Nyquist sampling advice for a short talk
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Moulding, Dale |
Nyquist sampling advice for a short talk
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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 all, I'm planning to make a short (15min) video on Nyquist sampling. I wonder if I could call on the list's hive mind for a little advice on any key points or resources I should include? For example: Resolution is not pixel size! Airy disk, Abbe, Raleigh. Camera vs Point scanning. Key resources: http://zeiss-campus.magnet.fsu.edu/articles/basics/resolution.html https://www.microscopyu.com/ https://www.leica-microsystems.com/science-lab/science-lab-home/ https://micro.magnet.fsu.edu/primer/index.html I'd be really grateful for any ideas. cheers Dale |
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James D. Manton-2 |
Re: Nyquist sampling advice for a short talk
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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 Dale, I'm going to make some suggestions, of which I think many on the list will find at least a few objectionable. I'll list them all first, then provide justification below. == Suggestions == 1. Don't bother mentioning the Airy disk, Rayleigh and Sparrow criteria, etc.. 2. Use the Abbe criterion for determining theoretically achievable resolution, both laterally and axially, with the sampling being at twice this rate. 3. Don't overemphasise the difference between a point scanner and a camera-based system. The point scanner lets you place your pixels where you want them, but the job being performed, and hence the sampling conditions (modulo confocal pinhole effects), are the same. 4. Measuring the resolution of an image is, in many cases, more useful than measuring the resolution of an instrument. While many people know how to measure PSFs, few seem to know how to achieve the former. For this, I recommend the Demmerle et al. article at https://doi.org/10.1016/j.ymeth.2015.07.001. Fourier Ring Correlation should be avoided if at all possible. 5. If you expect your audience to know Fourier transforms, it's worth talking about the OTF as the Fourier dual of the PSF. This lets you show how the noise floor alters the resolution limit given by Abbe, and hence the sampling condition, with a new cutoff of the Fourier support. 6. If you don't expect your audience to know Fourier transforms, don't try and include anything Fourier-related (including point 4). 15 minutes is not enough time. == Justifications == 1. The Rayleigh and Sparrow criteria were developed in a background of naked eye stellar astronomy, where the question was whether an observer could distinguish a double star from a single star. These observations are very different from the vast majority of microscopical observations for which the image is much more complicated. Only the Abbe criterion is based on fundamental physical law and is the only one which is readily combined with the understanding of signal theory that was developed later, in the 20th century (i.e. Abbe + Nyquist-Shannon makes sense, while Rayleigh + Nyquist-Shannon does not). 2. The Abbe criterion gives the lateral resolution as wavelength / (2 * numerical aperture), and the axial resolution as wavelength / (refractive index * (1 - cos(arcsin(numerical aperture / refractive index))). These can be derived from a consideration of the Ewald sphere, but I think that would be too much for a 15 minute video. Nyquist-Shannon shows that the sampling rate should be at half those distances. Extra factors of sqrt(2), or whatever, that people like to throw in because we have 'square pixels' are erroneous and should perhaps not be discussed for risk of confusion. 3. This falls over when we get into 'exotic' point scanning schemes like Lissajous patterns and the corresponding Chebyshev polynomial sampling theory, but hardly anyone in the world needs to worry about that. 4. The 'Radial Profile Extended' ImageJ plugin is quite useful for a basic version of the Demmerle et al. Fourier Spectral Analysis (https://imagej.nih.gov/ij/plugins/radial-profile-ext.html). Fourier Ring Correlation relies on arbitrary thresholds with no underlying physical justification and is harder to calculate. Showing a radially averaged Fourier spectrum is more informative and more clearly shows the difference between instruments where the absolute resolution limit is the same but the intermediate transfer is different (e.g. ISM/Airyscan vs SIM). 5. Both dominant noise types in microscopy (Poisson and Gaussian) are spectrally white and hence contribute a flat noise floor in the Fourier domain. Other sources of noise, such as the correlated noise from different sub-detectors in an Airyscan, are much harder to reason about, but they are infrequently as important. 6. True understanding of resolution limits and appropriate sampling comes when people are confident with autocorrelating (complex) functions and converting between real space and the Fourier domain. In my experience, even most physics graduate students, who have already been subjected to introductory courses on Fourier transforms, struggle with this for much longer than 15 minutes. I look forward to hearing people's arguments against these suggestions. Good luck with the video, James -- James Manton MRC Laboratory of Molecular Biology Cambridge CB2 0QH, UK +44 (0)1223 267788 |
