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Dear All,

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> 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.
>

In addition to Lutz' remarks, one could say that the widefield missing 
cone represents a severe limit on certain frequencies of the object, and 
the limit is imposed by diffraction. Depending on the sparseness of the 
object, and exploiting extra a priori knowledge besides knowledge of the 
PSF like non-negativity, noise characteristics (Poisson noise), possibly 
properties of the object itself, it is possible te reconstruct the 
missing frequencies -- but not always. Reconstruction of frequencies 
outside the bounding box of the widefield OTF is also possible, but 
requires good optical conditions and low noise to start with.

To give an extreme example: one can consider localization estimation in 
STORM as a special deconvolution case, one where a very powerful bit of 
a-priori knowledge is used: there is just one emitter present. The 
attainable accuracy then remains controlled by noise and the width of 
the PSF, but is much better than the width of the PSF. Deconvolution 
with standard methods of widefield images of point objects is also 
usually easy.


> 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.

In the confocal case the theoretical bandwidth is a good deal beyond the 
effective, noise determined limit. So there it is very hard to go beyond 
the theoretical limit, but improving on the effective bandlimit is 
nearly always possible, especially in Z. In my experience, it is often 
possible to gain 2x in Z, somewhat less, say 50%, in XY. This means that 
you go into the direction of isotropic resolution, but will not reach 
it. In good optical condition the measurement volume may go down by a 
factor 8.

Lastly, systems like STED which are based on a strong non-linear effect 
do not have a hard diffraction imposed bandlimit anymore. They still 
have an effective bandlimit, which we find deconvolution can improve 
much on.

-- Hans

SVI-Huygens


> -----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
>
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> To join, leave or search the confocal microscopy listserv, go to:
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>
> 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
>
>


-- 
-------------------------------------------------------------------
dr. Hans T.M. van der Voort                           ([log in to unmask])
Scientific Volume Imaging b.v.,             URL: http://www.svi.nl/