talking about "super resolution"

[Alberto Diaspro]

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Friends,
I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?

Thank you for your kind attention.
Have a great 2014
Alby

[John Oreopoulos]

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Alberto,

What term would you suggest as an alternative to "super-resolution" as a catch-all phrase for these techniques? I've heard the term "photon-limited" resolution before, but that wouldn't quite seem right here.  

John


On 2013-12-31, at 5:11 PM, Alberto Diaspro wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Friends,
> I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
> Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?
>
> Thank you for your kind attention.
> Have a great 2014
> Alby

[Alberto Diaspro]

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

well…super resolution is fine… i also like the neologism of optical nanoscopy…this last simply states that we moved from the “occhialino” by Galileo Galilei, first named as micro-scope (microscopic nominare libuit as Faber wrote to Accademia dei Lincei), allowing hundred microns resolution to new classes of microscopes that allow to distinguish objects closer than 200 nm…within the 30-40 nm range at room temperature, conventional conditions.
ciao
alby


On 31 Dec, 2013, at 23:23, John Oreopoulos <[hidden email]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Alberto,
>
> What term would you suggest as an alternative to "super-resolution" as a catch-all phrase for these techniques? I've heard the term "photon-limited" resolution before, but that wouldn't quite seem right here.  
>
> John
>
>
> On 2013-12-31, at 5:11 PM, Alberto Diaspro wrote:
>
>> *****
>> To join, leave or search the confocal microscopy listserv, go to:
>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>> *****
>>
>> Friends,
>> I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
>> Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?
>>
>> Thank you for your kind attention.
>> Have a great 2014
>> Alby

[Reto Fiolka]

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Dear all

Happy 2014!

I do not like the term "super resolution" nor "nanoscopy".

The term "Super" should only be used in physics for really extra-ordinary
phenomena, like super-conduction (really 0 resistance) or super-fluidics (0
viscosity). While some recent microscopy techniques have shown amazing
results, they have not achieved infinite resolution.

Nanoscopy, hmm, I have never heard of an atomic force nanoscope or of
transmission electron picoscopy (even though they go down to 0.05 nm). In
those fields they still call them microscopes, even though they achieve 1-2
orders of magnitude higher resolution than our optical "nanoscopes".

My humble opinion, but I guess Alberto's initial question was not about
nomencalture.

Best,
Reto

[David Baddeley]

I think that single molecule switching bas
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

An interesting exercise ...

I think that single molecule switching based super-resolution can clearly be interpreted in terms of the incorporation of additional data set / information and/or analytical continuation. To make it a bit more concrete: you know that your single molecule emission is coming from the equivalent of a delta function in real space, which means that it's a complex exponential in Fourier space. When imaging with a diffraction and photon limited system you end up getting a noisy version of a few periods (due to the band limit) of that complex exponential, and cannot accurately determine its exact frequency (ie the position). If you try and do analytical continuation, you're trying to extend this complex exponential out to infinity in the Fourier domain (which would give you a shifted delta function in space), but because of the frequency uncertainty there are a large number of possible analytical continuations with subtly different frequencies. Close to the
origin, these will all line up (more or less) and the mean will still be a complex exponential. As you get further from the origin, however, they'll go out of phase and interfere destructively (analagous to the coherence phenomena in broad-band light sources), giving you a new effective band limit.

It's a little harder, however, to see how the likes of STED can be framed in terms of analytical continuation. I see this more as a case of moving to a non-linear excitation (or depletion) regime and breaking out of the band limit through non-linearity (analagous to using heterodyne techniques to move radio signals down to the audio band). Also doing it in a very clever way so as not to need any post-processing (as for localisation or SIM). It's hard to see the information input into the system.




On Tuesday, 31 December 2013 5:14 PM, Alberto Diaspro <[hidden email]> wrote:
 
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Friends,
I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?

Thank you for your kind attention.
Have a great 2014
Alby

[Guy Cox-2]

Surely it is structured illumination that is strictly analogous to heterodyning?

