Leica TCS SP2, LCS and Win7

[Peng Xi-2]

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Dear Steffen,
     If all you need is a PSF and you use Matlab, then you may find the
following code helpful. It is mentioned in my new book "Optical Nanoscopy
and Novel Microscopy Techniques" published by CRC.
http://www.crcpress.com/product/isbn/9781466586291
%--------------------------------------
%% One dimension
rr=-2:0.001:2;
yy=PSF(rr*2*pi+0.305*2*pi);
plot(rr,yy)
yy2=PSF(rr*2*pi-0.305*2*pi);

hold on
plot(rr,yy2,'r')
yy12=yy+yy2;
plot(rr,yy12,'g')

%-------------------------
%Now let's do Abbe.
figure;
yy=PSF(rr*2*pi+0.255*2*pi);
plot(rr,yy)
yy2=PSF(rr*2*pi-0.255*2*pi);

hold on
plot(rr,yy2,'r')
yy12=yy+yy2;
plot(rr,yy12,'g--')


%-------------------------
%Now let's do Sparrow.
figure;
yy=PSF(rr*2*pi+0.235*2*pi);
plot(rr,yy)
yy2=PSF(rr*2*pi-0.235*2*pi);

hold on
plot(rr,yy2,'r')
yy12=yy+yy2;
plot(rr,yy12,'g--')

%------------------------------
%% This is a 2D case.
figure;
[xx yy]=meshgrid(-2:0.01:2,-2:0.01:2);
rr1=sqrt((xx+0.255).*(xx+0.255)+yy.*yy);
rr2=sqrt((xx-0.255).*(xx-0.255)+yy.*yy);
zz1=PSF(rr1*2*pi);
zz2=PSF(rr2*2*pi);
figure
imshow(zz1);title('Wide-field') % One of the PSF 2D
figure
confocal_PSF=zz1.*zz1;
imshow(confocal_PSF,[]); title('Confocal')%2-D confocal PSF
figure
zz12=zz1+zz2;
imshow(zz12,[])

%---------------------------------------------
function y=PSF(x)
temp=abs(2*besselj(1,x)./x);
y=temp.*temp;

--
Sincerely,
Peng Xi
Ph. D.    Associate Professor
Dept. of Biomedical Engineering, College of Engineering
Peking University, Beijing, China
Tel: [phone]
Email: [hidden email]
http://bme.pku.edu.cn/~xipeng/


On Mon, Nov 17, 2014 at 6:40 PM, Steffen Dietzel <[hidden email]>
wrote:

> *****
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> *****
>
> Dear Confocalists,
>
> for teaching purposes, I would like to have a graph with the following:
>
> 1) Intensity profile through the center of the Airy pattern (x,y) of a
> fluorescent point for a wavelength of 500 nm (as, say, mean between 488
> exc. and 512 em) in widefield, with the distance from the maximum on the
> x-axis in nano- or micrometers and the normalized intensity on the
> y-axis, say for a NA 1.4 Objective.
>
> 2) Same for confocal, closed pinhole.
>
> Bonus:
> 3) Same for confocal/two photon with 900 nm excitation
> 4) All of the above along the optical axis instead of the x,y plane.
>
>
> One purpose of this graph (more precisely: comparison of 1 and 2) would
> be to visualize with typical parameters why in the confocal/two-photon
> case with the steeper fall in intensity two Airy patterns can be closer
> together and still have a 26% dip in intensity between them (called
> extended Rayleigh-criterion, I believe?) although the ring with the
> first minimum has the same diameter.
>
> I am sure I could find that or a similar version in some book or
> article, however I would like to include this in material published on
> the web. And to avoid copyright issues the graphs have to be in the
> public domain or with a Creative Commons Attribution License (CC-by).
> Which probably means that they have to be made new. I would be perfectly
> happy to make such graphs myself if I had the respective data (i.e.
> columns with numbers for the x- and Y-values) to generate them in Excel,
> Calc or Graphpad. However, as a mere biologist I don't know how to
> generate such columns.
>
> Therefore I would like to ask if someone would be willing to help out
> and generate such columns with numbers. I assume that it is not that
> much work for somebody with good insight in Airy pattern formulas and
> the right program at hands - and hope I am not wrong with that
> assumption. In particular data for graphs 1 and 2 above would be very
> helpful.
>
> I am thinking that covering the distance from -5 to +5 µm in 10 nm steps
> would probably be more than sufficient.
>
> Cheers
>
> 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]

Steffen,

my personal opinion is that the Rayleigh criterion is a very good estimate what one can expect in terms of resolution. But clearly it is not a hard coded limit as it is neglecting any noise contribution. Looking at the Modulation transfer function of a microscope clearly indicates that the contrast (even without noise) is monotonically decreasing for patterns with higher frequencies. Therefore it is per definition difficult to define a resolution limit. But as mentioned above I think the Rayleigh criterion is doing a good job.

