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Hi Christophe,
the strange 'd' and 'l' parameters are the same as in the holtzer et al.
paper mentioned earlier in this thread.
In the 'bi-plane" method the 'l' parameter is the axial distance of the two
planes of focus in the sample space. In the astigmatic method it is the
amount of astigmatism, again referred to the sample space. That is the axial
distance between the best focus in x direction and best focus in the y
direction.
The 'd' parameter is (most likely) a measure of the depth of field and it
depends on the numerical aperture. But I haven't found any analytic
approximation. They simply got these parameters by fitting experimental
PSFs.
Regards,
zdenek svindrych
---------- Původní zpráva ----------
Od: Christophe Leterrier <[log in to unmask]>
Komu: [log in to unmask]
Datum: 5. 3. 2014 10:55:10
Předmět: Re: discussion is open...continues ... ab out localization and
super resolution
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Thank you for all these informative answers!
The Holtzer et al. article is providing a formula for Z-loclaization
precision in the astigmatism case (although they have a x2 factor between
theory and simulation because they don't explicitely take pixelation into
account).
I also found this recent article:
Rieger B, Stallinga S. The Lateral and Axial Localization Uncertainty in
Super-Resolution Light Microscopy. Chemphyschem. 2013 Dec 2. doi:
10.1002/cphc.201300711. [Epub ahead of print] PubMed PMID: 24302478.
http://onlinelibrary.wiley.com/doi/10.1002/cphc.201300711/abstract
Here they explicitly approximate the Z-localization precision of biplane,
astigmatism and double-helix modalities, taking into account pixelation and
background with a claimed <1% error. Although I don't really understand the
formulas yet, because they depend on the "the distance between focal lines"
and "a measure of the focal depth" that are "obtained by a calibration
measurement" but not explicited further it seems.
Thanks again,
Christophe
2014-03-04 23:33 GMT+01:00 Zdenek Svindrych <[log in to unmask]>:
> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Hi,
>
> also a brute force simulation of many images of many molecules and
> subsequent localisation with your preferred method is a straightforward
> (albeit a bit time consuming) way to get the localisation accuracy (and
> precision...) at nearly real-life conditions. You can simulate any photon
> counts, background, detector pixelation, effect of molecule density,
biases
> of the localisation algos and so on.
>
> Hopefully our group (Guy Hagen et al) will soon publish a software tool to
> greatly simplify this. But I still didn't find a satisfactory astigmatic
> PSF
> model to include into the simulation. The cylindrical gaussian is really
> not
> close approximation of our experimental results...
>
> Best,
>
> zdenek svindrych
> lf1.cuni.cz
>
>
>
> ---------- Původní zpráva ----------
> Od: Sripad Ram <[log in to unmask]>
> Komu: [log in to unmask]
> Datum: 4. 3. 2014 23:17:16
> Předmět: Re: discussion is open...continues ... about localization and
> super
> resolution
>
> "*****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> Hi Chris,
> The z-localization precision for astigmatism based 3D localization was
> worked out by holtzer et al., applied physics letters, 2007, 90, 053902.
>
> On a related note, the precise calculations for the X/Y localization
> precision that includes background and pixilation was published in 2004 by
> Raimund Ober group (Ober et al; Biophysical Journal, 2004, 86:1185-1200).
> You can download the software to calculate the localization precision from
> here (http://www.wardoberlab.com/software/fandplimittool/).
>
> Hope this helps.
>
> Regards,
> Sripad
>
>
> -----Original Message-----
> From: Confocal Microscopy List [mailto:[log in to unmask]]
> On
> Behalf Of Christophe Leterrier
> Sent: Tuesday, March 04, 2014 3:16 PM
> To: [log in to unmask]
> Subject: Re: discussion is open...continues ... about localization and
> super
> resolution
>
> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> This is a great introduction to a question a wanted to ask to the SMLM
> specialists (I did not find the answer in the above reference). I also
> posted it on the Nanoscopy LinkedIn group, so I'm sorry for people that
> will
> get it two times!
>
> There are several formulas to estimate the lateral (XY) precision of
> individual localization events in PALM/STORM microscopy. This goes from
the
> crude sigma(PSF)/√Nphotons to more elaborate formulas that includes
> pixelation and background (such as Thomson & Webb Biophys J 2002,
corrected
> in Mortensen Nat Methods 2010). What I'm looking for is an equation that
> allows to estimate the precision for the Z localization when using
> astigmatism-based 3D PALM/STORM. The reference I have found where this
> precision is studied theoretically (such as Badierostami Applied Phys Lett
> 2010, Shaevitz Int J Optics 2009) do not use a directly calculable
formula.
>
> I assume the precision depends on the photon number and the point on the Z
> calibration curve with the respective X and Y PSF width. Is anyone aware
of
> such a formula?
>
> Best Regards,
>
> Christophe
>
>
>
>
> 2014-03-04 21:52 GMT+01:00 Alberto Diaspro <[log in to unmask]>:
>
> > *****
> > To join, leave or search the confocal microscopy listserv, go to:
> > http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> > *****
> >
> > http://www.nature.com/nmeth/journal/v11/n3/full/nmeth.2843.html
> >"
>"
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