                                                           Guy

Guy Cox, Honorary Associate Professor
School of Medical Sciences

Australian Centre for Microscopy and Microanalysis,
Madsen, F09, University of Sydney, NSW 2006


-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of David Baddeley
Sent: Wednesday, 15 January 2014 10:39 AM
To: [hidden email]
Subject: Re: talking about "super resolution"

I think that single molecule switching bas
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

An interesting exercise ...

I think that single molecule switching based super-resolution can clearly be interpreted in terms of the incorporation of additional data set / information and/or analytical continuation. To make it a bit more concrete: you know that your single molecule emission is coming from the equivalent of a delta function in real space, which means that it's a complex exponential in Fourier space. When imaging with a diffraction and photon limited system you end up getting a noisy version of a few periods (due to the band limit) of that complex exponential, and cannot accurately determine its exact frequency (ie the position). If you try and do analytical continuation, you're trying to extend this complex exponential out to infinity in the Fourier domain (which would give you a shifted delta function in space), but because of the frequency uncertainty there are a large number of possible analytical continuations with subtly different frequencies. Close to the origin, these will all line up (more or less) and the mean will still be a complex exponential. As you get further from the origin, however, they'll go out of phase and interfere destructively (analagous to the coherence phenomena in broad-band light sources), giving you a new effective band limit.

It's a little harder, however, to see how the likes of STED can be framed in terms of analytical continuation. I see this more as a case of moving to a non-linear excitation (or depletion) regime and breaking out of the band limit through non-linearity (analagous to using heterodyne techniques to move radio signals down to the audio band). Also doing it in a very clever way so as not to need any post-processing (as for localisation or SIM). It's hard to see the information input into the system.




On Tuesday, 31 December 2013 5:14 PM, Alberto Diaspro <[hidden email]> wrote:
 
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Friends,
I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?

Thank you for your kind attention.
Have a great 2014
Alby

[David Baddeley]

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

You're absolutely right that structured illumination is the easiest to interpret in terms of heterodyning. 

STED can, however, be construed as a very specialised form of structured illumination. The depletion beam (or donut) is band limited. The non-linearity of the depletion, however, causes mixing of those frequency components (as it's an exponential non-linearity the Taylor series has terms out to infinity and you'll have lots of high-order mixing terms, albeit at decreasing amplitudes). This means that there will be lots of high frequency content in the effective depletion beam, which when multiplied with the target fluoresence will alias it down into the passband. It's a bit of a contrived interpretation, but it does give a Fourier domain explanation of how it works. It's probably actually better to just talk about the heterodyning on the excitation/depletion end - you image a band limited donut through objective which gets heterodyned up by the non-linearity to create your tighter effective excitation focus.

David



On Tuesday, 14 January 2014 8:41 PM, Guy Cox <[hidden email]> wrote:
 
Surely it is structured illumination that is strictly analogous to heterodyning?

                                                           Guy

Guy Cox, Honorary Associate Professor
School of Medical Sciences

Australian Centre for Microscopy and Microanalysis,
Madsen, F09, University of Sydney, NSW 2006


-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of David Baddeley

Sent: Wednesday, 15 January 2014 10:39 AM
To: [hidden email]
Subject: Re: talking about "super resolution"

I think that single molecule switching bas
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

An interesting exercise ...

I think that single molecule switching based super-resolution can clearly be interpreted in terms of the incorporation of additional data set / information and/or analytical continuation. To make it a bit more concrete: you know that your single molecule emission is coming from the equivalent of a delta function in real space, which means that it's a complex exponential in Fourier space. When imaging with a diffraction and photon limited system you end up getting a noisy version of a few periods (due to the band limit) of that complex exponential, and cannot accurately determine its exact frequency (ie the position). If you try and do analytical continuation, you're trying to extend this complex exponential out to infinity in the Fourier domain (which would give you a shifted delta function in space), but because of the frequency uncertainty there are a large number of possible analytical continuations with subtly different frequencies. Close to the
 origin, these will all line up (more or less) and the mean will still be a complex exponential. As you get further from the origin, however, they'll go out of phase and interfere destructively (analagous to the coherence phenomena in broad-band light sources), giving you a new effective band limit.

