Numerical aperture and spatial resolution

[F Javier Diez Guerra]

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Hello,

I wonder if anybody in the list could help.

I want to convey to biology undergraduate students (very allergic to
physics and mathematics) the understanding of the relationship between
numerical aperture and spatial resolution.

I have already given them links to the different microscopy primer
sites. They find difficult to understand why the airy disk is generated
in the image plane, how the diffraction orders affect resolution and why
increasing NA reduces the image spot.

Could anybody share a basic and intuitive infographic slide, animation
or any other resource that could help to ease comprehension in this context?

Thanks

Javier


--
Fco. Javier Diez-Guerra, PhD

Servicio de Microscopía Confocal
Centro de Biologia Molecular Severo Ochoa
C/ Nicolás Cabrera, 1
Campus de Cantoblanco
28049 Madrid
SPAIN

Tel     [phone]
e-mail: [hidden email]

[Julian Smith III]

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Hi, Javier
We don't teach this to first-year students, but I cover it in my microscopy course for 3&4th-year students and beginning graduate students.
The iBiology microscopy series does a pretty good job of it.
I don't know whether your course has a laboratory section or not, but in the lab portion of my course, we do several of the standard exercises:
Use a laser to generate diffractions patterns from inexpensive ruled gratings.
Set up Koehler illumination, add a green interference filter over the field iris, view an inexpensive singled ruled grating with various objectives to determine whether or not the vertical lines are resolvable.
Then, remove one eyepiece and replace it with a phase telescope, close both field and condenser diaphragms  fully.  The diffraction spots can easily be seen in the back focal plane.
We supplement this with an exercise in FIGI/ImageJ where the students start with a photo of the ruled grating, do a Fourier transform, confirm that the reverse transform restores the image, and then to the first transform, use the eraser to remove the first-order diffraction spots and all data to the outside of them, then do the reverse transform on that image, and confirm that the grating has disappeared.
Most of this, I owe to Ted Salmon from his microscopy course when I was a grad student, and to the excellent book by Douglas & Murphy (Fundamentals of light microscopy and electronic imaging, 2nd edition.
Best,
Julian
________________________________
From: Confocal Microscopy List <[hidden email]> on behalf of F Javier Diez Guerra <[hidden email]>
Sent: Saturday, September 19, 2020 5:38 AM
To: [hidden email] <[hidden email]>
Subject: [EXTERNAL] Numerical aperture and spatial resolution

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Hello,

I wonder if anybody in the list could help.

I want to convey to biology undergraduate students (very allergic to
physics and mathematics) the understanding of the relationship between
numerical aperture and spatial resolution.

I have already given them links to the different microscopy primer
sites. They find difficult to understand why the airy disk is generated
in the image plane, how the diffraction orders affect resolution and why
increasing NA reduces the image spot.

Could anybody share a basic and intuitive infographic slide, animation
or any other resource that could help to ease comprehension in this context?

Thanks

Javier


--
Fco. Javier Diez-Guerra, PhD

Servicio de Microscopía Confocal
Centro de Biologia Molecular Severo Ochoa
C/ Nicolás Cabrera, 1
Campus de Cantoblanco
28049 Madrid
SPAIN

Tel     [phone]
e-mail: [hidden email]

CAUTION: This message originated from an external source

[Benjamin Smith]

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The best demo I have found is to make it physically tangible - a demo using
your own hands.  Imagine that the wavelength of your light is the length of
your hand (fingertip to wrist).  That would mean that the base of your
fingers would be a 180° phase shift from your finger tip.  Now rest your
elbows on a table and point your hands in line with your forearms with the
finger tips touching one another.  This is the center of the Airy disk as
the waves are perfectly in phase.  Now, while keeping your elbows in place,
rotate your forearms until your fingertips on one hand reach the base of
the fingers on the other.  The light is now 180° out of phase - this is the
first dark ring (node) of the Airy disk.  Try this with your elbows close
together (small angle = low NA), and elbows wide apart (large angle = high
NA).  You will find you have to move a lot farther to the side to get the
first node with the small angle than the large angle.

Now, technically this demo traces a petzval surface, but the analogy works
well enough to get the point across.  I've even had students do this demo
during tests.

For more visual learners, Paul Falstad's wave applet:
http://falstad.com/ripple/ has a diffraction demo built in.  It also has a
lot of other great demos, including Rayleigh scattering, Mie
scattering/lensing, single vs multimode fiber, holographic gratings,
refraction, etc.  This other wave applet of his is also great:
http://falstad.com/wave2d/  As an added bonus, the site also has a circuit
simulator for when you want to cover CMOS cameras, an animation showing
orbital transitions which is perfect for fluorescence, second harmonic
excitation, and stimulated emission, and a Fourier Transform visualizer
which is perfect for explaining image processing and mode locking in lasers.

Hope this helps,
   Ben Smith

On Sat, Sep 19, 2020 at 2:40 AM F Javier Diez Guerra <[hidden email]>
wrote:

> *****
> 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.
> *****
>
> Hello,
>
> I wonder if anybody in the list could help.
>
> I want to convey to biology undergraduate students (very allergic to
> physics and mathematics) the understanding of the relationship between
> numerical aperture and spatial resolution.
>
> I have already given them links to the different microscopy primer
> sites. They find difficult to understand why the airy disk is generated
> in the image plane, how the diffraction orders affect resolution and why
> increasing NA reduces the image spot.
>
> Could anybody share a basic and intuitive infographic slide, animation
> or any other resource that could help to ease comprehension in this
> context?
>
> Thanks
>
> Javier
>
>
> --
> Fco. Javier Diez-Guerra, PhD
>
> Servicio de Microscopía Confocal
> Centro de Biologia Molecular Severo Ochoa
> C/ Nicolás Cabrera, 1
> Campus de Cantoblanco
> 28049 Madrid
> SPAIN
>
> Tel     [phone]
> e-mail: [hidden email]
>

--
Benjamin E. Smith, Ph. D.
Imaging Specialist, Vision Science
University of California, Berkeley
195 Life Sciences Addition
Berkeley, CA  94720-3200
Tel  [phone]
Fax [phone]
e-mail: [hidden email]
https://vision.berkeley.edu/faculty/core-grants-nei/core-grant-microscopic-imaging/

[Petro]

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Hi.
I do not know if how much lab work the course has, but I would show
difference in PSF on a confocal using an objective with variable NA.
Best.
Petro.

