The image formation for an optical system can be usually described by the convolution of the object intensity and the point-spread function (PSF) of the system. Localization microscopy (e.g. STORM or PALM) fits a PSF to each (sparse) emitter and collects many frames. Its localization precision is therefore not diffraction restricted. However, apparently there is no single PSF that describes the imaging. Do I see this correctly?
p.s.
the background for this question is certainly the following: In the absence of a convolution representation of the image formation I can not see how to define the image resolution properly. Classically the resolution is given by the cut-off of the optical transfer function (i.e. the Fourier transform of the PSF).
The usual way how to get around this problem is to define the resolution of localization microscopy in terms of localization precision. That is the precision of fitting the diffraction limited image of an emitter with a model of the PSF. It is determined by the signal-to-noise ratio; the noisier the diffraction limited image, the higher the uncertainty in the fit parameters and, therefore, the lower the confidence that the obtained point is the true position of the emitter.
Dear Radek,
Thanks for your remark and right, this is what the people do (in addition with applying the Nyquist criteria for the sampling density). However: Is the image formation given by a convolution or not...?
best regadrs,
Oliver
Dear Oliver,
yes, I see your point. The problem with localization microscopy is that the outcome is an image in the true sense, but rather a list of coordinates of emitters point. Therefore, the usual description of image formation may not be fully applicable here. Some authors regard it as an image formed with a PSF of the width given by the localization precision; however, this seems to me rather a formal workaround than a true description of the actual image formation process.
Best regards,
Radek
Dear Oliver,
in experimental approaches like dSTORM where every single fluorophore will be detected several times during one experiment, the image is intrinsically ‘convoluted’ with the localization precision, as every fluorophore generates a cloud of localizations. Therefore we often analyze these localization clouds of separated fluorophores in the sample to measure the experimental precision. But of course resolution is also affected by label density.
In PALM-like approaches where most fluorescent proteins will be detected once and bleached after detection in many approaches the localizations are rendered with the localization precision estimated from the SNR to generate a nice looking image.
Best
Thorge
Dear Thorge,
thanks for your answer! But would you agree that the image formation in, say, STED or confocal laser scanning or conventional widefield microscopy involves the convolution with a single (effective) PSF while STORM or PALM do not have a single PSF? Only if you take the PSF approximately invariant in the whole image plane does a convolution representation exist. Or to put it differently: the dSTORM "clouds of localization" you mention should in general yield a precision which is different for different positions in the fiel-of -view, or?
best,
Oliver
Dear Oliver,
even in CLSM you will observe slightly different PSF's especially if you think of aberration effects with increasing imaging depth in a thik sample. STED also shows blinking or bleaching artifacts disturbing the effective PSF of the sample. I would agree that dSTORM, STORM or PALM are further away from having a single PSF as every localization event has a another SNR an therefore precision. But in a well performed experiment the precision extracted from the localization clouds do not differ to much over the sample space.
In this article we showed a localization cloud in Fig1. .. http://www.nature.com/ncomms/2014/140818/ncomms5650/abs/ncomms5650.html
best,
Thorge
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