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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. ***** Well, the question was specifically about Nyquist, and, I gather, as an introduction of some sorts, not for advanced physics students. What I always stress when explaining sampling, is to first differentiate between the Abbe criterion, explained as the *physics-based theoretical limit* on resolution, and how we *detect *that resolution. You don't even need to explain Abbe very well, and the causes and the parts of the equation, as long as they understand that there exists something called the "Abbe criterion" that refers to the "best possible resolution physics allows". Then, I get into how to detect, or in sciencese, *sample*, what is allowable by physics. I have some slides (I think I got them originally from the wonderful lecture series by Paul Robinson from Purdue) showing the idea of sampling that Nyquist originated. (e.g. signal, sample, and if not enough sample, the recreated signal will be lacking thus "undersampled" etc). Once they understand the concept of sampling in general, it's now easy to show why pixel size in imaging is sampling and is important to determine the "Nyquist". (Pixel size for lateral and "slice number" for axial). For this I use a self-customized (I doubled the disk) version of the Zeiss "projected size of airy disk on ccd array" graphic showing an airy disk on four same size FoVs but with different pixel sizes. I show that when undersampled, even though the center of the disks of the two points of light are more than say 300nm from each other (so physics is not the limiting factor), you won't be able to detect it. I think that explaining the concept in this manner gives a very good intuitive understanding. I actually think it's very appropriate to mention point scanning systems, because only thus can you determine your pixel size. With camera-based systems, the max sampling is what it is - limited by the physical size of the chip pixels - you can't oversample even if you wanted to (though you can undersample by binning, of course.) Avi -- Avi Jacob, Ph.D. The Kanbar Light Microscopy Unit The Goodman Faculty of Life Sciences Bar-Ilan University, Ramat-Gan 5290002, Israel <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> Virus-free. www.avg.com <http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail> <#m_-3374090109714886774_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> |
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In reply to this post by Moulding, Dale
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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. ***** Dale, I really like the following applets for demonstrating resolution and sampling in practice, and connecting theory to experimental design. http://www.iscopecalc.com https://www.olympus-lifescience.com/en/microscope-resource/primer/java/imageformation/rayleighdisks/ Sara Parker Postdoctoral Fellow, Mouneimne Lab (520) 626-3860 [hidden email] Department of Cellular & Molecular Medicine University of Arizona |
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Craig Brideau |
Re: Nyquist sampling advice for a short talk
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In reply to this post by Avi Jacob
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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. ***** I also find instructors do not include the impact of dynamic range on resolution. If you consider the classic example of discerning two separate points, you have a pair of Gaussian curves sitting next to each other. As they approach, a valley forms between the curves. The 'floor' of this valley rises as the two curves begin to merge. Your ability to tell the two peaks apart depends on how well you can resolve the floor of the valley between the two Gaussians. If your image is over exposed, or has low dynamic range (8 bit say, vs 12 bit) you will have a harder time detecting that valley and thus the two peaks start to appear as a single peak. Many users tend to saturate their images, and if they are attempting segmentation or point counting this can severely impact the accuracy. Craig On Tue, Nov 10, 2020 at 8:58 AM Avi Jacob <[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. > ***** > > Well, the question was specifically about Nyquist, and, I gather, as an > introduction of some sorts, not for advanced physics students. > > What I always stress when explaining sampling, is to first differentiate > between the Abbe criterion, explained as the *physics-based theoretical > limit* on resolution, and how we *detect *that resolution. You don't even > need to explain Abbe very well, and the causes and the parts of the > equation, as long as they understand that there exists something called the > "Abbe criterion" that