On Sat, Sep 19, 2020, 12:25 PM Benjamin Smith <[hidden email]>
wrote:

> *****
> 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.
> *****
>
> The best demo I have found is to make it physically tangible - a demo using
> your own hands.  Imagine that the wavelength of your light is the length of
> your hand (fingertip to wrist).  That would mean that the base of your
> fingers would be a 180° phase shift from your finger tip.  Now rest your
> elbows on a table and point your hands in line with your forearms with the
> finger tips touching one another.  This is the center of the Airy disk as
> the waves are perfectly in phase.  Now, while keeping your elbows in place,
> rotate your forearms until your fingertips on one hand reach the base of
> the fingers on the other.  The light is now 180° out of phase - this is the
> first dark ring (node) of the Airy disk.  Try this with your elbows close
> together (small angle = low NA), and elbows wide apart (large angle = high
> NA).  You will find you have to move a lot farther to the side to get the
> first node with the small angle than the large angle.
>
> Now, technically this demo traces a petzval surface, but the analogy works
> well enough to get the point across.  I've even had students do this demo
> during tests.
>
> For more visual learners, Paul Falstad's wave applet:
> http://falstad.com/ripple/ has a diffraction demo built in.  It also has a
> lot of other great demos, including Rayleigh scattering, Mie
> scattering/lensing, single vs multimode fiber, holographic gratings,
> refraction, etc.  This other wave applet of his is also great:
> http://falstad.com/wave2d/  As an added bonus, the site also has a circuit
> simulator for when you want to cover CMOS cameras, an animation showing
> orbital transitions which is perfect for fluorescence, second harmonic
> excitation, and stimulated emission, and a Fourier Transform visualizer
> which is perfect for explaining image processing and mode locking in
> lasers.
>
> Hope this helps,
>    Ben Smith
>
> On Sat, Sep 19, 2020 at 2:40 AM F Javier Diez Guerra <[hidden email]>
> wrote:
>
> > *****
> > 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.
> > *****
> >
> > Hello,
> >
> > I wonder if anybody in the list could help.
> >
> > I want to convey to biology undergraduate students (very allergic to
> > physics and mathematics) the understanding of the relationship between
> > numerical aperture and spatial resolution.
> >
> > I have already given them links to the different microscopy primer
> > sites. They find difficult to understand why the airy disk is generated
> > in the image plane, how the diffraction orders affect resolution and why
> > increasing NA reduces the image spot.
> >
> > Could anybody share a basic and intuitive infographic slide, animation
> > or any other resource that could help to ease comprehension in this
> > context?
> >
> > Thanks
> >
> > Javier
> >
> >
> > --
> > Fco. Javier Diez-Guerra, PhD
> >
> > Servicio de Microscopía Confocal
> > Centro de Biologia Molecular Severo Ochoa
> > C/ Nicolás Cabrera, 1
> > Campus de Cantoblanco
> > 28049 Madrid
> > SPAIN
> >
> > Tel     [phone]
> > e-mail: [hidden email]
> >
>
>
> --
> Benjamin E. Smith, Ph. D.
> Imaging Specialist, Vision Science
> University of California, Berkeley
> 195 Life Sciences Addition
> Berkeley, CA  94720-3200
> Tel  [phone]
> Fax [phone]
> e-mail: [hidden email]
>
> https://vision.berkeley.edu/faculty/core-grants-nei/core-grant-microscopic-imaging/
>

[Davide Accardi-2]

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*****

Hi Javier,

This is a video with Peter Evennett, senior microscopist of the RMS, that explains it all.
Peter reproduces Abbe’s experiments and clearly demonstrates how resolution depends on lambda and NA.

https://youtu.be/60_jgZtyR6U

Good luck!

Davide
--
Davide Accardi, PhD.
Champalimaud ABBE Platform
Advanced BioImaging and BioOptics Experimental Platform
Scientific and Managing Leader

Champalimaud Centre for the Unknown
Av. Brasilia, Doca de Pedroucos
1400-038 Lisbon, Portugal
T ([phone]

www.fchampalimaud.org
[hidden email]

Sent from my iPhone

>> On 19. Sep 2020, at 10:40, F Javier Diez Guerra <[hidden email]> wrote:
> *****
> 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.
> *****
>
> Hello,
>
> I wonder if anybody in the list could help.
>
> I want to convey to biology undergraduate students (very allergic to physics and mathematics) the understanding of the relationship between numerical aperture and spatial resolution.
>
> I have already given them links to the different microscopy primer sites. They find difficult to understand why the airy disk is generated in the image plane, how the diffraction orders affect resolution and why increasing NA reduces the image spot.
>
> Could anybody share a basic and intuitive infographic slide, animation or any other resource that could help to ease comprehension in this context?
>
> Thanks
>
> Javier
>
>
> --
> Fco. Javier Diez-Guerra, PhD
>
> Servicio de Microscopía Confocal
> Centro de Biologia Molecular Severo Ochoa
> C/ Nicolás Cabrera, 1
> Campus de Cantoblanco
> 28049 Madrid
> SPAIN
>
> Tel     [phone]
> e-mail: [hidden email]

[George McNamara]

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*****

Hi Javier,

I suggest you ask the class if they have any interest in taking photos
with their smartphone or DSLR camera, and if they do, bring in a DSLR
and tripod and computer/projector (if the room does not have that
already), explain f/stop and NA are inverse of each other, and
demonstrate NA (resolution, intensity, depth of field) on the class by
focusing on faces in the middle row. Wavelength: yes, you could buy some
filters for the camera lens (or deal with separating channels in
Photoshop, fiji ImageJ, etc), but probably better done on a microscope.

