko



Hi, Mikko,

Welcome back!

There are a lot of interesting things going on in quantum imaging, some
of which might even be useful someday.  AFAIK most have theoretical SNR
advantages over the semiclassical approach, but only at very low power
levels--you almost always win big by just cranking up the power.

\'Quantum illumination\' looks like being an exception--it apparently
works even in sunlight.

I\'d be interested in what you find out about the plenoptic technique.

Cheers

Phil


So Quantum Illumination still rides on? I was left under impression
that the field is declining, judging by the overview
doi:10.1109/MAES.2019.2957870 (although I have only glanced through the
paper). Interesting to hear!

Regarding the plenoptic technique, the conference organizers have not
yet made the presentation slides available. I jotted down a reference
during the talk however, doi:10.1103/PhysRevLett.116.223602 . You can
probably see at a glance whether the technique makes sense at all, for
me it\'s slower to get. ( I just downloaded the PRL, it actually seems to
containt pretty much all that was presented in the talk).

Regards,
Mikko

I dug into it a bit, and it seems to be basically a Shack-Hartmann with
a coarse array of pinholes in front of it. Strange beast!

Cheers

Phil Hobbs

--
Dr Philip C D Hobbs
Principal Consultant
ElectroOptical Innovations LLC / Hobbs ElectroOptics
Optics, Electro-optics, Photonics, Analog Electronics
Briarcliff Manor NY 10510

http://electrooptical.net
http://hobbs-eo.com