Mario and group:

I would like to answer some of these questions.  I am burried today
so I will have to give a thorough answer later.  For now, the short answers
are:

1. The reason why deconvolution can surpass the diffraction limit along z is
that
it extrapolates the bandlimit of the optics.  It does not do so perfectly,
but,
well enough that features which are otherwise difficult to see become clear
after
deconvolution.  It effectively decreases the spot size by at least a factor
of 2.

2. For showing specific data sets, I don't have something readily accessible
at our
website.  I will see about putting something together which shows the
principle and
make it available to people who would like to see it.

Best wishes
Tim Holmes

-----Original Message-----
From: Confocal Microscopy List
[mailto:[log in to unmask]]On Behalf Of Mario Moronne
Sent: Thursday, December 13, 2001 3:21 PM
To: [log in to unmask]
Subject: Re: deconvolution


Hi All,

Forgive me if this question demonstrates laziness on my part (just
had shoulder surgery and don't feel like flipping journal pages: poor
me). Answers can be sent to me directly, or not.

I am stuck with the notion that the resolution in any direction will
be limited by the diffraction properties of the objective (and
specimen-e.g., RI mismatch). For the ubiquitous 1.4 NA oil that I
think goes unspoken as the point of reference, the FWHM distance in z
with no spherical aberration using 488 nm light is something like
0.45 um. In practice, even staying near to the coverslip (~10 um) it
is more like 0.8 um. However, let's forget the latter and stick with
0.45 um. Nonetheless, if we use the idea of overlapping
distinguishable objects in z how can one achieve 0.2 um resolution
through deconvolution?

I have no doubt that deconvolution can help confocal z-resolution,
but how does it get below the nominal diffraction limit? Is this
meant to refer to visibility or formulaic calculation. I don't mean
to dredge up arguments about what one can see as opposed to
mathematical conventions such as the Rayleigh limit, but perhaps this
is unavoidable. Okay, so in a simplistic fashion one must consider at
minimum two things: the z-resolution stated in terms that are
reasonably approximated by a SINC function which gives us the FWHM
0.45 um and the Rose Criterion which pertains to human recognition of
differing contrast, telling us that for those not especially gifted,
contrast difference must be 3 to 5 times larger than the noise of the
objects being visualized. The 3-5 range depends on the geometry of
the object and for overlapping objects in z, I am not clear what is
the better number. Nonetheless, the issue of noise seems to me to be
very important when contemplating the ability of a deconvolved
confocal stack to obtain 0.2 um resolution or distinguishability. For
one thing it implies that the noise level is reduced to very low
levels. Even in conventional W.F. deconvolution, noise which is often
many many time lower than in confocal, is an important factor in
deriving good reconstructions; hence all the smoothing operations in
most methods. Confocal is aided by the fact that deconvolution is
already partly or nearly entirely completed. Still, how many people
are using photon counting, which actually is representative of the
statistical noise in the sample? How much averaging is required to
get good enough contrast to give 0.2 um?

As a practical matter, the ability of a program to provide 0.2 um z
resolution of confocal stacks along with its application in typical
W.F. decon. for me would definitely tilt me in the direction of a
package like AutoQuant's. So, can it really do it and under what
circumstances?

Tim, if you have some example images on your website etc., I would
really like to see them. Can you point me the way to profile plots or
send me some jpegs demonstrating such z resolution? Overlapping
microtubules, maybe? Thanks and hope that I am sounding merely
ignorant rather than Grinchy.

Happy Holidays,
Mario

>AutoQuant sells a deconvolution package for the confocal microscope and for
>widefield optics.  www.aqi.com
>
>There are some papers on the topic you brought up about which modality
gives
>sharper
>images.
>
>See the paper by Peter Shaw,   Prog. Biophys. molec. Biol., Vol. 56, pp.
>187- 213, 1991.
>and the chapter by me in The Handbook of Biological Confocal Microscopy, by
>J. Pawley.
>
>Generally, our experience and as pointed out by Peter Shaw is that:
>
>Widefield deconvolution and confocal microscopy without deconvolution
>provide
>    comparable resolution in all 3 directions (x, y and z).  The widefield
>case provides a little resoution improvement, but it is subtle. If you are
>making it
>    choice between these 2 modalities, lower noise (better signal to
noise),
>lower
>         photobleaching, faster acquisition and some other advantages speak
in
>         favor of widefield.  The fact that no time is needed for
deconvolution
>         and that there are no deconvolution-induced artifacts speaks
>in favor of
>         confocal.
>
>Confocal with deconvolution provides far superior resolution, especially
>along z,
>compared to widefield with deconvolution.  Depending upon the settup, you
>can expect on the order of 0.2 micrometers resolution along z, compared to
>about 0.5 to 0.8 with widefield.
--
_____________________________________________________________________
Mario M. Moronne, Ph.D.
NanoMed Technologies
FAX (510) 528-8076
Berkeley, CA
94706

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