http://confocal-microscopy-list.275.s1.nabble.com/AQLM-2013-Last-chance-tp7579522p7579543.html
diaphragm. Indeed, some of the best work on
performance. The Agard and Sedat group wrote a
Hiraoka, Y., Sedat, J.W., and Agard, D.A. (1990).
microscopy. Biophys. J., 57: 325-333.
>
>
>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 <
[hidden email]> 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
>>
>>
>>
>> ---------- PÛvodní zpráva ----------
>> Od: Steffen Dietzel <
[hidden email]>
>> Datum: 21. 1. 2013
>> PÞedmût: 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"
>>