refers to the "best possible > resolution physics allows". > Then, I get into how to detect, or in sciencese, *sample*, what is > allowable by physics. > > I have some slides (I think I got them originally from the > wonderful lecture series by Paul Robinson from Purdue) showing the idea of > sampling that Nyquist originated. (e.g. signal, sample, and if not enough > sample, the recreated signal will be lacking thus "undersampled" etc). > > Once they understand the concept of sampling in general, it's now easy to > show why pixel size in imaging is sampling and is important to determine > the "Nyquist". (Pixel size for lateral and "slice number" for axial). For > this I use a self-customized (I doubled the disk) version of the Zeiss > "projected size of airy disk on ccd array" graphic showing an airy disk on > four same size FoVs but with different pixel sizes. I show that when > undersampled, even though the center of the disks of the two points of > light are more than say 300nm from each other (so physics is not the > limiting factor), you won't be able to detect it. > > I think that explaining the concept in this manner gives a very good > intuitive understanding. > > I actually think it's very appropriate to mention point scanning systems, > because only thus can you determine your pixel size. With > camera-based systems, the max sampling is what it is - limited by the > physical size of the chip pixels - you can't oversample even if you wanted > to (though you can undersample by binning, of course.) > > Avi > -- > Avi Jacob, Ph.D. > The Kanbar Light Microscopy Unit > The Goodman Faculty of Life Sciences > Bar-Ilan University, Ramat-Gan 5290002, Israel > > > > < > http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail > > > Virus-free. > www.avg.com > < > http://www.avg.com/email-signature?utm_medium=email&utm_source=link&utm_campaign=sig-email&utm_content=webmail > > > <#m_-3374090109714886774_DAB4FAD8-2DD7-40BB-A1B8-4E2AA1F9FDF2> > |
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Benjamin Smith |
Re: Nyquist sampling advice for a short talk
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In reply to this post by sparker
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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. ***** GIven that most microscopy has the luxury of being a simpler specific case of the Nyquist sampling theorem, I like to simplify it to a discrete model using a checkerboard. I first show a grid of squares and ask, "What is the smallest feature we can resolve on this grid?" I then show a checkerboard pattern next to a grid with all white squares. I point out that in order to resolve two objects means to be able to distinguish between two point sources and one bigger solid source. Therefore, you need to sample not only the peak intensities (your resolution) but also a local minimum between them to distinguish a pair of points from a solid object. Therefore, you need to sample at 2x your resolution. The hope here is to give people an intuitive sense of where Nyquist sampling theory comes from without delving into more complex issues like aliasing. On Tue, Nov 10, 2020 at 8:26 AM Sara Parker <[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. > ***** > > Dale, > > I really like the following applets for demonstrating resolution and > sampling in practice, and connecting theory to experimental design. > > http://www.iscopecalc.com > > https://www.olympus-lifescience.com/en/microscope-resource/primer/java/imageformation/rayleighdisks/ > > Sara Parker > Postdoctoral Fellow, Mouneimne Lab > (520) 626-3860 > [hidden email] > Department of Cellular & Molecular Medicine > University of Arizona > -- Benjamin E. Smith, Ph. D. Imaging Specialist, Vision Science University of California, Berkeley 195 Life Sciences Addition Berkeley, CA 94720-3200 Tel (510) 642-9712 Fax (510) 643-6791 e-mail: [hidden email] https://vision.berkeley.edu/faculty/core-grants-nei/core-grant-microscopic-imaging/ |
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Glyn Nelson |
Re: Nyquist sampling advice for a short talk
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In reply to this post by Moulding, Dale
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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 Dale, I found (via Twitter I think) this video by Peter Evennett. As a practical demonstration of resolution about half way through it is excellent, and may be easier to grasp for students than the purely dry physics theory. Mind you, beware that it is using transmission rather than reflection, so the 2 NAs are not necessarily the same for the calculations, so this may confuse them further! https://www.youtube.com/watch?v=60_jgZtyR6U&t=2468s about 20 mins in and further on. Even demonstrates the difference with wavelength. Really well done I think. Otherwise, I'd '+1' Avi and Craig's answers. Glyn. |
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Straatman, Kees (Dr.) |
Re: Nyquist sampling advice for a short talk
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Carina Monico-2 |
Re: Nyquist sampling advice for a short talk