George

p.s. this post was inspired by a conversation yesterday -- Friday happy
hour -- with a colleague, Prof. Jim Potter, who told me about a
conversation he had with someone with a very expensive digital camera
hobby, who only used their cameras set to auto. Jim explained f/stop,
ISO and more (framing scene etc). My thanks to Jim for good story with
nice timing and especially foraging for the beverages.

A fun (in theory, but probably not practical or wise) wavelength test
would be to use bring in blue (~400 nm) and NIR (~800nm would be nice,
values chosen to be 2 fold, not necessarily practical) and a smoke
machine (and some 400nm and NIR friendly lighting in case room lights
too dim at those wavelength), and demonstration resolution vs ability to
see through the smoke (Mie scattering etc). If you do this, and the
smoke alarm turns on, your school may not be happy with you (though all
the students may be happy to escape class early).

Of course if they vote no to learning about f/stop and NA, you can ask
them how they expect to get to a million TikTok followers each without
knowing how to take good quality videos. Come ot think of it, if they do
vote yes, and you put your demo on your TikTok feed and make a lot of
money, you can send me the URL and a thank you check.

On 9/19/2020 5:38 AM, F Javier Diez Guerra wrote:

> *****
> 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.
> *****
>
> Hello,
>
> I wonder if anybody in the list could help.
>
> I want to convey to biology undergraduate students (very allergic to
> physics and mathematics) the understanding of the relationship between
> numerical aperture and spatial resolution.
>
> I have already given them links to the different microscopy primer
> sites. They find difficult to understand why the airy disk is
> generated in the image plane, how the diffraction orders affect
> resolution and why increasing NA reduces the image spot.
>
> Could anybody share a basic and intuitive infographic slide, animation
> or any other resource that could help to ease comprehension in this
> context?
>
> Thanks
>
> Javier
>
>

[Zdenek Svindrych-2]

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*****

Hi George and Javier,

regarding aperture and resolution of DSLR (actually mirror-less) I put some
photos together here:
https://drive.google.com/file/d/1vDYqDBPgapZYad3JahRm8R5W5Bkwu4T6
But, it will only work with some lenses (well, with most, but not in the
full F-stop range), and only with some cameras (more pixels is better here,
kind of an exception :-).

Davide, the Evenett's video is great! Many demonstrations were quite
surprising, and I have nothing to add to it (maybe a note, that the phase
contrast method in all its simplicity still yielded Zernike a Nobel prize!).
But even though one thought follows from another nicely, at the end if you
ask your students "So why does higher NA mean higher resolution?" they'll
say "Well, uhm..." It's not very likely they'll gain a deeper understanding
of how all these concepts fit together.

Good luck!

zdenee

On Sat, Sep 19, 2020 at 12:25 PM George McNamara <[hidden email]>
wrote:

> *****
> 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.
> *****
>
> Hi Javier,
>
> I suggest you ask the class if they have any interest in taking photos
> with their smartphone or DSLR camera, and if they do, bring in a DSLR
> and tripod and computer/projector (if the room does not have that
> already), explain f/stop and NA are inverse of each other, and
> demonstrate NA (resolution, intensity, depth of field) on the class by
> focusing on faces in the middle row. Wavelength: yes, you could buy some
> filters for the camera lens (or deal with separating channels in
> Photoshop, fiji ImageJ, etc), but probably better done on a microscope.
>
> George
>
> p.s. this post was inspired by a conversation yesterday -- Friday happy
> hour -- with a colleague, Prof. Jim Potter, who told me about a
> conversation he had with someone with a very expensive digital camera
> hobby, who only used their cameras set to auto. Jim explained f/stop,
> ISO and more (framing scene etc). My thanks to Jim for good story with
> nice timing and especially foraging for the beverages.
>
> A fun (in theory, but probably not practical or wise) wavelength test
> would be to use bring in blue (~400 nm) and NIR (~800nm would be nice,
> values chosen to be 2 fold, not necessarily practical) and a smoke
> machine (and some 400nm and NIR friendly lighting in case room lights
> too dim at those wavelength), and demonstration resolution vs ability to
> see through the smoke (Mie scattering etc). If you do this, and the
> smoke alarm turns on, your school may not be happy with you (though all
> the students may be happy to escape class early).
>
> Of course if they vote no to learning about f/stop and NA, you can ask
> them how they expect to get to a million TikTok followers each without
> knowing how to take good quality videos. Come ot think of it, if they do
> vote yes, and you put your demo on your TikTok feed and make a lot of
> money, you can send me the URL and a thank you check.
>
> On 9/19/2020 5:38 AM, F Javier Diez Guerra wrote:
> > *****
> > 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.
> > *****
> >
> > Hello,
> >
> > I wonder if anybody in the list could help.
> >
> > I want to convey to biology undergraduate students (very allergic to
> > physics and mathematics) the understanding of the relationship between
> > numerical aperture and spatial resolution.
> >
> > I have already given them links to the different microscopy primer
> > sites. They find difficult to understand why the airy disk is
> > generated in the image plane, how the diffraction orders affect
> > resolution and why increasing NA reduces the image spot.
> >
> > Could anybody share a basic and intuitive infographic slide, animation
> > or any other resource that could help to ease comprehension in this
> > context?
> >
> > Thanks
> >
> > Javier
> >
> >
>

--
--
Zdenek Svindrych, Ph.D.
Research Scientist - Microscopy Imaging Specialist
Department of Biochemistry and Cell Biology
Geisel School of Medicine at Dartmouth

[F Javier Diez Guerra]

*****
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*****

Hi,

Thanks to all contributors for the excellent suggestions.

