Posted by
Zdenek Svindrych on
URL: http://confocal-microscopy-list.275.s1.nabble.com/AQLM-2013-Last-chance-tp7579522p7579525.html
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Hi Steffen,
nice question!
The resolution can be nicely defined for confocal, where the PSF is
approximately an ellipsoid, but the widefield case is more complicated.
In WF case the results depends strongly on how you define 'z-resolution' and
what PSF model you use.
For example, from the point of view of the 'missing cone' problem of the
widefield OTF, there is no z-resolution, really.
Also practical test will give you different results whether you're looking
at fluorescent beads or some structure that is dense in 3D.
So, according to my feelings the highest value from your list is the most
appropriate... :-).
Regards,
zdenek svindrych
---------- Původní zpráva ----------
Od: Steffen Dietzel <
[hidden email]>
Datum: 21. 1. 2013
Předmět: formula for z-resolution
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Dear confocalists,
I am confused about the correct formula for diffraction limmited
resolution along the z-axis. Starting with conventional fluoresence
microscopy:
I used to use the following formula given by Inoue in the first chapter
of the Handbook
(1) z-min = 2*lambda*n /NA^2
where lambda is the wavelength in air, n the refraction index of the
immersion medium, NA the numerical aperture of the objective and ^2
means to the power of 2.
The text says that this is the distance from the center of the peak to
the first minimum of the diffraction pattern.
The same is said by F Quercioli in Diaspro's "Optical Fluorescence
microscopy".
In the new Murphy and Davidson (Fundamentals of Light Microscopy and
Electronic Imaging, 2nd edition, page 109) I find the following formula:
(2) z = lambda*n /NA^2
Note that the "2" is missing, suggesting a resolution twice as good.
However, this is not explained as Rayleigh criterion but as "depth of field"
Formula (2) is also given as "resolution in a conventional microscope"
defined as "distance between points where the intensity is 80% of the
peak intensity" by Amos, McConnell and Wilson (Confocal Microscop,
Chapter in Handbook of Comprehensive Biophysics), but only for cases
with an NA <0.5. (Note that the clasical Rayleigh criterion in the focal
plane leads to 73,5 % intensity at the minimum between peaks)
For high NA objectives Amos et al give the following Depth of field =
80% limit:
(3) 0.51*lambda/(n-sqrt(n^2-NA^2))
This paper also gives a formula for theoretical confocal/two photon,
although not for resolution but for FWHM, so that is a little different.
Example: 500 nm, NA=1.4, n =1.515, resolution according to the various
formulas:
(1) 773 nm
(2) 386 nm
(3) 272 nm
This sounds very wrong and my gut feeling is I missed something. I'd be
happy if you could clarify this for me.
Steffen
--
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Steffen Dietzel, PD Dr. rer. nat
Ludwig-Maximilians-Universität München
Walter-Brendel-Zentrum für experimentelle Medizin (WBex)
Head of light microscopy
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