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Steffen Dietzel |
Re: Nyquist sampling advice for a short talk
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In reply to this post by Moulding, Dale
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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. ***** Dale, you can find my shot at explaining this in a powerpoint here: https://www.bioimaging.bmc.med.uni-muenchen.de/learn/materialdownload/index.html The one "Basics of Digital Imaging" contains slides on that, and on Poisson noise. As Craig pointed out, resolution makes not much sense without intensities. And thus noise. I do use Rayleigh criterion to explain this. I feel for Biologists, that makes kind of sense. Good Luck! Steffen Am 10.11.2020 um 13:51 schrieb Dale Moulding: > ***** > 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 all, > > I'm planning to make a short (15min) video on Nyquist sampling. I > wonder if I could call on the list's hive mind for a little advice on > any key points or resources I should include? > For example: > Resolution is not pixel size! > Airy disk, Abbe, Raleigh. > Camera vs Point scanning. > > Key resources: > http://zeiss-campus.magnet.fsu.edu/articles/basics/resolution.html > https://www.microscopyu.com/ > https://www.leica-microsystems.com/science-lab/science-lab-home/ > https://micro.magnet.fsu.edu/primer/index.html > > I'd be really grateful for any ideas. > > cheers > > Dale -- ------------------------------------------------------------ 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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Craig Brideau |
Re: Nyquist sampling advice for a short talk
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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. ***** On Wed, Nov 11, 2020 at 6:57 AM Steffen Dietzel <[hidden email]> wrote: > > The one "Basics of Digital Imaging" contains slides on that, and on > Poisson noise. As Craig pointed out, resolution makes not much sense > without intensities. And thus noise. > > That's an excellent point, Steffen. Contrast is required to separate two objects (the aforementioned "valley" between two hills) and contrast requires dynamic range and low noise. A poor dynamic range would be very vulnerable to noise contamination, and even a high dynamic range would be vulnerable to a high noise floor. Quite a bit to consider here! Craig |
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Moulding, Dale |
Re: Nyquist sampling advice for a short talk
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In reply to this post by Glyn Nelson
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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. ***** Wow, thanks for all the responses. As a biologist I admit some may have gone straight over my head (the fourier domain will likely remain a place of mystery and magic to me), but I’ve got plenty to get my teeth into here. The plan is to keep it nice and simple. Nothing too much more technical than my checkerboard mouse mat that's regularly used as a Nyquist teaching tool. Love the applets, these will be really helpful. Cheers Dale -----Original Message----- From: Confocal Microscopy List <[hidden email]> On Behalf Of Glyn Nelson Sent: 11 November 2020 08:38 To: [hidden email] Subject: Re: Nyquist sampling advice for a short talk ***** To join, leave or search the confocal microscopy listserv, go to: https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=04%7C01%7C%7C010ecac4e50f4b34fcb008d886e99556%7C1faf88fea9984c5b93c9210a11d9a5c2%7C0%7C1%7C637407685103690142%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=CdZXoy%2BVw3JTpwv04n9zuBsauDrdW9dSeHg68iDQHgg%3D&reserved=0 Post images on https://eur01.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com%2F&data=04%7C01%7C%7C010ecac4e50f4b34fcb008d886e99556%7C1faf88fea9984c5b93c9210a11d9a5c2%7C0%7C1%7C637407685103690142%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=D%2F5K%2BdV547VnaptLfEQdRBxRvufgitFW5OPhjpfNq5Y%3D&reserved=0 and include the link in your posting. ***** Hi Dale, I found (via Twitter I think) this video by Peter Evennett. As a practical demonstration of resolution about half way through it is excellent, and may be easier to grasp for students than the purely dry physics theory. Mind you, beware that it is using transmission rather than reflection, so the 2 NAs are not necessarily the same for the calculations, so this may confuse them further! https://eur01.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D60_jgZtyR6U%26t%3D2468s&data=04%7C01%7C%7C010ecac4e50f4b34fcb008d886e99556%7C1faf88fea9984c5b93c9210a11d9a5c2%7C0%7C1%7C637407685103690142%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C3000&sdata=NIknXGHDKq4xIRajulKMWmI60SoS77uCuo1Hnqoyues%3D&reserved=0 about 20 mins in and further on. Even demonstrates the difference with wavelength. Really well done I think. Otherwise, I'd '+1' Avi and Craig's answers. Glyn. |
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Tim Feinstein |
Re: Nyquist sampling advice for a short talk