Unfortunately, at the present times, at least here in Madrid, most if
not all university lectures are Teams sessions. So on-site demos are not
a choice.

I also align with Zdenee's view. "Why does higher NA mean higher
resolution?" is a question with no trivial answer for biologists. The
demo of looking the diffraction orders at the BFP with a Bertrand lens,
using objectives with different NA and gratings of different densities,
worked best for me when I first learned about spatial resolution. Still,
for a biology undergraduate is difficult to comprehend intuitively why
capturing more diffraction orders means higher resolution.

Javier


El 19/09/2020 a las 20:27, Zdenek Svindrych escribió:

> *****
> 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.
> *****
>
> Hi George and Javier,
>
> regarding aperture and resolution of DSLR (actually mirror-less) I put some
> photos together here:
> https://drive.google.com/file/d/1vDYqDBPgapZYad3JahRm8R5W5Bkwu4T6
> But, it will only work with some lenses (well, with most, but not in the
> full F-stop range), and only with some cameras (more pixels is better here,
> kind of an exception :-).
>
> Davide, the Evenett's video is great! Many demonstrations were quite
> surprising, and I have nothing to add to it (maybe a note, that the phase
> contrast method in all its simplicity still yielded Zernike a Nobel prize!).
> But even though one thought follows from another nicely, at the end if you
> ask your students "So why does higher NA mean higher resolution?" they'll
> say "Well, uhm..." It's not very likely they'll gain a deeper understanding
> of how all these concepts fit together.
>
> Good luck!
>
> zdenee
>
> On Sat, Sep 19, 2020 at 12:25 PM George McNamara <[hidden email]>
> wrote:
>
>> *****
>> 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.
>> *****
>>
>> Hi Javier,
>>
>> I suggest you ask the class if they have any interest in taking photos
>> with their smartphone or DSLR camera, and if they do, bring in a DSLR
>> and tripod and computer/projector (if the room does not have that
>> already), explain f/stop and NA are inverse of each other, and
>> demonstrate NA (resolution, intensity, depth of field) on the class by
>> focusing on faces in the middle row. Wavelength: yes, you could buy some
>> filters for the camera lens (or deal with separating channels in
>> Photoshop, fiji ImageJ, etc), but probably better done on a microscope.
>>
>> George
>>
>> p.s. this post was inspired by a conversation yesterday -- Friday happy
>> hour -- with a colleague, Prof. Jim Potter, who told me about a
>> conversation he had with someone with a very expensive digital camera
>> hobby, who only used their cameras set to auto. Jim explained f/stop,
>> ISO and more (framing scene etc). My thanks to Jim for good story with
>> nice timing and especially foraging for the beverages.
>>
>> A fun (in theory, but probably not practical or wise) wavelength test
>> would be to use bring in blue (~400 nm) and NIR (~800nm would be nice,
>> values chosen to be 2 fold, not necessarily practical) and a smoke
>> machine (and some 400nm and NIR friendly lighting in case room lights
>> too dim at those wavelength), and demonstration resolution vs ability to
>> see through the smoke (Mie scattering etc). If you do this, and the
>> smoke alarm turns on, your school may not be happy with you (though all
>> the students may be happy to escape class early).
>>
>> Of course if they vote no to learning about f/stop and NA, you can ask
>> them how they expect to get to a million TikTok followers each without
>> knowing how to take good quality videos. Come ot think of it, if they do
>> vote yes, and you put your demo on your TikTok feed and make a lot of
>> money, you can send me the URL and a thank you check.
>>
>> On 9/19/2020 5:38 AM, F Javier Diez Guerra wrote:
>>> *****
>>> 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.
>>> *****
>>>
>>> Hello,
>>>
>>> I wonder if anybody in the list could help.
>>>
>>> I want to convey to biology undergraduate students (very allergic to
>>> physics and mathematics) the understanding of the relationship between
>>> numerical aperture and spatial resolution.
>>>
>>> I have already given them links to the different microscopy primer
>>> sites. They find difficult to understand why the airy disk is
>>> generated in the image plane, how the diffraction orders affect
>>> resolution and why increasing NA reduces the image spot.
>>>
>>> Could anybody share a basic and intuitive infographic slide, animation
>>> or any other resource that could help to ease comprehension in this
>>> context?
>>>
>>> Thanks
>>>
>>> Javier
>>>
>>>
>

[JOEL B. SHEFFIELD]

*****
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*****

About 20 years ago, Jim Pawley and Guy Cox developed a wonderful simulation
of the original Abbe experiment along with a clear analysis of the optics
involved. It focuses (pardon the pun) on the diffraction component rather
than the wavelength.   You can "mount" a slide with a grating as a
specimen, and insert a slider at the back focal plane to block orders lines.
If you can still get it, I suppose Guy Cox would be the resource.
Alternatively, I have the files if someone is interested.

I should say that in my microscopy course, I have the students use several
samples with fine repeats, a stage micrometer, a hemocytometer, some trick
"rainbow" glasses, and I have them look at the back focal plane to see
what's going on.