In the end I think it is much more straightforward to measure the PSF from a microscope than calculating it. Although I want to mention that PSFLab is for example can explain why your PSF gets asymmetric when using linearly polarized light for excitation (something which we stumbled across when we examined PSFs coming from a confocal microscope with small pinhole=0.3 AU). So theory clearly has its place.

But from the perspective of a light microscope user I would always prefer the experiment.

Best regards
Arne  

-----Original Message-----
From: Confocal Microscopy List [mailto:[hidden email]] On Behalf Of Steffen Dietzel
Sent: mardi 18 novembre 2014 18:52
To: [hidden email]
Subject: Re: Numbers for Airy pattern graphs?

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David,

that is a good idea. So with the one-photon PSF data from PSFLab, image multiplication in Fiji and normalization in Excel I should be getting somewhere.

However, when I create a psf intensity distribution in the focal plane with PSFlab for NA 1.4, lambda 0.5 µm (all Ris set to 1.518, calculation in x from -1 µm to +1 µm in 10 nm steps, in y 30 nm wide), I get the first minimum at 0.27 µm away from the maximum intensity. But according to r=0.61*lambda/NA it should be at 0.22 µm.

Also, when I superimpose two intensity profiles with the max of the second in the first min of the first (Rayleigh-criterion), the maximal intensity drop between the two profiles is about 55% while it should be only 26%. As Arne mentioned, PSFlab describes the excitation PSF only, not the theoretical confocal 1/sqrt(2) case.

So apparently PSFlab does not calculate the simple theoretical Airy pattern but some more complicated (and supposedly more realistic) case, resulting in different results.

I am wondering, does that mean we should throw the Rayleigh formula out the window, including the 26%-intensity dip if the max of one is on the first min of the other pattern? Else, I am still looking for the right numbers. I didn't yet get around to try Cosmos, as was suggested by Sergey.


Steffen



Am 17.11.2014 15:29, schrieb David Baddeley:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your posting.
> *****
>
> Dear Steffen,
> just to add to the suggestions already made, confocal and two-photon PSFs are really easy to derive from an emission or excitation case, if you have a psf generation program for widefield.
> To a 1st appoximation (i.e. infinitely small pinhole):
> confocal PSF = widefield PSF at exctitation wavelength multiplied by
> widefield PSF at detection wavelength Or for a large pinhole in
> 2-photon 2-photon PSF = widefield PSF at excitation wavelength squared.
> These multiplications should be easy to do in ImageJ (convert the data
> type to floating point first) If you want to model a finite pinhole size you can convolve the detection PSF with a flat disc with the pinhole diameter before doing the multiplication (doable in ImageJ, but somewhat harder, as the disc needs to be centred to avoid shifting the excitation and detection PSFS wrt each other).
> cheers,David
>

--
------------------------------------------------------------
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

[Sergey Tauger]

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Arne,

All resolution limits are formulated for optics only: continuous space and
some rather strict assumptions. Noise and pixelation are not taken into
account. For discussion of camera influence on total resolution there is
article by Stelzer (DOI: 10.1046/j.1365-2818.1998.00290.x) and book by
G.Boreman (ISBN 0-8194-4143-0), and I hope I'll have a more detailed article
submitted this year on the topic.

I agree, the most accurate way to estimate PSF is to average images of beads
for given imaging conditions, but we cannot get them for all possible
objectives, depth, wavelengths and combinations of embedding and immersion.

Best,
Sergey

[Stanislav Vitha-2]

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Steffen,
In a PSF created with CUDA Deconvolution plugin in ImageJ (1) I measured
0.25 um from the center to the first minimum. (100x/1.4 NA, oil imm,
lambda 500 nm, or maybe 525nm)

The wide-field PSF from the COSM package looks essentially the same.  I
like that I can model spherical aberration with CosmPsf.exe but I could not
create a confocal PSF with it. It always comes out looking like wide-field
PSF. Perhaps I have some parameters wrong. If you have better luck with
it, I would be interested to know your settings.
I suspect the calculation of backprojected pinhole diameter has something
to do with it, or actually using this info to calculate the PSF.