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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. ***** I must be weird, because I find that a fairly complex concept like the denoising feature of deconvolution makes the overall lesson about sampling much easier to teach. Most trainees aren't ready for a physics lecture, but they get that an algorithm can flag a signal as 'real' as long as you sample with enough resolution to make sure that each point source shows up in two adjacent voxels. Since the intensity of a noise pixel is uncorrelated with any adjacent pixel, you can detect most of them and filter them out. Then I explain how the imaging system & sample prep determine the PSF size, and I show trainees how to find a PSF calculator like the one SVI has on their site when they need to work out the necessary dimensions for themselves (no commercial interest; why doesn't Autoquant's website have one?). I think the focus on problem solving helps with retention. All the best, T Timothy Feinstein, Ph.D. Research Scientist Department of Developmental Biology University of Pittsburgh On 11/12/20, 8:49 AM, "Confocal Microscopy List on behalf of Moulding, Dale" <[hidden email] on behalf of [hidden email]> wrote: ***** To join, leave or search the confocal microscopy listserv, go to: https://nam12.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=04%7C01%7Ctnf8%40PITT.EDU%7C41ed5352ae574cc3059708d88711b786%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1%7C0%7C637407857447790338%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=qqeGg40R9MNEZuAwORSBYTCVQ4YOcCKjOdj4GdlhmZY%3D&reserved=0 Post images on https://nam12.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com%2F&data=04%7C01%7Ctnf8%40PITT.EDU%7C41ed5352ae574cc3059708d88711b786%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1%7C0%7C637407857447790338%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=evK3ek2xw9ygLfYQZfks46gm6L9vDAo%2BaeKHK1%2Fe6CU%3D&reserved=0 and include the link in your posting. ***** Wow, thanks for all the responses. As a biologist I admit some may have gone straight over my head (the fourier domain will likely remain a place of mystery and magic to me), but I’ve got plenty to get my teeth into here. The plan is to keep it nice and simple. Nothing too much more technical than my checkerboard mouse mat that's regularly used as a Nyquist teaching tool. Love the applets, these will be really helpful. Cheers Dale -----Original Message----- From: Confocal Microscopy List <[hidden email]> On Behalf Of Glyn Nelson Sent: 11 November 2020 08:38 To: [hidden email] Subject: Re: Nyquist sampling advice for a short talk ***** To join, leave or search the confocal microscopy listserv, go to: https://nam12.safelinks.protection.outlook.com/?url=http%3A%2F%2Flists.umn.edu%2Fcgi-bin%2Fwa%3FA0%3Dconfocalmicroscopy&data=04%7C01%7Ctnf8%40PITT.EDU%7C41ed5352ae574cc3059708d88711b786%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1%7C0%7C637407857447790338%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=qqeGg40R9MNEZuAwORSBYTCVQ4YOcCKjOdj4GdlhmZY%3D&reserved=0 Post images on https://nam12.safelinks.protection.outlook.com/?url=http%3A%2F%2Fwww.imgur.com%2F&data=04%7C01%7Ctnf8%40PITT.EDU%7C41ed5352ae574cc3059708d88711b786%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1%7C0%7C637407857447790338%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=evK3ek2xw9ygLfYQZfks46gm6L9vDAo%2BaeKHK1%2Fe6CU%3D&reserved=0 and include the link in your posting. ***** Hi Dale, I found (via Twitter I think) this video by Peter Evennett. As a practical demonstration of resolution about half way through it is excellent, and may be easier to grasp for students than the purely dry physics theory. Mind you, beware that it is using transmission rather than reflection, so the 2 NAs are not necessarily the same for the calculations, so this may confuse them further! https://nam12.safelinks.protection.outlook.com/?url=https%3A%2F%2Fwww.youtube.com%2Fwatch%3Fv%3D60_jgZtyR6U%26t%3D2468s&data=04%7C01%7Ctnf8%40PITT.EDU%7C41ed5352ae574cc3059708d88711b786%7C9ef9f489e0a04eeb87cc3a526112fd0d%7C1%7C0%7C637407857447790338%7CUnknown%7CTWFpbGZsb3d8eyJWIjoiMC4wLjAwMDAiLCJQIjoiV2luMzIiLCJBTiI6Ik1haWwiLCJXVCI6Mn0%3D%7C1000&sdata=FCJ1iamWAtfD8bAQBBP2puPouKdpuK0ZsxYTu4W6dVo%3D&reserved=0 about 20 mins in and further on. Even demonstrates the difference with wavelength. Really well done I think. Otherwise, I'd '+1' Avi and Craig's answers. Glyn. |
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In reply to this post by Carina Monico-2
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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 all, Anyone got a spare/used Olympus LD405nm for sale or barter? Ours is ageing fast and needs to be replaced. There are limited options on ebay , but I am a bit sceptical of the condition, in particular the output power. I would prefer to get it from somebody on this list. All the best Peter Centre for Microscopy and Imaging National University of Ireland Galway Ireland www.imaging.nuigalway.ie<http://www.imaging.nuigalway.ie> |
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