Full Text Search Results

Searching for "Nyquist rate" .....

Faq Items To Import*
Faq Microscopy: This is part of the HuygensFaq. * What are the internal magnifications of the Biorad 1024 and the Biorad Radiance? Answer. * What's a bandlimited sys [...]; This is part of the HuygensFaq.; * Literature reference on widefield and confocal Nyquist rates? [Answer|NyquistAliasingBandwidthBandpassImpFaq].; * Is the sampling rate a function of the structure that you're modeling? [Answer|BandlimitedSystemShannonSamplingImpFaq].; * What is an undersampled stack of images? [Answer|UndersampledStackNyquistSamplingImpFaq].; * Nyquist rate - What's an asin? [Answer|NyquistAsinImpFaq].; * How to compute the Nyquist rate for an image? [Answer|NyquistBandwidthImpFaq].; * How to compute the Nyquist rate with 2-photon excitation? [Answer|ExcitationWavelength2-photonNyquistImpFaq].; * Does the pinhole size affect the Nyquist rate? [Answer|PinholeSizeNyquistRateTwo-photonImpFaq].; * What is the maximal voxel size at which Huygens can still do a good job. [Answer|SamplingNaNyquistNumericalApertureImpFaq].
Sphere Bandlimited Ringing Imp Faq*
Nyquist Aliasing Bandwidth Bandpass Imp Faq: For a general discussion on correct sampling and aliasing see: / Gonzalez, R.C. and R.E. Woods. (1992) Digital Image Processing. / Addison-Wesley. IS [...]; !! Literature reference on widefield and confocal Nyquist rates?; For a practical discussion see also SVI's 'Deconvolution Recipes' manual or the NyquistCalculator and NyquistRate.; '-__Keywords:__ Nyquist aliasing bandwidth bandpass-'%%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Undersampled Stack Nyquist Sampling Imp Faq: Is a stack called undersampled when the Z intervals between images, i.e. the voxel height, is too large with regard to the objective magnification an [...]; Undersampling means that the sampling interval is too large to capture all information about the object generated by the microscope. In Huygens Essential the sampling values will be colored orange in case of undersampling. In case of severe undersampling the color will be red. %%%; In Huygens Pro the optimal sampling density for the optical conditions under which an image is recorded can be computed by selecting its thumbnail and then Edit->Nyquist. When an image is recorded at this so called Nyquist frequency the digitized sequence contains *all* information carried in the signal. This makes it possible to reconstruct the image at any location, so not limited to the sampling positions. The Nyquist frequency is twice the highest spatial frequency (bandlimit) transmitted by the microscope.; '-__Keywords:__ undersampled stack Nyquist sampling-'%%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Nyquist Bandwidth Imp Faq: See NyquistRate and NyquistCalculator. The following formulas can be used to compute the Nquist rate: Widefield microscope: / Nyquist_lateral = lambd [...]; !! How to compute the Nyquist rate for an image?; See NyquistRate and NyquistCalculator.; The following formulas can be used to compute the Nquist rate:; Nyquist_lateral = lambda / ( 4 n sin(alpha)) %%%; Nyquist_axial = lambda / ( 4 n (1 - cos(alpha))); Assuming the excitation and emission wavelength are equal a confocal microscope *doubles* the bandwidth so *halves* the Nyquist sampling density.; Both Huygens Pro and Essential take the exact wavelength into account when computing the Nyquist rate. In case of multi photon excitation they also take the number of excitation photons into account. Both will color the background of X, Y, Z sampling density entry fields orange (moderate undersampling) or red (serious undersampling) when detecting undersampling.; In Huygens Pro you can look up the Nyquist rate for a particular image by selecting it and Edit->Nyquist rate.; '-__Keywords:__ Nyquist bandwidth-'%%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Option Modules Imp Faq: How does each module work and what are is advantage in using these modules for each type of image. To start: the time, multi photon options are indep [...]; - a number of basic values is computed differently, for instance the Nyquist rate, the expected two-point resolution, and so on. %%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Excitation Wavelength 2-photon Nyquist Imp Faq: If in 2-photon excitation a pinhole is not used it is the excitation distribution which determines the imaging properties of the microscope and