I even looked at the source code, all seems fine there:
The COSM software (file completeXcosm.cxx) calculates the backprojected
pinhole diameter in mm using this expression
fsize =  fsize_/(lm * magY_*1E3)     where “fsize_” is the pinhole size in
micrometers entered by the user,  “lm” is lateral magnification of the
objective, “magY” is the magnification of the relay optics in front of the
pinhole.  

1. Bruce, M. A., and Butte, M. J. (2013) Real-time GPU-based 3D
Deconvolution, Opt. Express 21, 4766-4773.

I have the confocal PSF (1 Airy, 3 Airy) stacks calculated with CUDA
deconvolution plugin, can send them to you if you are interested.  

Stan


Stanislav Vitha
Texas A&M University
Microscopy and Imaging Center


On Tue, 18 Nov 2014 18:51:38 +0100, Steffen Dietzel
<[hidden email]> wrote:
.
>
>However, when I create a psf intensity distribution in the focal plane
>with PSFlab for NA 1.4, lambda 0.5 µm (all Ris set to 1.518, calculation
>in x from -1 µm to +1 µm in 10 nm steps, in y 30 nm wide), I get the
>first minimum at 0.27 µm away from the maximum intensity. But
according

>to r=0.61*lambda/NA it should be at 0.22 µm.
>
>Also, when I superimpose two intensity profiles with the max of the
>second in the first min of the first (Rayleigh-criterion), the maximal
>intensity drop between the two profiles is about 55% while it should be
>only 26%. As Arne mentioned, PSFlab describes the excitation PSF only,
>not the theoretical confocal 1/sqrt(2) case.
>
>So apparently PSFlab does not calculate the simple theoretical Airy
>pattern but some more complicated (and supposedly more realistic) case,
>resulting in different results.
>
>I am wondering, does that mean we should throw the Rayleigh formula

out
>the window, including the 26%-intensity dip if the max of one is on the
>first min of the other pattern? Else, I am still looking for the right
>numbers. I didn't yet get around to try Cosmos, as was suggested by
Sergey.
>
>
>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

[Steffen Dietzel]

*****
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*****

Stan and all,

I just finished to examine a PSF calculated with Cosm PSF, 500 nm,
NA1.4, all Ris 1.518, in 1 nm steps and I indeed find that the first
minimum is 218 nm away from the maximum, as it should be. So that is
reassuring.

When I copy the intensity values in Excel, paste them shifted 218 nm so
that the max of the second is on the first min of the first and then add
the values of the two, I indeed get an intensity of 0.73 - close enough
for me to the 26% dip discussed earlier. So I am going to work with
those values.

Thanks everybody for the help.

For the confocal PSFs, I plan to simply square the values of the
(normalized) WF-PSF in Excel. Since for the purpose I have in mind I
need the theoretical values with closed pinhole, that should do.

Steffen

Am 19.11.2014 17:24, schrieb Stanislav Vitha:

> *****
> To join, leave or search the confocal microscopy listserv, go to:
> http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
> Post images on http://www.imgur.com and include the link in your posting.
> *****
>
> Steffen,
> In a PSF created with CUDA Deconvolution plugin in ImageJ (1) I measured
> 0.25 um from the center to the first minimum. (100x/1.4 NA, oil imm,
> lambda 500 nm, or maybe 525nm)
>
> The wide-field PSF from the COSM package looks essentially the same.  I
> like that I can model spherical aberration with CosmPsf.exe but I could not
> create a confocal PSF with it. It always comes out looking like wide-field
> PSF. Perhaps I have some parameters wrong. If you have better luck with
> it, I would be interested to know your settings.
> I suspect the calculation of backprojected pinhole diameter has something
> to do with it, or actually using this info to calculate the PSF.
>
> I even looked at the source code, all seems fine there:
> The COSM software (file completeXcosm.cxx) calculates the backprojected
> pinhole diameter in mm using this expression
> fsize =  fsize_/(lm * magY_*1E3)     where “fsize_” is the pinhole size in
> micrometers entered by the user,  “lm” is lateral magnification of the
> objective, “magY” is the magnification of the relay optics in front of the
> pinhole.  
>
> 1. Bruce, M. A., and Butte, M. J. (2013) Real-time GPU-based 3D
> Deconvolution, Opt. Express 21, 4766-4773.
>
> I have the confocal PSF (1 Airy, 3 Airy) stacks calculated with CUDA
> deconvolution plugin, can send them to you if you are interested.  
>
> Stan
>
>
> Stanislav Vitha
> Texas A&M University
> Microscopy and Imaging Center
>

--
------------------------------------------------------------
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