AQLM 2013-- Last chance!!!

[Jason Swedlow-2]

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Dear Listers:

Just a reminder about this year's run of Analytical and Quantitative Light
Microscopy, held at the Marine Biological Laboratory, Woods Hole, MA, USA.
The course will run May 1-10, 2013.

*Applications are due on Monday!!!!*

AQLM is a comprehensive and intensive course in light microscopy for
researchers in biology, medicine, and material sciences. This course
provides a systematic and in-depth examination of the theory of image
formation and application of video and digital methods for exploring subtle
interactions between light and the specimen. This course emphasizes the
quantitative issues that are critical to the proper interpretation of
images obtained with modern wide-field and confocal microscopes.

Laboratory exercises, demonstrations, and discussions include: (1)
geometrical and physical optics of microscope image formation including
Abbe's theory of the microscope and Fourier optics; (2) interaction of
light and matter; (3) phase contrast polarization and interference
microscopy for the nondestructive analysis of molecular and fine-structural
organization in living cells; (4) fluorescence microscopy, quantification
of fluorescence, and GFP; (5) principles and application of digital video
imaging, recording, analysis, and display; (6) digital image processing and
quantitative digital image deconvolution; (7) ratiometric measurement of
intracellular ion concentrations; (8) confocal microscopy; and (9) new
advances in light microscopy such as FRET, FLIM, TIRF, FCS, PALM, STORM and
SIM.

The course web site is at
http://hermes.mbl.edu/education/courses/special_topics/aqlm.html

Within the course, we often refer to AQLM as "Microscopy Boot Camp".  It's
intense, it's hardcore, but it's really fun.

Why not join us for AQLM?  You'll never forget it.

Applications due January 21, 2013.

Directors: Greenfield Sluder, University of Massachusetts Medical Center,
Worcester
Jason Swedlow, University of Dundee
Jagesh Shah, Harvard Medical School
Justin Taraska, National Institutes of Health

Cheers,

Jason

--
**************************
Wellcome Trust Centre for Gene Regulation & Expression
College of Life Sciences
MSI/WTB/JBC Complex
University of Dundee
Dow Street
Dundee  DD1 5EH
United Kingdom

phone [phone]
Intl phone:  [phone]
FAX   [phone]
email: [hidden email]

Lab Page: http://www.lifesci.dundee.ac.uk/gre/staff/jason-swedlow
Open Microscopy Environment: http://openmicroscopy.org
**************************

[Steffen Dietzel]

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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

[Zdenek Svindrych]

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To join, leave or search the confocal microscopy listserv, go to:
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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

"*****
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"

[Arne Seitz]

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Dear Steffen,

I found (and use) the following definition for z-resolution (Jerome Mertz, Optical Microscopy, Roberts and Company Publishers, p. 297)

delta z (WF)=n*lambda)/NA^2
 
delta z(conf)=n*lambda/2*NA^2

Both formulas are derived from the frequency support of the different microscopes. Thus theoretically the frequency of a confocal microscope is twice as good as that of a wide-field microscope. This is (and the author is explicitly stating it) overly optimistic and only true in the case of an infinitesimal small pinhole. Thus is will be hardly reached in practice. Nevertheless I like these definitions as the can be obtained from "pure" theory.

The formula I presented here is identical with your second one. To my understanding his is often named "depth of field" due to the missing cone problem.

Just my 2 c.

Regards
Arne

   

> -----Original Message-----
> From: Confocal Microscopy List
> [mailto:[hidden email]] On Behalf Of Steffen
> Dietzel
> Sent: lundi 21 janvier 2013 09:01
> To: [hidden email]
> Subject: 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

[Chen, Jianbo (NIH/NCI) [E]]

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http://www.microscopyu.com/articles/formulas/formulasfielddepth.html

________________________________________
From: Steffen Dietzel [[hidden email]]
Sent: Monday, January 21, 2013 3:00 AM
To: [hidden email]
Subject: 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

[Shalin Mehta]

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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 <[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
>
>
>
> ---------- Původní zpráva ----------
> Od: Steffen Dietzel <[hidden email]>
> 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"
>

[Shalin Mehta]

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

Hi Steffen,

I should correct a mix-up:
axial profile of PSF integrated in XY plane = Fourier transform of (axial
profile of the OTF).

For example, the axial profile of widefield OTF is peak only at origin
(delta function) and the axial profile of integrated PSF is constant.


Best
Shalin
On Mon, Jan 21, 2013 at 8:36 PM, Shalin Mehta <[hidden email]>wrote:

> 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.
>



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

[James Pawley]

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

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) 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"
>>

--
James and Christine Pawley, PO Box 2348, 5446
Burley Place (PO Box 2348), Sechelt, BC, Canada,
V0N3A0, 604-885-0840 NEW! Cell (when I remember
to turn it on!) 1-765-637-1917,
<[hidden email]>

[Shalin Mehta]

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

Hello Jim,
Thanks for pointing out this excellent (and often overlooked as far as I
know) reference.

Pardon the digression  from Steffen's question:  Hiraoka et al. paper adds
to the remarkable thought that any structured illumination leads to some
form of depth sectioning by virtue of having nonzero lateral frequency and
hence avoiding missing cone. As I have heard often from structured
illumination microscopists, confocal is a structured illumination method
too - the illumination structure being the point spread function.

Couple of interesting papers based on this idea:
M. Neil, R. Juskaitis, and T. Wilson, "Method of obtaining optical
sectioning by using structured light in a conventional microscope," Opt.
Lett.  22, 1905-1907 (1997).
Santos S, Chu KK, Lim D, et al; Optically sectioned fluorescence
endomicroscopy with hybrid-illumination imaging through a flexible fiber
bundle. J. Biomed. Opt. 0001;14(3):030502-030502-3.

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 Tue, Jan 22, 2013 at 2:10 AM, James Pawley <[hidden email]> wrote:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/**wa?A0=confocalmicroscopy<http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy>
> *****
>
> 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:
>>
>>   *****
>>>  To join, leave or search the confocal microscopy listserv, go to:
>>>  http://lists.umn.edu/cgi-bin/**wa?A0=confocalmicroscopy<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<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"
>>>
>>>
>
> --
> James and Christine Pawley, PO Box 2348, 5446 Burley Place (PO Box 2348),
> Sechelt, BC, Canada, V0N3A0, 604-885-0840 NEW! Cell (when I remember to
> turn it on!) 1-765-637-1917, <[hidden email]>