there [...]; !! How to compute the Nyquist rate with 2-photon excitation?; If in 2-photon excitation a pinhole is not used it is the excitation distribution which determines the imaging properties of the microscope and therefore the Nyquist rate.; microscope, but since due to the 2-photon effect the effective excitation distribution is the square of the intensity distribution, the imaging properties are vastly different. The squaring operation makes the distribution more 'peaked', resulting in an improved resolution. It also causes the bandwidth (and with that the Nyquist rate) in x, y, z to be twice that of a widefield microscope at the same wavelength. %%%; '-__Keywords:__ excitation wavelength 2-photon nyquist-'%%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Sampling Confocal Widefield Imp Faq: Widefield and confocal microscopes differ in the amount of information they are able to extract from a specimen. One way to express this is to look a [...]; According to the Nyquist theorem a signal should be sampled at twice its highest bandwidth so confocal microscopes need twice the sampling density of widefield microscopes. %%%; Although the confocal microscope is able to transmit twice as fine details as the widefield microscope, unfortunately it attenuates these very strongly. Beyond say 60% of the highest frequency practically nothing is transmitted, especially for not-ideal pinhole cases. Therefore, if you use the theoretical Nyquist sampling rate you are very much in the clear. But it is defensible to use a practical Nyquist rate at 60% of the theoretical rate, or one sample per 50/0.6= 80nm. %%%; For more details see SamplingDensity and NyquistRate.; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Super Resolution Sampling Imp Faq: Am I correct to think that the ideal sampling rate is infinite, and anything else represents a compromise. The formula in the manual seems to imply t [...]; Am I correct to think that the ideal sampling rate is infinite, and anything else represents a compromise. The formula in the manual seems to imply that there are physical limits to one's ability to deconvolve that are solidly based on optics--not on photobleaching, detector sensitivity, numbers of photons emitted or the size of the bead.; The NyquistRate (similar to the Shannon theorem) says that IF a signal is [bandlimitedImpFaq], it is sufficient to sample it at twice the highest frequency. Then, it is possible to reconstruct the signal at ALL locations, perfectly. So in principle it is sufficient to sample at the Nyquist rate. Taking more samples does not get you more information about the object. In short, the ideal sampling rate is not infinite. Still, taking more samples with the same number of photons per pixel will improve the quality of the deconvolution result. Vice versa, taking more samples allows you to achieve the same quality in the deconvolution result at lower photon counts per pixel. %%%; BTW: If you sample below the Nyquist rate you get AliasingArtifacts (moire patterns, straircasing).; A different matter is two-point SpatialResolution: separating two objects. It is very hard to separate two objects reliably at distances smaller than the Nyquist distance.; To see what is the ideal sampling for your setup see NyquistCalculator.; '-__Keywords:__ sampling nyquist psf SNR noise superresolution super-resolution-'%%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Sampling Density ZImp Faq: What is an optimal sampling density in Z? The ConfocalMicroscope provides more information than the widefield system; in theory the confocal Sampling [...]; In the same typical confocal case a nice sampling rate would be 50 nm in Z, 150 nm axially. In case of [bleaching|BleachingEffects] problems you can stretch this up to 75 nm lateral, and after that increase the Z-sampling.; See NyquistRate.; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Pinhole Size Nyquist Rate Two-photon Imp Faq: See PinholeAndBandwidth. In principle, the Nyquist rate is independent of the pinhole size. This is due to the choice to relate the Nyquist rate to t [...]; !! Does the pinhole size affect the Nyquist rate?; In principle, the Nyquist rate is independent of the pinhole size. This is due to the choice to relate the Nyquist rate to the theoretical bandwidth of the system: the spatial frequency beyond which *nothing* is transferred by the microscope.; It would be a different story if we would