*****
To join, leave or search the confocal microscopy listserv, go to:
http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
*****

Hi Steffen,

I also find it useful to think about spatial frequencies when thinking of
resolution. I find it instructive to consider two extreme cases (in terms
of spatial frequencies they contain) to think about depth resolution in
fluorescence microscope.

case-1: point specimen (a point contains all lateral spatial frequencies).
- at what axial distance are two points resolved?

The first zero along axis  of the 3D PSF occurs at 2n*lambda/NA^2. If we
employ the Rayleigh criterion used to define lateral two point resolution
(the zero of one PSF overlaps with the maximum of the other), this is the
distance by which two points need to be separated to 'be resolved'. The
exact % drop in intensity from peak differs because the lateral PSF has a
functional form of jinc^2 whereas the axial PSF has a functional form of
sinc^2.

The axial cutoff of the OTF depends on the lateral spatial frequency and
the maximal axial cutoff occurs at lateral frequency=1/2*lateral cutoff. A
paper by Rainer Heintzmann and Colin Sheppard (
http://dx.doi.org/10.1016/j.micron.2006.07.017) has useful derivations of
equations for cutoffs of OTF in widefield and confocal.

case-2:  uniform plane of fluorescence (a plane contains only the zero
lateral spatial frequency).
- at what axial distance are two uniform planes of fluorescence resolved?
This is typically what we mean by 'depth sectioning' ability
of wide-filed vs confocal.

In this case, the widefield microscope does not offer any resolution
(because of missing cone problem). Even at axial distance of 2n*lambda/NA^2
(theoretically at any axial distance), image of the uniform plane will be
the same as in focus. But image of uniform plane does change in confocal.
The intensity drop in image of uniform plane along axis is equal to
integrated intensity of the PSF in XY plane. Axial profile obtained by
integrating PSF in XY plane (which is the same as axial profile of the OTF)
is widely used definition of depth sectioning.

Cheers,
Shalin

website: http://mshalin.com
(office) Lillie 110, (ph) 508-289-7374.

HFSP Postdoctoral Fellow,
Marine Biological Laboratory,
7 MBL Street, Woods Hole MA 02543, USA


On Mon, Jan 21, 2013 at 5:41 AM, Zdenek Svindrych <[log in to unmask]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> 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 <[log in to unmask]>
> Datum: 21. 1. 2013
> Předmět: formula for z-resolution
>
> "*****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> *****
>
> 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
> --
> ------------------------------------------------------------
> Steffen Dietzel, PD Dr. rer. nat
> Ludwig-Maximilians-Universität München
> Walter-Brendel-Zentrum für experimentelle Medizin (WBex)
> Head of light microscopy
>
> Mail room:
> Marchioninistr. 15, D-81377 München
>
> Building location:
> Marchioninistr. 27, München-Großhadern"
>