It's a little harder, however, to see how the likes of STED can be framed in terms of analytical continuation. I see this more as a case of moving to a non-linear excitation (or depletion) regime and breaking out of the band limit through non-linearity (analagous to using heterodyne techniques to move radio signals down to the audio band). Also doing it in a very clever way so as not to need any post-processing (as for localisation or SIM). It's hard to see the information input into the system.




On Tuesday, 31 December 2013 5:14 PM, Alberto Diaspro <[hidden email]> wrote:

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Friends,
I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?

Thank you for your kind attention.
Have a great 2014
Alby

[Kevin Ryan]

[Disclaimer - I am _not_ a theoretical mathematician, and may be out of my depth here]

I'm afraid I wouldn't consider either molecule switching based or STED super-resolution an analytical continuation, , but rather specific applications of _detection_ rather than analytic _resolution_.

 In single molecule imaging (PALM, STORM, etc) you are illuminating the entire sample, but imaging only a very sparse set of well separated fluorescent particles at any time. Molecular switching is the technique used to successively fluoresce subsets, but not directly part of the single image data. By detecting diffraction-limited spots extending over multiple pixels, with the knowledge that they represent single molecules, you can use the data from those multiple pixels to estimate the center of the detected diffraction spot to a sub-pixel location. (And yes, there are various approaches to handling tuples of molecules in those methods.)

In STED things are the other way around - the diffraction limited excitation and the donut-shaped suppression illumination combine to illuminate only a sub-resolution point, only a tiny point of the sample at any one time. The detection of the fluorescence results in (again) a diffraction limited image, but given the knowledge of sub-resolution effective illumination you get super-resolution results.

These are in essence inverse techniques - in both cases the results are applying detection of samples with specific properties, not resolution - of either detection of sub-resolution samples (widely separated molecules) or sub-resolution illumination regions. I don't think that they are expressible as the complex (real and imaginary) extension of convergent power series. Although if anyone has formulated such a thing, I would be very interested to look at it.

I don't know if SIM might be formulated that way - resolution extended through phased interference and use of beat frequencies that fall under the resolution limit - but I'll leave that to the math experts :)

Kevin Ryan
Media Cybernetics, Inc.


-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of David Baddeley
Sent: Tuesday, January 14, 2014 6:39 PM
To: [hidden email]
Subject: Re: talking about "super resolution"

I think that single molecule switching bas
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

An interesting exercise ...

I think that single molecule switching based super-resolution can clearly be interpreted in terms of the incorporation of additional data set / information and/or analytical continuation. To make it a bit more concrete: you know that your single molecule emission is coming from the equivalent of a delta function in real space, which means that it's a complex exponential in Fourier space. When imaging with a diffraction and photon limited system you end up getting a noisy version of a few periods (due to the band limit) of that complex exponential, and cannot accurately determine its exact frequency (ie the position). If you try and do analytical continuation, you're trying to extend this complex exponential out to infinity in the Fourier domain (which would give you a shifted delta function in space), but because of the frequency uncertainty there are a large number of possible analytical continuations with subtly different frequencies. Close to the origin, these will all line up (more or less) and the mean will still be a complex exponential. As you get further from the origin, however, they'll go out of phase and interfere destructively (analagous to the coherence phenomena in broad-band light sources), giving you a new effective band limit.

It's a little harder, however, to see how the likes of STED can be framed in terms of analytical continuation. I see this more as a case of moving to a non-linear excitation (or depletion) regime and breaking out of the band limit through non-linearity (analagous to using heterodyne techniques to move radio signals down to the audio band). Also doing it in a very clever way so as not to need any post-processing (as for localisation or SIM). It's hard to see the information input into the system.




On Tuesday, 31 December 2013 5:14 PM, Alberto Diaspro <[hidden email]> wrote:
 
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Friends,
I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?