Joel


Joel B. Sheffield, Ph.D
Department of Biology
Temple University
Philadelphia, PA 19122
Voice: 215 204 8839
e-mail: [hidden email]
Office:  Biolife 311
URL:  *https://bio.cst.temple.edu/~jbs/ <https://bio.cst.temple.edu/~jbs/>
<http://tinyurl.com/khbouft>*


On Sat, Sep 19, 2020 at 3:22 PM F Javier Diez Guerra <[hidden email]>
wrote:

> *****
> 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.
> *****
>
> Hi,
>
> Thanks to all contributors for the excellent suggestions.
>
> Unfortunately, at the present times, at least here in Madrid, most if
> not all university lectures are Teams sessions. So on-site demos are not
> a choice.
>
> I also align with Zdenee's view. "Why does higher NA mean higher
> resolution?" is a question with no trivial answer for biologists. The
> demo of looking the diffraction orders at the BFP with a Bertrand lens,
> using objectives with different NA and gratings of different densities,
> worked best for me when I first learned about spatial resolution. Still,
> for a biology undergraduate is difficult to comprehend intuitively why
> capturing more diffraction orders means higher resolution.
>
> Javier
>
>
> El 19/09/2020 a las 20:27, Zdenek Svindrych escribió:
> > *****
> > 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.
> > *****
> >
> > Hi George and Javier,
> >
> > regarding aperture and resolution of DSLR (actually mirror-less) I put
> some
> > photos together here:
> > https://drive.google.com/file/d/1vDYqDBPgapZYad3JahRm8R5W5Bkwu4T6
> > But, it will only work with some lenses (well, with most, but not in the
> > full F-stop range), and only with some cameras (more pixels is better
> here,
> > kind of an exception :-).
> >
> > Davide, the Evenett's video is great! Many demonstrations were quite
> > surprising, and I have nothing to add to it (maybe a note, that the phase
> > contrast method in all its simplicity still yielded Zernike a Nobel
> prize!).
> > But even though one thought follows from another nicely, at the end if
> you
> > ask your students "So why does higher NA mean higher resolution?" they'll
> > say "Well, uhm..." It's not very likely they'll gain a deeper
> understanding
> > of how all these concepts fit together.
> >
> > Good luck!
> >
> > zdenee
> >
> > On Sat, Sep 19, 2020 at 12:25 PM George McNamara <
> [hidden email]>
> > wrote:
> >
> >> *****
> >> 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.
> >> *****
> >>
> >> Hi Javier,
> >>
> >> I suggest you ask the class if they have any interest in taking photos
> >> with their smartphone or DSLR camera, and if they do, bring in a DSLR
> >> and tripod and computer/projector (if the room does not have that
> >> already), explain f/stop and NA are inverse of each other, and
> >> demonstrate NA (resolution, intensity, depth of field) on the class by
> >> focusing on faces in the middle row. Wavelength: yes, you could buy some
> >> filters for the camera lens (or deal with separating channels in
> >> Photoshop, fiji ImageJ, etc), but probably better done on a microscope.
> >>
> >> George
> >>
> >> p.s. this post was inspired by a conversation yesterday -- Friday happy
> >> hour -- with a colleague, Prof. Jim Potter, who told me about a
> >> conversation he had with someone with a very expensive digital camera
> >> hobby, who only used their cameras set to auto. Jim explained f/stop,
> >> ISO and more (framing scene etc). My thanks to Jim for good story with
> >> nice timing and especially foraging for the beverages.
> >>
> >> A fun (in theory, but probably not practical or wise) wavelength test
> >> would be to use bring in blue (~400 nm) and NIR (~800nm would be nice,
> >> values chosen to be 2 fold, not necessarily practical) and a smoke
> >> machine (and some 400nm and NIR friendly lighting in case room lights
> >> too dim at those wavelength), and demonstration resolution vs ability to
> >> see through the smoke (Mie scattering etc). If you do this, and the
> >> smoke alarm turns on, your school may not be happy with you (though all
> >> the students may be happy to escape class early).
> >>
> >> Of course if they vote no to learning about f/stop and NA, you can ask
> >> them how they expect to get to a million TikTok followers each without
> >> knowing how to take good quality videos. Come ot think of it, if they do
> >> vote yes, and you put your demo on your TikTok feed and make a lot of
> >> money, you can send me the URL and a thank you check.
> >>
> >> On 9/19/2020 5:38 AM, F Javier Diez Guerra wrote:
> >>> *****
> >>> 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.
> >>> *****
> >>>
> >>> Hello,
> >>>
> >>> I wonder if anybody in the list could help.
> >>>
> >>> I want to convey to biology undergraduate students (very allergic to
> >>> physics and mathematics) the understanding of the relationship between
> >>> numerical aperture and spatial resolution.
> >>>
> >>> I have already given them links to the different microscopy primer
> >>> sites. They find difficult to understand why the airy disk is
> >>> generated in the image plane, how the diffraction orders affect
> >>> resolution and why increasing NA reduces the image spot.
> >>>
> >>> Could anybody share a basic and intuitive infographic slide, animation
> >>> or any other resource that could help to ease comprehension in this
> >>> context?
> >>>
> >>> Thanks
> >>>
> >>> Javier
> >>>
> >>>
> >
>

[Julio MATEOS_LANGERAK]

*****
To join, leave or search the confocal microscopy listserv, go to:
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Post images on http://www.imgur.com and include the link in your posting.
*****

Hi,

This is the same demonstration by Peter Evennett as a series of videos. The format is possibly more suited for teaching. It's one of the most beautyful demonstrations I've ever seen.

https://www.youtube.com/watch?v=6mGEGs7vI00&list=PLN3i-H51ZELg6SZqAUIU3EI3F0_2igL_x&index=1

Best, Julio

________________________________
From: Confocal Microscopy List <[hidden email]> on behalf of Davide Accardi <[hidden email]>
Sent: 19 September 2020 17:54
To: [hidden email] <[hidden email]>
Subject: Re: Numerical aperture and spatial resolution

*****
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*****

Hi Javier,

This is a video with Peter Evennett, senior microscopist of the RMS, that explains it all.
Peter reproduces Abbe’s experiments and clearly demonstrates how resolution depends on lambda and NA.

https://youtu.be/60_jgZtyR6U

Good luck!

