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. ***** Dear listers, I am confused about the formulas for the Full Width Half Maximum of the point spread function along the optical axis. According to this paper: B. Amos, G. McConnell, T. Wilson: Confocal microscopy. In: E. Egelman (Hrsg.): Biophysical Techniques for Characterization of Cells (= Comprehensive Biophysics). Volume2. Elsevier, Academic Press, Amsterdam 2012, ISBN 978-0-12-374920-8 <https://de.wikipedia.org/wiki/Spezial:ISBN-Suche/9780123749208>, chapter 2, pages3–23, doi <https://de.wikipedia.org/wiki/Digital_Object_Identifier>:10.1016/B978-0-12-374920-8.00203-4 <https://doi.org/10.1016/B978-0-12-374920-8.00203-4> (free download here: http://www2.mrc-lmb.cam.ac.uk/images/groupleaders/Confocal_microscopy_Amos_McConnell_Wilson.pdf) on page 15 the formula (3) for a conventional microscope for FWHM(z) with high NA (> 0.5) is FWHM(z) = (0.88*lambda) / (n-sqrt(n^2 - NA^2)) where n is refractive index of the immersion medium. For NA <0.5 this reduces to formula (4): FWHM(z) = (1.77*n*lambda)/(NA^2) Now, let us assume we compare two objectives with the same NA but one oil immersion (n=1.518), one water immersion (n=1.33). Then, with both formulas we get bigger (and thus worse resolution) FWHMs with the oil objective. All other things the same, the bigger the RI of the immersion medium, the worse is the resolution in z. That does not sound right. Or is it? What am I missing? The same would apply to a confocal microscope, just with a slightly different formula (see paper, formulas 7 and 8). Best Steffen -- ------------------------------------------------------------ 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 |
James D. Manton-2 |
*****
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, The issue here is that you've fixed the NAs of the water and oil immersion lenses in your comparison, not the semiaperture angles. By fixing the NA, you've given the oil immersion lens a smaller semiaperture angle as NA = n sin (semiaperture angle) and n is larger. As the waves have a smaller range of angles to the optical axis, the length scale over which interference effects occur is larger. When considering the lateral resolution, this effect is balanced out by the reduction is wavelength by a factor of n from the vacuum wavelength, such that all lenses with the same NA provide the same lateral resolution, irrespective of n. However, this is not the case axially. I hope this explanation hasn't made things even more confusing than they were before... Best wishes, James On 19/02/2021 11:40, Steffen Dietzel 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. > ***** > > Dear listers, > > I am confused about the formulas for the Full Width Half Maximum of > the point spread function along the optical axis. According to this > paper: > > B. Amos, G. McConnell, T. Wilson: Confocal microscopy. In: E. Egelman > (Hrsg.): Biophysical Techniques for Characterization of Cells (= > Comprehensive Biophysics). Volume2. Elsevier, Academic Press, > Amsterdam 2012, ISBN 978-0-12-374920-8 > <https://de.wikipedia.org/wiki/Spezial:ISBN-Suche/9780123749208>, > chapter 2, pages3–23, doi > <https://de.wikipedia.org/wiki/Digital_Object_Identifier>:10.1016/B978-0-12-374920-8.00203-4 > <https://doi.org/10.1016/B978-0-12-374920-8.00203-4> > > (free download here: > http://www2.mrc-lmb.cam.ac.uk/images/groupleaders/Confocal_microscopy_Amos_McConnell_Wilson.pdf) > > on page 15 the formula (3) for a conventional microscope for FWHM(z) > with high NA (> 0.5) is > > FWHM(z) = (0.88*lambda) / (n-sqrt(n^2 - NA^2)) where n is refractive > index of the immersion medium. > > For NA <0.5 this reduces to formula (4): > > FWHM(z) = (1.77*n*lambda)/(NA^2) > > Now, let us assume we compare two objectives with the same NA but one > oil immersion (n=1.518), one water immersion (n=1.33). Then, with both > formulas we get bigger (and thus worse resolution) FWHMs with the oil > objective. All other things the same, the bigger the RI of the > immersion medium, the worse is the resolution in z. > > That does not sound right. Or is it? > > What am I missing? > > The same would apply to a confocal microscope, just with a slightly > different formula (see paper, formulas 7 and 8). > > Best > > Steffen > -- James Manton MRC Laboratory of Molecular Biology Cambridge CB2 0QH, UK +44 (0)1223 267788 |
Mark Cannell-2 |