Thank you for your kind attention.
Have a great 2014
Alby

[Guy Cox-2]

I cannot agree with Kevin's assessment of STED.  While the geometry used in commercial systems may be confocal (without pinhole) it doesn't need to be.  It is in effect a pure scanning system, with (effectively) widefield detection.  There is no requirement to form an image of the scanned spot.  As such, resolution is determined only by the size of the (effective) scanning spot.  This is much the same as in a scanning electron microscope.  Mathematically it can be shown (not by me!) that widefield illumination and imaging is formally equivalent to scanned imaging with widefield detection.  So in other words with STED we do have an optical imaging system which is formally equivalent to widefield fluorescence imaging at a higher resolution than is actually obtainable in widefield.  This, to me, differentiates STED from other super-resolution techniques.  

                                                Guy

Guy Cox, Honorary Associate Professor
School of Medical Sciences

Australian Centre for Microscopy and Microanalysis,
Madsen, F09, University of Sydney, NSW 2006

-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Kevin Ryan
Sent: Wednesday, 15 January 2014 3:22 PM
To: [hidden email]
Subject: Re: talking about "super resolution"

[Disclaimer - I am _not_ a theoretical mathematician, and may be out of my depth here]

I'm afraid I wouldn't consider either molecule switching based or STED super-resolution an analytical continuation, , but rather specific applications of _detection_ rather than analytic _resolution_.

 In single molecule imaging (PALM, STORM, etc) you are illuminating the entire sample, but imaging only a very sparse set of well separated fluorescent particles at any time. Molecular switching is the technique used to successively fluoresce subsets, but not directly part of the single image data. By detecting diffraction-limited spots extending over multiple pixels, with the knowledge that they represent single molecules, you can use the data from those multiple pixels to estimate the center of the detected diffraction spot to a sub-pixel location. (And yes, there are various approaches to handling tuples of molecules in those methods.)

In STED things are the other way around - the diffraction limited excitation and the donut-shaped suppression illumination combine to illuminate only a sub-resolution point, only a tiny point of the sample at any one time. The detection of the fluorescence results in (again) a diffraction limited image, but given the knowledge of sub-resolution effective illumination you get super-resolution results.

These are in essence inverse techniques - in both cases the results are applying detection of samples with specific properties, not resolution - of either detection of sub-resolution samples (widely separated molecules) or sub-resolution illumination regions. I don't think that they are expressible as the complex (real and imaginary) extension of convergent power series. Although if anyone has formulated such a thing, I would be very interested to look at it.

I don't know if SIM might be formulated that way - resolution extended through phased interference and use of beat frequencies that fall under the resolution limit - but I'll leave that to the math experts :)

Kevin Ryan
Media Cybernetics, Inc.


-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of David Baddeley
Sent: Tuesday, January 14, 2014 6:39 PM
To: [hidden email]
Subject: Re: talking about "super resolution"

I think that single molecule switching bas
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

An interesting exercise ...

I think that single molecule switching based super-resolution can clearly be interpreted in terms of the incorporation of additional data set / information and/or analytical continuation. To make it a bit more concrete: you know that your single molecule emission is coming from the equivalent of a delta function in real space, which means that it's a complex exponential in Fourier space. When imaging with a diffraction and photon limited system you end up getting a noisy version of a few periods (due to the band limit) of that complex exponential, and cannot accurately determine its exact frequency (ie the position). If you try and do analytical continuation, you're trying to extend this complex exponential out to infinity in the Fourier domain (which would give you a shifted delta function in space), but because of the frequency uncertainty there are a large number of possible analytical continuations with subtly different frequencies. Close to the origin, these will all line up (more or less) and the mean will still be a complex exponential. As you get further from the origin, however, they'll go out of phase and interfere destructively (analagous to the coherence phenomena in broad-band light sources), giving you a new effective band limit.

It's a little harder, however, to see how the likes of STED can be framed in terms of analytical continuation. I see this more as a case of moving to a non-linear excitation (or depletion) regime and breaking out of the band limit through non-linearity (analagous to using heterodyne techniques to move radio signals down to the audio band). Also doing it in a very clever way so as not to need any post-processing (as for localisation or SIM). It's hard to see the information input into the system.