Davide
--
Davide Accardi, PhD.
Champalimaud ABBE Platform
Advanced BioImaging and BioOptics Experimental Platform
Scientific and Managing Leader

Champalimaud Centre for the Unknown
Av. Brasilia, Doca de Pedroucos
1400-038 Lisbon, Portugal
T ([phone]

www.fchampalimaud.org<http://www.fchampalimaud.org>
[hidden email]

Sent from my iPhone

>> On 19. Sep 2020, at 10:40, F Javier Diez Guerra <[hidden email]> wrote:
> *****
> 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.
> *****
>
> Hello,
>
> I wonder if anybody in the list could help.
>
> I want to convey to biology undergraduate students (very allergic to physics and mathematics) the understanding of the relationship between numerical aperture and spatial resolution.
>
> I have already given them links to the different microscopy primer sites. They find difficult to understand why the airy disk is generated in the image plane, how the diffraction orders affect resolution and why increasing NA reduces the image spot.
>
> Could anybody share a basic and intuitive infographic slide, animation or any other resource that could help to ease comprehension in this context?
>
> Thanks
>
> Javier
>
>
> --
> Fco. Javier Diez-Guerra, PhD
>
> Servicio de Microscopía Confocal
> Centro de Biologia Molecular Severo Ochoa
> C/ Nicolás Cabrera, 1
> Campus de Cantoblanco
> 28049 Madrid
> SPAIN
>
> Tel     [phone]
> e-mail: [hidden email]

[JOEL B. SHEFFIELD]

*****
To join, leave or search the confocal microscopy listserv, go to:
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Post images on http://www.imgur.com and include the link in your posting.
*****

I agree.  This is excellent!  His analysis of phase contrast is about the
best I've seen.


Joel B. Sheffield, Ph.D
Department of Biology
Temple University
Philadelphia, PA 19122
Voice: 215 204 8839
e-mail: [hidden email]
Office:  Biolife 311
URL:  *https://bio.cst.temple.edu/~jbs/ <https://bio.cst.temple.edu/~jbs/>
<http://tinyurl.com/khbouft>*


On Sun, Sep 20, 2020 at 8:42 AM Julio MATEOS_LANGERAK <
[hidden email]> wrote:

> *****
> 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.
> *****
>
> Hi,
>
> This is the same demonstration by Peter Evennett as a series of videos.
> The format is possibly more suited for teaching. It's one of the most
> beautyful demonstrations I've ever seen.
>
>
> https://www.youtube.com/watch?v=6mGEGs7vI00&list=PLN3i-H51ZELg6SZqAUIU3EI3F0_2igL_x&index=1
>
> Best, Julio
>
> ________________________________
> From: Confocal Microscopy List <[hidden email]> on
> behalf of Davide Accardi <[hidden email]>
> Sent: 19 September 2020 17:54
> To: [hidden email] <[hidden email]>
> Subject: Re: Numerical aperture and spatial resolution
>
> *****
> 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.
> *****
>
> Hi Javier,
>
> This is a video with Peter Evennett, senior microscopist of the RMS, that
> explains it all.
> Peter reproduces Abbe’s experiments and clearly demonstrates how
> resolution depends on lambda and NA.
>
> https://youtu.be/60_jgZtyR6U
>
> Good luck!
>
> Davide
> --
> Davide Accardi, PhD.
> Champalimaud ABBE Platform
> Advanced BioImaging and BioOptics Experimental Platform
> Scientific and Managing Leader
>
> Champalimaud Centre for the Unknown
> Av. Brasilia, Doca de Pedroucos
> 1400-038 Lisbon, Portugal
> T ([phone]
>
> www.fchampalimaud.org<http://www.fchampalimaud.org>
> [hidden email]
>
> Sent from my iPhone
>
> >> On 19. Sep 2020, at 10:40, F Javier Diez Guerra <[hidden email]>
> wrote:
> > *****
> > 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.
> > *****
> >
> > Hello,
> >
> > I wonder if anybody in the list could help.
> >
> > I want to convey to biology undergraduate students (very allergic to
> physics and mathematics) the understanding of the relationship between
> numerical aperture and spatial resolution.
> >
> > I have already given them links to the different microscopy primer
> sites. They find difficult to understand why the airy disk is generated in
> the image plane, how the diffraction orders affect resolution and why
> increasing NA reduces the image spot.
> >
> > Could anybody share a basic and intuitive infographic slide, animation
> or any other resource that could help to ease comprehension in this context?
> >
> > Thanks
> >
> > Javier
> >
> >
> > --
> > Fco. Javier Diez-Guerra, PhD
> >
> > Servicio de Microscopía Confocal
> > Centro de Biologia Molecular Severo Ochoa
> > C/ Nicolás Cabrera, 1
> > Campus de Cantoblanco
> > 28049 Madrid
> > SPAIN
> >
> > Tel     [phone]
> > e-mail: [hidden email]
>

[Steffen Dietzel]

*****
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.
*****

Hi Javier,

> why capturing more diffraction orders means higher resolution.
well, in my understanding it does not. As far as I get it, it is only
about the first diffraction order that you need to collect. But you
probably meant that anyway, just speaking about different sized objects.

When teaching, I split the explanation up in two parts:

1. Higher NA means larger acceptance angle. (Trivial to microscopists,
but worth mentioning with the students). This also helps with intensity
(in fluorescence microscopy).

2. the smaller an object/structure is, the larger the angle of its
diffraction pattern will be. (WHY this is the case, that is the
difficult bit. But in my experience biology students are happy to just
accept this as a fact without going into the physical reasons.)