In reply to this post by 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. ***** Would it help to substitute n.sin(alpha) for NA and think about the behaviour of the cone of rays coming from the sample? Cheers Mark B. Cannell. Ph.D. FRSNZ FISHR Department of Physiology, Pharmacology & Neuroscience School of Medical Sciences University Walk Bristol BS8 1TD [hidden email] On 19/02/21, 12:29 PM, "Confocal Microscopy List on behalf of Steffen Dietzel" <[hidden email] on behalf of [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. ***** Dear listers, I am confused about the formulas for the Full Width Half Maximum of the point spread function along the optical axis. According to this paper: B. Amos, G. McConnell, T. Wilson: Confocal microscopy. In: E. Egelman (Hrsg.): Biophysical Techniques for Characterization of Cells (= Comprehensive Biophysics). Volume2. Elsevier, Academic Press, Amsterdam 2012, ISBN 978-0-12-374920-8 <https://de.wikipedia.org/wiki/Spezial:ISBN-Suche/9780123749208>, chapter 2, pages3–23, doi <https://de.wikipedia.org/wiki/Digital_Object_Identifier>:10.1016/B978-0-12-374920-8.00203-4 <https://doi.org/10.1016/B978-0-12-374920-8.00203-4> (free download here: http://www2.mrc-lmb.cam.ac.uk/images/groupleaders/Confocal_microscopy_Amos_McConnell_Wilson.pdf) on page 15 the formula (3) for a conventional microscope for FWHM(z) with high NA (> 0.5) is FWHM(z) = (0.88*lambda) / (n-sqrt(n^2 - NA^2)) where n is refractive index of the immersion medium. For NA <0.5 this reduces to formula (4): FWHM(z) = (1.77*n*lambda)/(NA^2) Now, let us assume we compare two objectives with the same NA but one oil immersion (n=1.518), one water immersion (n=1.33). Then, with both formulas we get bigger (and thus worse resolution) FWHMs with the oil objective. All other things the same, the bigger the RI of the immersion medium, the worse is the resolution in z. That does not sound right. Or is it? What am I missing? The same would apply to a confocal microscope, just with a slightly different formula (see paper, formulas 7 and 8). Best Steffen -- ------------------------------------------------------------ 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 |
Zdenek Svindrych-2 |
In reply to this post by James D. Manton-2
*****
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. ***** Perfect explanation, James, thanks! I made the same observation when I was playing with PSF generators - the accurate models produced more elongated PSF at higher RI, given the same NA. zd On Fri, Feb 19, 2021 at 7:38 AM James D. Manton <[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. > ***** > > Dear Steffen, > > The issue here is that you've fixed the NAs of the water and oil > immersion lenses in your comparison, not the semiaperture angles. By > fixing the NA, you've given the oil immersion lens a smaller > semiaperture angle as NA = n sin (semiaperture angle) and n is larger. > As the waves have a smaller range of angles to the optical axis, the > length scale over which interference effects occur is larger. When > considering the lateral resolution, this effect is balanced out by the > reduction is wavelength by a factor of n from the vacuum wavelength, > such that all lenses with the same NA provide the same lateral > resolution, irrespective of n. However, this is not the case axially. > > I hope this explanation hasn't made things even more confusing than they > were before... > > Best wishes, > James > > > > > On 19/02/2021 11:40, Steffen Dietzel 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. > > ***** > > > > Dear listers, > > > > I am confused about the formulas for the Full Width Half Maximum of > > the point spread function along the optical axis. According to this > > paper: > > > > B. Amos, G. McConnell, T. Wilson: Confocal microscopy. In: E. Egelman > > (Hrsg.): Biophysical Techniques for Characterization of Cells (= > > Comprehensive Biophysics). Volume2. Elsevier, Academic Press, > > Amsterdam 2012, ISBN 978-0-12-374920-8 > > <https://de.wikipedia.org/wiki/Spezial:ISBN-Suche/9780123749208>, > > chapter 2, pages3–23, doi > > <https://de.wikipedia.org/wiki/Digital_Object_Identifier>:10.1016/B978-0-12-374920-8.00203-4 > > > <https://doi.org/10.1016/B978-0-12-374920-8.00203-4> > > > > (free download here: > > > http://www2.mrc-lmb.cam.ac.uk/images/groupleaders/Confocal_microscopy_Amos_McConnell_Wilson.pdf > ) > > > > on page 15 the formula (3) for a conventional microscope for FWHM(z) > > with high NA (> 0.5) is > > > > FWHM(z) = (0.88*lambda) / (n-sqrt(n^2 - NA^2)) where n is refractive > > index of the immersion medium. > > > > For NA <0.5 this