On Tuesday, 31 December 2013 5:14 PM, Alberto Diaspro <[hidden email]> wrote:
 
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Friends,
I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?

Thank you for your kind attention.
Have a great 2014
Alby

[Antonius M J Van Dongen]

It's a bit off-topic, but for me the most important property  that differentiates STED from other (SIM/PALM/STORM) SR methods is that it doesn’t require computations: it is a 'pure' optical method. Computations typically come with assumptions that may be valid to variable extents.

Tony  

-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Guy Cox
Sent: Thursday, January 16, 2014 9:29 AM
To: [hidden email]
Subject: Re: talking about "super resolution"

I cannot agree with Kevin's assessment of STED.  While the geometry used in commercial systems may be confocal (without pinhole) it doesn't need to be.  It is in effect a pure scanning system, with (effectively) widefield detection.  There is no requirement to form an image of the scanned spot.  As such, resolution is determined only by the size of the (effective) scanning spot.  This is much the same as in a scanning electron microscope.  Mathematically it can be shown (not by me!) that widefield illumination and imaging is formally equivalent to scanned imaging with widefield detection.  So in other words with STED we do have an optical imaging system which is formally equivalent to widefield fluorescence imaging at a higher resolution than is actually obtainable in widefield.  This, to me, differentiates STED from other super-resolution techniques.  

                                                Guy

Guy Cox, Honorary Associate Professor
School of Medical Sciences

Australian Centre for Microscopy and Microanalysis, Madsen, F09, University of Sydney, NSW 2006

-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Kevin Ryan
Sent: Wednesday, 15 January 2014 3:22 PM
To: [hidden email]
Subject: Re: talking about "super resolution"

[Disclaimer - I am _not_ a theoretical mathematician, and may be out of my depth here]

I'm afraid I wouldn't consider either molecule switching based or STED super-resolution an analytical continuation, , but rather specific applications of _detection_ rather than analytic _resolution_.

 In single molecule imaging (PALM, STORM, etc) you are illuminating the entire sample, but imaging only a very sparse set of well separated fluorescent particles at any time. Molecular switching is the technique used to successively fluoresce subsets, but not directly part of the single image data. By detecting diffraction-limited spots extending over multiple pixels, with the knowledge that they represent single molecules, you can use the data from those multiple pixels to estimate the center of the detected diffraction spot to a sub-pixel location. (And yes, there are various approaches to handling tuples of molecules in those methods.)

In STED things are the other way around - the diffraction limited excitation and the donut-shaped suppression illumination combine to illuminate only a sub-resolution point, only a tiny point of the sample at any one time. The detection of the fluorescence results in (again) a diffraction limited image, but given the knowledge of sub-resolution effective illumination you get super-resolution results.

These are in essence inverse techniques - in both cases the results are applying detection of samples with specific properties, not resolution - of either detection of sub-resolution samples (widely separated molecules) or sub-resolution illumination regions. I don't think that they are expressible as the complex (real and imaginary) extension of convergent power series. Although if anyone has formulated such a thing, I would be very interested to look at it.

I don't know if SIM might be formulated that way - resolution extended through phased interference and use of beat frequencies that fall under the resolution limit - but I'll leave that to the math experts :)

Kevin Ryan
Media Cybernetics, Inc.


-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of David Baddeley
Sent: Tuesday, January 14, 2014 6:39 PM
To: [hidden email]
Subject: Re: talking about "super resolution"

I think that single molecule switching bas
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

An interesting exercise ...