To visualize that smaller structures produce higher angle diffraction
patterns, a slide (slide for a slide projector from the olden days) with
various stripe patterns can be used. Just shine a laser through it and
look at the different diffraction patterns on the wall behind. That you
can do in a video class. Even better is to produce a small white dot
with a flash light on the wall and have the students put the various
patterns in front of their eye. Then you also see the differences for
the wavelengths. But this won't work online. Maybe it someone did a
video of this, with the different patterns in front of the camera? The
stripe pattern slide idea again goes back to Peter Evennett. We have a
template for it on our web site,
https://www.bioimaging.bmc.med.uni-muenchen.de/learn/materialdownload/index.html

With the two points above, it also can be made clear why a condenser
increases resolution in transmission bright field, since it it
sufficient to collect the first order from one side of the diffraction
pattern.

Happy teaching

Steffen


Am 19.09.2020 um 21:21 schrieb F Javier Diez Guerra:

> *****
> 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.
> *****
>
> Hi,
>
> Thanks to all contributors for the excellent suggestions.
>
> Unfortunately, at the present times, at least here in Madrid, most if
> not all university lectures are Teams sessions. So on-site demos are
> not a choice.
>
> I also align with Zdenee's view. "Why does higher NA mean higher
> resolution?" is a question with no trivial answer for biologists. The
> demo of looking the diffraction orders at the BFP with a Bertrand
> lens, using objectives with different NA and gratings of different
> densities, worked best for me when I first learned about spatial
> resolution. Still, for a biology undergraduate is difficult to
> comprehend intuitively why capturing more diffraction orders means
> higher resolution.
>
> Javier
>
>
> El 19/09/2020 a las 20:27, Zdenek Svindrych escribió:
>> *****
>> 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.
>> *****
>>
>> Hi George and Javier,
>>
>> regarding aperture and resolution of DSLR (actually mirror-less) I
>> put some
>> photos together here:
>> https://drive.google.com/file/d/1vDYqDBPgapZYad3JahRm8R5W5Bkwu4T6
>> But, it will only work with some lenses (well, with most, but not in the
>> full F-stop range), and only with some cameras (more pixels is better
>> here,
>> kind of an exception :-).
>>
>> Davide, the Evenett's video is great! Many demonstrations were quite
>> surprising, and I have nothing to add to it (maybe a note, that the
>> phase
>> contrast method in all its simplicity still yielded Zernike a Nobel
>> prize!).
>> But even though one thought follows from another nicely, at the end
>> if you
>> ask your students "So why does higher NA mean higher resolution?"
>> they'll
>> say "Well, uhm..." It's not very likely they'll gain a deeper
>> understanding
>> of how all these concepts fit together.
>>
>> Good luck!
>>
>> zdenee
>>
>> On Sat, Sep 19, 2020 at 12:25 PM George McNamara
>> <[hidden email]>
>> wrote:
>>
>>> *****
>>> 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.
>>> *****
>>>
>>> Hi Javier,
>>>
>>> I suggest you ask the class if they have any interest in taking photos
>>> with their smartphone or DSLR camera, and if they do, bring in a DSLR
>>> and tripod and computer/projector (if the room does not have that
>>> already), explain f/stop and NA are inverse of each other, and
>>> demonstrate NA (resolution, intensity, depth of field) on the class by
>>> focusing on faces in the middle row. Wavelength: yes, you could buy
>>> some
>>> filters for the camera lens (or deal with separating channels in
>>> Photoshop, fiji ImageJ, etc), but probably better done on a microscope.
>>>
>>> George
>>>
>>> p.s. this post was inspired by a conversation yesterday -- Friday happy
>>> hour -- with a colleague, Prof. Jim Potter, who told me about a
>>> conversation he had with someone with a very expensive digital camera
>>> hobby, who only used their cameras set to auto. Jim explained f/stop,
>>> ISO and more (framing scene etc). My thanks to Jim for good story with
>>> nice timing and especially foraging for the beverages.
>>>
>>> A fun (in theory, but probably not practical or wise) wavelength test
>>> would be to use bring in blue (~400 nm) and NIR (~800nm would be nice,
>>> values chosen to be 2 fold, not necessarily practical) and a smoke
>>> machine (and some 400nm and NIR friendly lighting in case room lights
>>> too dim at those wavelength), and demonstration resolution vs
>>> ability to
>>> see through the smoke (Mie scattering etc). If you do this, and the
>>> smoke alarm turns on, your school may not be happy with you (though all
>>> the students may be happy to escape class early).
>>>
>>> Of course if they vote no to learning about f/stop and NA, you can ask
>>> them how they expect to get to a million TikTok followers each without
>>> knowing how to take good quality videos. Come ot think of it, if
>>> they do
>>> vote yes, and you put your demo on your TikTok feed and make a lot of
>>> money, you can send me the URL and a thank you check.
>>>
>>> On 9/19/2020 5:38 AM, F Javier Diez Guerra wrote:
>>>> *****
>>>> 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.
>>>> *****
>>>>
>>>> Hello,
>>>>
>>>> I wonder if anybody in the list could help.
>>>>
>>>> I want to convey to biology undergraduate students (very allergic to
>>>> physics and mathematics) the understanding of the relationship between
>>>> numerical aperture and spatial resolution.
>>>>
>>>> I have already given them links to the different microscopy primer
>>>> sites. They find difficult to understand why the airy disk is
>>>> generated in the image plane, how the diffraction orders affect
>>>> resolution and why increasing NA reduces the image spot.
>>>>
>>>> Could anybody share a basic and intuitive infographic slide, animation
>>>> or any other resource that could help to ease comprehension in this
>>>> context?
>>>>
>>>> Thanks
>>>>
>>>> Javier
>>>>
>>>>
>>

--
------------------------------------------------------------
Steffen Dietzel, PD Dr. rer. nat
Ludwig-Maximilians-Universität München
Biomedical Center (BMC)
Head of the Core Facility Bioimaging

Großhaderner Straße 9
D-82152 Planegg-Martinsried
Germany

http://www.bioimaging.bmc.med.uni-muenchen.de

[lgelman]

*****
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http://lists.umn.edu/cgi-bin/wa?A0=confocalmicroscopy
Post images on http://www.imgur.com and include the link in your posting.
*****

Hi everybody,
I found the link between NA and PSF/Resolution pretty well illustrated in this video:
https://www.ibiology.org/talks/point-spread-function/
Very best regards,
Laurent.