have used a criterion based on attenuation of spatial frequencies below a certain factor. (Larger pinhole sizes attenuate higher frequencies more, but still are not zero). Although a practical approach (because about last third of the band has so low intensities that they can be considered zero most of the times) this involves an arbitrary choice, so therefore we base the Nyquist rate on the well defined theoretical bandwidth.; A problem occurs with extremely large pinholes like those used in two-photon systems. In these cases the optical properties are practically identical to a widefield system whereas due to the presence of the pinhole the theoretical bandlimit is still that of a confocal microscope. In the two-photon case it is best to set the microscope type to 'widefield' when doing deconvolution with the Huygens Software, since this will result in the same optical properties but with a more practical Nyquist rate.; '-__Keywords:__ pinhole size Nyquist rate two-photon-'%%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Single Tiff Image Imp Faq: Yes. Huygens Essential treats the image as the only known plane of a 3D stack and proceeds as usual. Set the z-sampling distance to the Nyquist rate [...]; Yes. Huygens Essential treats the image as the only known plane of a 3D stack and proceeds as usual. Set the z-sampling distance to the Nyquist rate as explained in 'sampling densities' from the Huygens User Guide.; '-__Categories:__ FaqDeconvolution, HuygensFaq, ImportedFaqs-'%%%
Bandlimited System Shannon Sampling Imp Faq: About the Nyquist rate-I can imagine that SNR limits resolution. But how does SNR work into the formula in the manual, that looks like pure optics to [...]; !! Is the sampling rate a function of the structure that you're modeling?; About the Nyquist rate-I can imagine that SNR limits resolution. But how does SNR work into the formula in the manual, that looks like pure optics to me? If you had a structure with details that measured, say, 80 nm, wouldn't you necessarily need a sampling interval of 40 nm in x, y, and/or z?; It all revolves around the Shannon theorem, that states that for a bandlimited system (all our microscopes) it is totally sufficient to sample at the Nyquist rate. Now suppose the maximum spatial frequency passing a microscope is one cycle per 100nm (1.3 NA oil, confocal, 488/520nm, sampling at 50nm to sample peaks and valleys of the 100nm periodic wave). If you have a periodic structure of lumps spaced 80nm apart then this structure is not imaged, apart from its average value, nothing of it. Can't restore it, no way. If there is omly one single object and you know it is a sphere then restoration could consist of determining its center of mass. The accuracy of that depends on the SNR, but you could easily reach 10nm. Job done! The regular restoration procedure could also do it for you, but obviously to get such an accuracy in determining the peak location of the object you would have to resample the data to a higher sampling interval of 10nm. (You could also play it a bit dirty by not deconvolving with the PSF, but with the known image of the object; out comes a single peak where the center of the object is). A more interesting object is for instance a two-blob object with a spacing at the Nyquist rate. Now the most interesting parts of the object spectrum are cut off by the microscope. The problem now is that the transmitted piece is the same for a whole family of objects. The family which has a spectrum quite like it is even larger. The restoration algorithm must now choose among them, the first selection being to exclude all objects with negative values. The better the SNR, the better the restoration algorithm can exclude objects of which the spectrum is slightly dissimilar to the measured spectrum. For confocals the situation is worse because they already attenuate everything beyond say 60% of the band practically to zero (depending on the pinhole). So in practice there is little hope for resolving objects at the edge of the band.; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Nyquist Asin Imp Faq: In the manual you give the formula for alpha: alpha=asin(N.A./n). arcsin or sin^-1 the 'reverse' of the sin function: / / if x=sin(y) then y=asin(x), [...]; !! Nyquist rate - What's an asin?; '-__Keywords:__ nyquist asin-'%%%; '-__Categories:__ FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Bead Nyquist Sampling Imp