I think that single molecule switching based super-resolution can clearly be interpreted in terms of the incorporation of additional data set / information and/or analytical continuation. To make it a bit more concrete: you know that your single molecule emission is coming from the equivalent of a delta function in real space, which means that it's a complex exponential in Fourier space. When imaging with a diffraction and photon limited system you end up getting a noisy version of a few periods (due to the band limit) of that complex exponential, and cannot accurately determine its exact frequency (ie the position). If you try and do analytical continuation, you're trying to extend this complex exponential out to infinity in the Fourier domain (which would give you a shifted delta function in space), but because of the frequency uncertainty there are a large number of possible analytical continuations with subtly different frequencies. Close to the origin, these will all line up (more or less) and the mean will still be a complex exponential. As you get further from the origin, however, they'll go out of phase and interfere destructively (analagous to the coherence phenomena in broad-band light sources), giving you a new effective band limit.

It's a little harder, however, to see how the likes of STED can be framed in terms of analytical continuation. I see this more as a case of moving to a non-linear excitation (or depletion) regime and breaking out of the band limit through non-linearity (analagous to using heterodyne techniques to move radio signals down to the audio band). Also doing it in a very clever way so as not to need any post-processing (as for localisation or SIM). It's hard to see the information input into the system.




On Tuesday, 31 December 2013 5:14 PM, Alberto Diaspro <[hidden email]> wrote:
 
*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Friends,
I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?

Thank you for your kind attention.
Have a great 2014
Alby

[George McNamara]

*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Hi Tony,

I disagree: Andy York's and Hari Shroff's 2013 SIM method is 'pure'
optical, and single exposure per frame:

Instant super-resolution imaging in live cells and embryos via analog
image processing. <http://www.ncbi.nlm.nih.gov/pubmed/24097271>

York AG, Chandris P, Nogare DD, Head J, Wawrzusin P, Fischer RS, Chitnis
A, *Shroff H*.

Nat Methods. 2013 Nov;10(11):1122-6. doi: 10.1038/nmeth.2687. Epub 2013
Oct 6.

PMID:
    24097271


and doughnuts are not just for STED:

Nanoscopy with more than 100,000 'doughnuts'.
<http://www.ncbi.nlm.nih.gov/pubmed/23832150>

Chmyrov A, Keller J, Grotjohann T, Ratz M, d'Este E, Jakobs S, Eggeling
C, Hell SW.

Nat Methods. 2013 Aug;10(8):737-40. doi: 10.1038/nmeth.2556. Epub 2013
Jul 7.

PMID:
    23832150


George


On 1/15/2014 7:59 PM, Antonius M J Van Dongen wrote:

> It's a bit off-topic, but for me the most important property  that differentiates STED from other (SIM/PALM/STORM) SR methods is that it doesn’t require computations: it is a 'pure' optical method. Computations typically come with assumptions that may be valid to variable extents.
>
> Tony
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Guy Cox
> Sent: Thursday, January 16, 2014 9:29 AM
> To: [hidden email]
> Subject: Re: talking about "super resolution"
>
> I cannot agree with Kevin's assessment of STED.  While the geometry used in commercial systems may be confocal (without pinhole) it doesn't need to be.  It is in effect a pure scanning system, with (effectively) widefield detection.  There is no requirement to form an image of the scanned spot.  As such, resolution is determined only by the size of the (effective) scanning spot.  This is much the same as in a scanning electron microscope.  Mathematically it can be shown (not by me!) that widefield illumination and imaging is formally equivalent to scanned imaging with widefield detection.  So in other words with STED we do have an optical imaging system which is formally equivalent to widefield fluorescence imaging at a higher resolution than is actually obtainable in widefield.  This, to me, differentiates STED from other super-resolution techniques.
>
>                                                  Guy
>
> Guy Cox, Honorary Associate Professor
> School of Medical Sciences
>
> Australian Centre for Microscopy and Microanalysis, Madsen, F09, University of Sydney, NSW 2006
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Kevin Ryan
> Sent: Wednesday, 15 January 2014 3:22 PM
> To: [hidden email]
> Subject: Re: talking about "super resolution"
>
> [Disclaimer - I am _not_ a theoretical mathematician, and may be out of my depth here]
>
> I'm afraid I wouldn't consider either molecule switching based or STED super-resolution an analytical continuation, , but rather specific applications of _detection_ rather than analytic _resolution_.
>
>   In single molecule imaging (PALM, STORM, etc) you are illuminating the entire sample, but imaging only a very sparse set of well separated fluorescent particles at any time. Molecular switching is the technique used to successively fluoresce subsets, but not directly part of the single image data. By detecting diffraction-limited spots extending over multiple pixels, with the knowledge that they represent single molecules, you can use the data from those multiple pixels to estimate the center of the detected diffraction spot to a sub-pixel location. (And yes, there are various approaches to handling tuples of molecules in those methods.)
>
> In STED things are the other way around - the diffraction limited excitation and the donut-shaped suppression illumination combine to illuminate only a sub-resolution point, only a tiny point of the sample at any one time. The detection of the fluorescence results in (again) a diffraction limited image, but given the knowledge of sub-resolution effective illumination you get super-resolution results.
>
> These are in essence inverse techniques - in both cases the results are applying detection of samples with specific properties, not resolution - of either detection of sub-resolution samples (widely separated molecules) or sub-resolution illumination regions. I don't think that they are expressible as the complex (real and imaginary) extension of convergent power series. Although if anyone has formulated such a thing, I would be very interested to look at it.
>
> I don't know if SIM might be formulated that way - resolution extended through phased interference and use of beat frequencies that fall under the resolution limit - but I'll leave that to the math experts :)
>
> Kevin Ryan
> Media Cybernetics, Inc.
>
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of David Baddeley
> Sent: Tuesday, January 14, 2014 6:39 PM
> To: [hidden email]
> Subject: Re: talking about "super resolution"
>
> I think that single molecule switching bas
> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> An interesting exercise ...
>
> I think that single molecule switching based super-resolution can clearly be interpreted in terms of the incorporation of additional data set / information and/or analytical continuation. To make it a bit more concrete: you know that your single molecule emission is coming from the equivalent of a delta function in real space, which means that it's a complex exponential in Fourier space. When imaging with a diffraction and photon limited system you end up getting a noisy version of a few periods (due to the band limit) of that complex exponential, and cannot accurately determine its exact frequency (ie the position). If you try and do analytical continuation, you're trying to extend this complex exponential out to infinity in the Fourier domain (which would give you a shifted delta function in space), but because of the frequency uncertainty there are a large number of possible analytical continuations with subtly different frequencies. Close to the origin, these will all line up (more or less) and the mean will still be a complex exponential. As you get further from the origin, however, they'll go out of phase and interfere destructively (analagous to the coherence phenomena in broad-band light sources), giving you a new effective band limit.
>
> It's a little harder, however, to see how the likes of STED can be framed in terms of analytical continuation. I see this more as a case of moving to a non-linear excitation (or depletion) regime and breaking out of the band limit through non-linearity (analagous to using heterodyne techniques to move radio signals down to the audio band). Also doing it in a very clever way so as not to need any post-processing (as for localisation or SIM). It's hard to see the information input into the system.
>
>
>
>
> On Tuesday, 31 December 2013 5:14 PM, Alberto Diaspro<[hidden email]>  wrote:
>
> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Friends,
> I, we, use the term super resolution for a variety of (comparatively) new optical approaches, mainly based on the fluorescence mechanism of contrast.
> Thinking about early Toraldo’s papers, sometime I think that we use the term “super resolution” for a sort of sake of simplicity towards “final users”. My very simple point on this aspect it is related to the possibility of predicting an analytical continuation of the optical transfer function using acquired data and some additional information. Coming back to the spatial domain one can get an improvement of spatial resolution beyond the diffraction limit. Now, my question is: may ( may and not can…) we consider the knowledge of the photo physical properties of the fluorescent molecules as an additional data set?
>
> Thank you for your kind attention.
> Have a great 2014
> Alby
>    

--



George McNamara, Ph.D.
Single Cells Analyst
L.J.N. Cooper Lab
University of Texas M.D. Anderson Cancer Center
Houston, TX 77054
Tattletales http://works.bepress.com/gmcnamara/26/