reduces to formula (4): > > > > FWHM(z) = (1.77*n*lambda)/(NA^2) > > > > Now, let us assume we compare two objectives with the same NA but one > > oil immersion (n=1.518), one water immersion (n=1.33). Then, with both > > formulas we get bigger (and thus worse resolution) FWHMs with the oil > > objective. All other things the same, the bigger the RI of the > > immersion medium, the worse is the resolution in z. > > > > That does not sound right. Or is it? > > > > What am I missing? > > > > The same would apply to a confocal microscope, just with a slightly > > different formula (see paper, formulas 7 and 8). > > > > Best > > > > Steffen > > > > -- > James Manton > MRC Laboratory of Molecular Biology > Cambridge CB2 0QH, UK > +44 (0)1223 267788 > -- -- Zdenek Svindrych, Ph.D. Research Scientist - Microscopy Imaging Specialist Department of Biochemistry and Cell Biology Geisel School of Medicine at Dartmouth |
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. ***** Thanks guys, the explanation sounds reasonable even to me. I am now confused on a much higher level compared to before ;-) Best Steffen Am 19.02.2021 um 14:36 schrieb Zdenek Svindrych: > ***** > 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. > ***** > > Perfect explanation, James, thanks! > I made the same observation when I was playing with PSF generators - the > accurate models produced more elongated PSF at higher RI, given the same NA. > zd > > On Fri, Feb 19, 2021 at 7:38 AM James D. Manton <[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. >> ***** >> >> Dear Steffen, >> >> The issue here is that you've fixed the NAs of the water and oil >> immersion lenses in your comparison, not the semiaperture angles. By >> fixing the NA, you've given the oil immersion lens a smaller >> semiaperture angle as NA = n sin (semiaperture angle) and n is larger. >> As the waves have a smaller range of angles to the optical axis, the >> length scale over which interference effects occur is larger. When >> considering the lateral resolution, this effect is balanced out by the >> reduction is wavelength by a factor of n from the vacuum wavelength, >> such that all lenses with the same NA provide the same lateral >> resolution, irrespective of n. However, this is not the case axially. >> >> I hope this explanation hasn't made things even more confusing than they >> were before... >> >> Best wishes, >> James >> >> >> >> >> On 19/02/2021 11:40, Steffen Dietzel 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. >>> ***** >>> >>> Dear listers, >>> >>> I am confused about the formulas for the Full Width Half Maximum of >>> the point spread function along the optical axis. According to this >>> paper: >>> >>> B. Amos, G. McConnell, T. Wilson: Confocal microscopy. In: E. Egelman >>> (Hrsg.): Biophysical Techniques for Characterization of Cells (= >>> Comprehensive Biophysics). Volume2. Elsevier, Academic Press, >>> Amsterdam 2012, ISBN 978-0-12-374920-8 >>> <https://de.wikipedia.org/wiki/Spezial:ISBN-Suche/9780123749208>, >>> chapter 2, pages3–23, doi >>> <https://de.wikipedia.org/wiki/Digital_Object_Identifier>:10.1016/B978-0-12-374920-8.00203-4 >>> <https://doi.org/10.1016/B978-0-12-374920-8.00203-4> >>> >>> (free download here: >>> >> http://www2.mrc-lmb.cam.ac.uk/images/groupleaders/Confocal_microscopy_Amos_McConnell_Wilson.pdf >> ) >>> on page 15 the formula (3) for a conventional microscope for FWHM(z) >>> with high NA (> 0.5) is >>> >>> FWHM(z) = (0.88*lambda) / (n-sqrt(n^2 - NA^2)) where n is refractive >>> index of the immersion medium. >>> >>> For NA <0.5 this reduces to formula (4): >>> >>> FWHM(z) = (1.77*n*lambda)/(NA^2) >>> >>> Now, let us assume we compare two objectives with the same NA but one >>> oil immersion (n=1.518), one water immersion (n=1.33). Then, with both >>> formulas we get bigger (and thus worse resolution) FWHMs with the oil >>> objective. All other things the same, the bigger the RI of the >>> immersion medium, the worse is the resolution in z. >>> >>> That does not sound right. Or is it? >>> >>> What am I missing? >>> >>> The same would apply to a confocal microscope, just with a slightly >>> different formula (see paper, formulas 7 and 8). >>> >>> Best >>> >>> Steffen >>> >> -- >> James Manton >> MRC Laboratory of Molecular Biology >> Cambridge CB2 0QH, UK >> +44 (0)1223 267788 >> > ------------------------------------------------------------ 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 |
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