Faq: Using the Nyquist calculation I calculate that the minimum step in Z should be 170nm (x40water, NA 1.15, ex 364nm). I see from the example in the man [...]; Using the Nyquist calculation I calculate that the minimum step in Z should be 170nm (x40water, NA 1.15, ex 364nm). I see from the example in the manual that you sampled a 230nm bead at 25nm steps.; If you like you can oversample the beads at say 2x the Nyquist rate in the lateral direction. %%%; In general it is best to really match the Nyquist criterion (or better) in z since highest resolution gain is in Z. It also depends on the capabilities of the z-stepper. If you use finer 170nm beads instead of 230nm beads (and get sufficient signal), so much the better. It has no impact on the sampling density. Of course there is a relation between the Nyquist rate and the bead size, but it is a weak one. Literature: van der Voort HTM and Strasters KC (1995) Restoration of confocal images for quantitative image analysis. J.Micr. Vol 178, pp 43-54.; '-__Keywords:__ bead Nyquist sampling-'%%%; '-__Categories:__ FaqDeconvolution, HuygensFaq, ImportedFaqs-'%%%
Faq Deconvolution: This is part of the HuygensFaq. * Equalize Flux Reports Error. Answer. * What are the internal magnifications of the Biorad 1024 and the Biorad Radia [...]; This is part of the HuygensFaq.; * Literature reference on widefield and confocal Nyquist rates? [Answer|NyquistAliasingBandwidthBandpassImpFaq].; * Is the sampling rate a function of the structure that you're modeling? [Answer|BandlimitedSystemShannonSamplingImpFaq].; * What is an undersampled stack of images? [Answer|UndersampledStackNyquistSamplingImpFaq].; * Do you have to generate individual PSF's for each channel? [Answer|Mult-channelImagesPsfImpFaq].; * How to compute the Nyquist rate for an image? [Answer|NyquistBandwidthImpFaq].; * Should I oversample since the beads I'm using are only 175nm diameter? [Answer|BeadNyquistSamplingImpFaq].; * How to compute the Nyquist rate with 2-photon excitation? [Answer|ExcitationWavelength2-photonNyquistImpFaq].; * Does the pinhole size affect the Nyquist rate? [Answer|PinholeSizeNyquistRateTwo-photonImpFaq].; * What is the maximal voxel size at which Huygens can still do a good job. [Answer|SamplingNaNyquistNumericalApertureImpFaq].
Sampling Na Nyquist Numerical Aperture Imp Faq: This greatly depends on the optical paramaters, in particular on the NA and microscope type. Together with the wavelenghts and refractive indexes the [...]; This greatly depends on the optical paramaters, in particular on the NA and microscope type. Together with the wavelenghts and refractive indexes these determine the so called Nyquist sample distance, the maximum sampling distance at which all image information is captured. For a plot of the dependancy of the Nyquist rate on the NA and microscope type see the User guides, or go to NyquistRate. To calculate this figures online see the NyquistCalculator.; While sampling at the Nyquist rate is a very good idea, it is in many practical situations hard to attain. In these cases larger sampling distances may be used. For confocal images sampling distance may be up to 1.7 of the Nyquist distance. When large pinholes are used, up to 2x.; To compute the ideal Nyquist rate of an image in HuygensProfessional, select the image and choose Edit -> Nyquist rate.; '-__Keywords:__ sampling NA Nyquist numerical aperture-'%%%; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Zoom Scale Psf Sampling Density Imp Faq: Do we have to deal with the same PSF when we record fluorescent beads with the zooming function from our confocal microscope while we record the spec [...]; Why is the NyquistRate sampling so relevant for deconvolution? The (degrading) imaging process acts at the scale of the PSF, and therefore this must be precisely acquired in order to restore the image properly. See IdealSampling for more details.; Therefore, __in any case__, the [beads for PSF acquisition|RecordingBeads] should be imaged with a SamplingDensity at least according to the NyquistRate, or even better. Like that the PSF would contain all the information about the imaging properties of the microscope, and can be adapted to other imaging conditions that are → [slightly undersampled|SamplingNaNyquistNumericalApertureImpFaq].; The NyquistRate is the minimum sampling required for a proper PSF measurement. OverSampling the bead image can be a good idea (it increases the SignalToNoiseRatio of this fundamental image), but in practice this is not possible in the widefield case, because the image would be too large. Because other microscope's PSF are smaller, you can afford some oversampling there. If possible limit the differences in sampling density to factors 2 or 3, thus making the later scaling of the PSF easier and more precise.; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
