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If resolution improvement in transmission microscopy were possible, it might be very useful to apply it to interferometry. There you have a nanometer resolution in the vertical dimension, but it all is undermined by diffraction-limited lateral resolution (the situation is the same in "transmission through dye" for cell profile measurements). And since it is not confocal or fluorescence, noise probably would not be that much of an issue. I have talked to a few companies that make interferometric microscopes, it seems that they haven't though much about it.

Mike 

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From: Confocal Microscopy List [[log in to unmask]] on behalf of Tim Holmes [[log in to unmask]]
Sent: Wednesday, October 24, 2012 7:31 AM
To: [log in to unmask]
Subject: Re: Question about deconvolution

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To be honest our group has not done any sort of scientific analysis of the
resolution improvement you can achieve.  On the other hand, we anecdotally
experienced about 1.5 (possibly 2, but that's pushing it) reduction in FWHM
along x, y.  Generally, along z, our experience has always been that you
(practically speaking, day-to-day) can't really surpass the depth-of-field.
On the other hand, with a confocal, you CAN cut that
axial resolution in about 1/2 (as I recall.  It might be a little bit better
than that actually.  Mmmmmm, possibly 3, I don't really remember.).   There
is an interesting paper by Peter Shaw where he takes axial measurements of
resolution improvement, comparing widefield to confocal, but maybe that's a
different topic.

The trade-off that comes with the resolution improvement, when you try to go
past the diffraction limit, is that it comes with ringing (oscillations at
edges of objects) that gets enhanced in the x,y dimension.  That does not
make the idea useless - you just have to be able to accept the trade-off to
get the resolving power improvement.   There are ways to reduce the ringing
that we have played with and that actually do work, but to my understanding
they have not been refined, made to work in a repeatable way and thereby
commercialized.

-----Original Message-----
From: Confocal Microscopy List [mailto:[log in to unmask]] On
Behalf Of Lutz Schaefer
Sent: Tuesday, October 23, 2012 10:16 PM
To: [log in to unmask]
Subject: Re: Question about deconvolution

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I do agree with most of the posts here and like to add a few more things.

From a theoretical point of view and preferably in noiseless continuous
space, there is a clear limitation of restoration of spatial frequencies up
to the optical resolution for an unconstrained linear regularized inverse
system. It will improve the FWHM of a point object, but not beyond the Airy
disk. Using a nonlinear, for example positivity constrained iterative
method, this limitation becomes lifted as frequencies beyond that limit are
allowed to enter (to understand how, there is a paper from Merserau et al.).

Especially in the widefield case, the gain in axial resolution becomes
easily apparent but only with this class of methods and with proper
background correction. From the theory, I would see no limitation in
regaining spatial frequencies beyond optical resolution. Awakening usually
strikes in the real world, where we deal with photon limited discrete
measurements as George points out. In the end it is a battle with the signal
to noise and the ill-posed-ness of the underlying problem to be solved. This
battle is lost to these factors and regularization has to be chosen to mend
noise amplification which diminishes the goal as it suppresses high
frequencies. There are older papers from Jose Conchello and Rainer Heitzmann
(sorry I don't have the references handy) who try to achieve the utmost
improvement, but with only mild success. Also Walter Carrington's paper,
mentioned from Guy lies in this category, but he was rather focusing on a
very solid rigorous mathematical concept, that would achieve this goal.

To make a long story short. Deconvolution can greatly improve the contrast
of fine structures. Some methods can in theory break the diffraction limit,
but with real data this can only be achieved at best in axial dimension of a
widefield modality.

Regards
Lutz

__________________________________
L u t z   S c h a e f e r
Sen. Scientist
Mathematical modeling / Image processing Advanced Imaging Methodology
Consultation
16-715 Doon Village Rd.
Kitchener, ON, N2P 2A2, Canada
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Email:     [log in to unmask]
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--------------------------------------------------
From: "George McNamara" <[log in to unmask]>
Sent: Tuesday, October 23, 2012 21:48
To: <[log in to unmask]>
Subject: Re: Question about deconvolution