Laurent Gelman
Facility for Advanced Imaging and Microscopy
Head Light Microscopy
Friedrich Miescher Institute for Biomedical Research
Maulbeerstrasse 66
4058 Basel
Switzerland
[phone]
www.fmi.ch
www.microscopynetwork.unibas.ch/en/home/





-----Original Message-----
From: Confocal Microscopy List <[hidden email]> On Behalf Of F Javier Diez Guerra
Sent: Saturday, September 19, 2020 21:22
To: [hidden email]
Subject: Re: Numerical aperture and spatial resolution

*****
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.
*****

Hi,

Thanks to all contributors for the excellent suggestions.

Unfortunately, at the present times, at least here in Madrid, most if not all university lectures are Teams sessions. So on-site demos are not a choice.

I also align with Zdenee's view. "Why does higher NA mean higher resolution?" is a question with no trivial answer for biologists. The demo of looking the diffraction orders at the BFP with a Bertrand lens, using objectives with different NA and gratings of different densities, worked best for me when I first learned about spatial resolution. Still, for a biology undergraduate is difficult to comprehend intuitively why capturing more diffraction orders means higher resolution.

Javier


El 19/09/2020 a las 20:27, Zdenek Svindrych escribió:

> *****
> 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.
> *****
>
> Hi George and Javier,
>
> regarding aperture and resolution of DSLR (actually mirror-less) I put
> some photos together here:
> https://drive.google.com/file/d/1vDYqDBPgapZYad3JahRm8R5W5Bkwu4T6
> But, it will only work with some lenses (well, with most, but not in
> the full F-stop range), and only with some cameras (more pixels is
> better here, kind of an exception :-).
>
> Davide, the Evenett's video is great! Many demonstrations were quite
> surprising, and I have nothing to add to it (maybe a note, that the
> phase contrast method in all its simplicity still yielded Zernike a Nobel prize!).
> But even though one thought follows from another nicely, at the end if
> you ask your students "So why does higher NA mean higher resolution?"
> they'll say "Well, uhm..." It's not very likely they'll gain a deeper
> understanding of how all these concepts fit together.
>
> Good luck!
>
> zdenee
>
> On Sat, Sep 19, 2020 at 12:25 PM George McNamara
> <[hidden email]>
> wrote:
>
>> *****
>> 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.
>> *****
>>
>> Hi Javier,
>>
>> I suggest you ask the class if they have any interest in taking
>> photos with their smartphone or DSLR camera, and if they do, bring in
>> a DSLR and tripod and computer/projector (if the room does not have
>> that already), explain f/stop and NA are inverse of each other, and
>> demonstrate NA (resolution, intensity, depth of field) on the class
>> by focusing on faces in the middle row. Wavelength: yes, you could
>> buy some filters for the camera lens (or deal with separating
>> channels in Photoshop, fiji ImageJ, etc), but probably better done on a microscope.
>>
>> George
>>
>> p.s. this post was inspired by a conversation yesterday -- Friday
>> happy hour -- with a colleague, Prof. Jim Potter, who told me about a
>> conversation he had with someone with a very expensive digital camera
>> hobby, who only used their cameras set to auto. Jim explained f/stop,
>> ISO and more (framing scene etc). My thanks to Jim for good story
>> with nice timing and especially foraging for the beverages.
>>
>> A fun (in theory, but probably not practical or wise) wavelength test
>> would be to use bring in blue (~400 nm) and NIR (~800nm would be
>> nice, values chosen to be 2 fold, not necessarily practical) and a
>> smoke machine (and some 400nm and NIR friendly lighting in case room
>> lights too dim at those wavelength), and demonstration resolution vs
>> ability to see through the smoke (Mie scattering etc). If you do
>> this, and the smoke alarm turns on, your school may not be happy with
>> you (though all the students may be happy to escape class early).
>>
>> Of course if they vote no to learning about f/stop and NA, you can
>> ask them how they expect to get to a million TikTok followers each
>> without knowing how to take good quality videos. Come ot think of it,
>> if they do vote yes, and you put your demo on your TikTok feed and
>> make a lot of money, you can send me the URL and a thank you check.
>>
>> On 9/19/2020 5:38 AM, F Javier Diez Guerra wrote:
>>> *****
>>> 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.
>>> *****
>>>
>>> Hello,
>>>
>>> I wonder if anybody in the list could help.
>>>
>>> I want to convey to biology undergraduate students (very allergic to
>>> physics and mathematics) the understanding of the relationship
>>> between numerical aperture and spatial resolution.
>>>
>>> I have already given them links to the different microscopy primer
>>> sites. They find difficult to understand why the airy disk is
>>> generated in the image plane, how the diffraction orders affect
>>> resolution and why increasing NA reduces the image spot.
>>>
>>> Could anybody share a basic and intuitive infographic slide,
>>> animation or any other resource that could help to ease
>>> comprehension in this context?
>>>
>>> Thanks
>>>
>>> Javier
>>>
>>>
>