2-photon Pinhole Ndd Imp Faq: If there is a non-descanned detector (NDD), or a very large (say 10 Airy disks) pinhole, the contribution of the pinhole to the image formation can b [...]; If there is a non-descanned detector (NDD), or a very large (say > 10 Airy disks) pinhole, the contribution of the pinhole to the image formation can be ignored. In this case the microscope type can be widefield in combination with 2p photon. This will result in more realistic values for the Nyquist rate than a confocal setting.; '-__Categories:__ FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Sampling 2-photon Imp Faq: I am processing a 2-Photon widefield stack. I assumed that the axial resolution of the 2-Photon mic was not too good so that 500 nm sampling was prob [...]; To find out the ideal sampling, you can always use the online NyquistCalculator, entering the image parameters (including the number of photons: 2).; You can also use the HuygensSoftware in your computer. To find out how large are your samples in relation with the ideal NyquistRate, do the following:; * If you have an image for which you want to compute the Nyquist rate, open it and check its parameters (right click -> "Show parameters").; * Whenever you change the MicroscopicParameters of an image, the Nyquist rate is recalculated. Modify the image parameters to match the microscopic conditions for which you want to compute the Nyquist rate, then check the parameters again (right click -> "Show parameters").; * Select the image, select Edit -> Nyquist rate in the main menu. You'll get a popup displaying the Nyquist rate.; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%
Older Changes: To avoid that the RecentChanges list becomes too large, old entries are manually moved to this other list from time to time. July 31, 2008 * MemoryBoo [...]; * [NyquistRate] ([diff|phpwiki:?diff=NyquistRate]) ..... JoseViña (SVI); * [SamplingNaNyquistNumericalApertureImpFaq] ([diff|phpwiki:?diff=SamplingNaNyquistNumericalApertureImpFaq]) ..... sysadmin; * [CommaSeparatedValues] ([diff|phpwiki:?diff=CommaSeparatedValues]) ..... JoseViña (SVI); * [HuygensFaq] ([diff|phpwiki:?diff=HuygensFaq]) ..... 72.232.85.186; * [NyquistIdealSamplingCalculator] ([diff|phpwiki:?diff=NyquistIdealSamplingCalculator]) ..... JoseViña (SVI); * [NyquistBandwidthImpFaq] ([diff|phpwiki:?diff=NyquistBandwidthImpFaq]) ..... JoseViña (SVI); * [PinholeSizeNyquistRateTwo-photonImpFaq] ([diff|phpwiki:?diff=PinholeSizeNyquistRateTwo-photonImpFaq]) ..... JoseViña (SVI); * [NyquistAliasingBandwidthBandpassImpFaq] ([diff|phpwiki:?diff=NyquistAliasingBandwidthBandpassImpFaq]) ..... JoseViña (SVI); * [NyquistCalculator*] ([diff|phpwiki:?diff=NyquistCalculator%2A]) ..... JoseViña (SVI); * [NyquistCriterion] ([diff|phpwiki:?diff=NyquistCriterion]) ..... JoseViña (SVI)
Scaling Psf Bandlimited Interpolation Imp Faq: In principle, it is sufficient to record bead images for a PSF calculation at the system Nyquist rate, say 50 nm times; 50 nm times; 150 nm for a con [...]; In principle, it is sufficient to record bead images for a PSF calculation at the system Nyquist rate, say 50 nm × 50 nm × 150 nm for a confocal setup (or doubled figures for widefield).; If your sample of interest has been imaged at a different sampling rate, then the PSF can be adjusted by bandlimited interpolation. This is automatically done by the Huygens CMLE and QMLE deconvolution methods.; You can use our NyquistCalculator for determining the ideal sampling values for your experimental conditions.; * In case of widefield data, the Nyquist sampled PSF might be too small (in terms of microns) to be used in deconvolving physically large data. Make sure you specify, during the PSF distillation, a large enough required size for the final PSF. However, in extreme cases memory limits might get in the way.; '-__Categories:__ FaqDeconvolution, FaqMicroscopy, HuygensFaq, ImportedFaqs-'%%%

213 matches found in 23 pages.
Not logged in: only contents of public pages are shown. Login