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Confocal and multiphoton excitation fluorescence deconvolution will
> greatly benefit from customers requiring vendors to include fast,
> quantitative (precise, accurate) deconvolution on all confocal/MPEF
> systems bought/sold. GPU enabled deconvolution. If three academics can
> make GPU SIM (pretty much) realtime (and a heck of a lot faster
> processing than OMX), the hardware vendors ought to be able to do it (or
license it):
>
>    Lefman J, Scott K, Stranick S. Live, video-rate super-resolution
>    microscopy using structured illumination and rapid GPU-based
>    parallel processing. Microsc Microanal. 2011 Apr;17(2):191-6. Epub
>    2011 Mar 9. PMID: 21385522
>
> If the vendors don't get it done, I hope everyone goes for do it
> yourself nanoscopes, such as:
>
>    *York* AG, Parekh SH, Dalle Nogare D, Fischer RS, Temprine K, Mione
>    M, Chitnis AB, Combs CA, *Shroff* H. Resolution doubling in live,
>    multicellular organisms via multifocal structured illumination
>    microscopy. Nat Methods. 2012 May 13;9(7):749-54. doi:
>    10.1038/nmeth.2025. PMID: 22581372
>    http://code.google.com/p/msim/
>
> Good luck with the vendors.
>
> ***
>
> As for deconvolution "breaking" the optical limit: of course not. The
> deconvolution is done on your computer, the optical part ended when
> the photons slammed into the detector(s). I go with Paul Goodwin's
> (Applied
> Precision) rule of thumb (or maybe pinky finger?): deconvolution can
> improve the IMAGE resolution by ~20%.
>
> There are other ways to get improvement in resolution - I am very
> pleased with the increase in IMAGE resolution of PiMP:*
>
> *
>
>    *Munck S*, Miskiewicz K, Sannerud R, Menchon SA, Jose L, Heintzmann
>    R, Verstreken P, Annaert W. Sub-diffraction imaging on standard
>    microscopes through photobleaching microscopy with non-linear
>    processing J Cell Sci. 2012 May 1;125(Pt 9):2257-66. PMID: 22357945.
>
> On the Leica SP5 inverted and Zeiss LSM710 confocal microscopes i
> manage here at the U, I use 30 nm pixel size (vs 60 nm for "standard"
> high resolution confocal images), 25 to 50 images (when I'm acquiring
> for a user, my core makes more money if image acquisition time takes
> longer, single channel (makes dealing with Fiji ImageJ easier - would
> be nice if someone took the time to develop ImageJ into a real program
> with user, not anti-user, interface), no averaging, unidirectional
> scanning. My SP5 has both standard and resonant scanners - both work
> (resonant is faster). Goal is modest photobleaching (ideally ~5%
> according to the paper). Since 30 nm pixel size is smaller than the
> PiMP plugin default, I use filter size = 1.65. My thanks to Sebastian
> Munck and Glen Macdonald for the recommendation and for putting in
> 16-bit output mode, which I routinely use. Does PiMP work? Yes. Don't
> take my word for it: go look at Figure 2 of the paper and/or get the
plugin from the corresponding author.
>
> George
>
>
> On 10/23/2012 9:23 PM, Guy Cox wrote:
>> *****
>> To join, leave or search the confocal microscopy listserv, go to:
>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>> *****
>>
>> There's no simple answer.  Some people have aimed to use
>> deconvolution to go beyond the optical resolution limit.  The best
example I know is:
>> Carrington, W.A., Lynch, R.M., Moore, E.D.W., Isenberg, G., Fogarty, K.E.

>> and Fay, F.S., 1995.  Superresolution Three-Dimensional Images of
>> Fluorescence in Cells with Minimal Light Exposure. Science 268,
>> 1483-1487
>>
>> Commercial deconvolution systems are not usually aiming at that.  The
>> aim is to separate in focus and out of focus light and thereby
>> achieve optical sectioning in wide field.  Since the light budget is
>> always better in wide field than in confocal this has certain
>> advantages, but it has the disadvantage that the wide field OTF has a
>> 'missing cone' of directions in which no information is present.
>> This limits what can be achieved.
>>
>> The confocal OTF has no missing cone which makes it quite a good
>> target for deconvolution.  The confocal PSF Is far from optimal,
>> being very streaked out in the Z direction, and deconvolution can do
>> a lot to improve it.  Several people (including me) have advocated 1D
>> deconvolution in just the Z direction, which can greatly improve
>> image quality.  My papers on this are a bit hard to find but there is
>> an example in my chapter in Jim Pawley's book.  However deconvolution
>> of confocal images hasn't really caught on as much as it should have.
>>
>>
>> Guy
>>
>>
>>
>> -----Original Message-----
>> From: Confocal Microscopy List
>> [mailto:[log in to unmask]]
>> On Behalf Of Christophe Leterrier
>> Sent: Wednesday, 24 October 2012 3:28 AM
>> To: [log in to unmask]
>> Subject: Question about deconvolution
>>
>> *****
>> To join, leave or search the confocal microscopy listserv, go to:
>> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
>> *****
>>
>> Hi folks,
>>
>> I have a long-standing question regarding deconvolution (as
>> processing widefield or confocal images to reassign light from where
>> it originated using a PSF).
>>
>> Is there a theoretical limit to the resolution one could obtain using
>> deconvolution? Is is theoretically possible to "break" the
>> diffraction limit with deconvolution? That is, to get under the
>> classical 200x200x600nm spot? I think it is not the case, but then
>> why would you deconvolve widefield or confocal images? What do you
>> gain by doing so on a system that is reasonably close to its
>> theoretical capabilities in terms of optical performances?
>>
>> Thanks for your help,
>>
>> Christophe
>>
>> --
>> Christophe Leterrier
>> Researcher
>> Axonal Domains Architecture Team
>> CRN2M CNRS UMR 7286
>> Aix Marseille University, France
>>
>>