http://confocal-microscopy-list.275.s1.nabble.com/AQLM-2013-Last-chance-tp7579522p7579546.html
Pardon the digression from Steffen's question: Hiraoka et al. paper adds
hence avoiding missing cone. As I have heard often from structured
M. Neil, R. Juskaitis, and T. Wilson, "Method of obtaining optical
Lett. 22, 1905-1907 (1997).
bundle. J. Biomed. Opt. 0001;14(3):030502-030502-3.
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>
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>
> Hello all,
>
> I can only add to the many excellent contributions that the widefield case
> only has NO z-resolution when the field diaphragm is infinitely large
> (i.e., when the illumination power density at the plane of fluorescent
> material) does not change as the objective focuses up and down).
>
> As this is never the case, there is in fact always some z-resolution, and
> it can be quite pronounced if the excitation really does fill the objective
> aperture and one uses a small field diaphragm. Indeed, some of the best
> work on nuclei was done with the field diaphram set to about 5-10µm in the
> focus plane and under these conditions the system shows partial-confocal
> performance. The Agard and Sedat group wrote a paper detailing this effect
>
> Hiraoka, Y., Sedat, J.W., and Agard, D.A. (1990). Determination of the
> three-dimensional imaging properties of an optical microscope system:
> partial confocal behavior in epi-fluorescence microscopy. Biophys. J., 57:
> 325-333.
>
> A careful reading of this paper makes clear why one must control the field
> diaphragm diameter (as well as NA, lambda, specimen RI, and other
> variables) when determining the widefield PSF.
>
> Regards,
>
> Jim Pawley
>
>
>
>
>>
>> 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<
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:
>>
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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
>>>
>>>
>>>
>>> ---------- PÛvodní zpráva ----------
>>>
>>> Od: Steffen Dietzel <
[hidden email]>
>>> Datum: 21. 1. 2013
>>> PÞedmût: 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
>>> --
>>> ------------------------------**------------------------------
>>> 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"
>>>
>>>
>
> --
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> Sechelt, BC, Canada, V0N3A0, 604-885-0840 NEW! Cell (when I remember to
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