Measuring PSF questions

Manufacturers supply the average size along with a standard deviation. Should we look for very tightly specified beads?

The spheres we developed and tested this technique with, had a coefficient of variation of 2% at 230nm diameter. This variation was smaller that the precision at which we could locate the center of the beads, at best 1/4 pixel. So if the c.v. is a good deal better than say 1/4 of a pixel it is good enough.

Around 30 optical units — an optical unit is (for NA=1.3 and lambda = 500nm) 61nm — so about 2 micron. Because the software doesn't know whether there is a bead just over the edge of the image, the bead-edge rejection distance is the same.

If the 175 nm beads yield enough signal best use them.

During the "Reconstruct psf from bead image" phase in Huygens Professional, or during the PSF distillation in the PSF Distiller, the question "center of mass of the image containing the averaged bead is far (0.482 microns) from the center of the image - proceed anyway" popped up.

This is a check in the Reconstruct PSF tool to prevent the cones (fans) of WF PSFs to be cut off too asymmetrically. Also, this effect can be caused by large spherical aberration making the PSF (and therefore the bead images) highly asymmetrical. This check was built in the software to make people aware of sub-optimal properties of their data which should be corrected during acquisition.

The averaging procedure can increase the signal of the accumulated bead as much as needed. BUT it makes an alignment error which is worse when signal is poor. The alignment error effectively increases the bead size, but not in a way which can be predicted easily. As soon as the bead signal is sufficient for alignment the SNR can be increased by averaging, but if it is insufficient you're sunk. We've never seen enough signal from 50nm beads. On *very* sensitive microscopes 110nm beads are good enough, but we doubt whether they are safe to use on regular commercial microscopes.

For more information you can have a look at DeconvolvingBeads

Several restoration operations can optionally center the channels of the PSF. The option "Center PSF" aligns the center of mass of the channels of the PSF. A non-centered PSF will cause a shift of the restoration result. This can be advantageous to correct the image for chromatic shifts, but we advice to use the Chromatic Shift Corrector for that after deconvolution.

See also Color Shift.

Each image has a microscope type associated to the microscope (sensor) with which it was taken. Currently confocal, spinning disc, widefield, multiple photon, 4 PI and STED images are supported by Huygens. By default Huygens does not know the sensor type and assigns "Generic". However, the method for generating a PSF is different for each of the microscope types. There is no particular method to generate PSFs for generic (unknown) microscope types.

To assign a microscope type to the image:
  • select the image
  • choose "Edit Parameters" or press Alt-P
  • change the field "Microscope Type" from "Generic" to the correct microscope type
  • save the changes.
A PSF can now be generated based on the image.

The message about the axial criterium may mean that the beads are too close to the top and bottom edges. In that case a bead below or above might disrupt the PSF. Since usually the beads are adherent to the glass there is little danger of this so you can ignore it.

But it may also mean that the image is indeed having not enough information about the PSF along the optical axis Z. The recorded volume around beads, specially in widefield microscopes, must be large enough to containg information about the light cone. If this is the case, better image the beads again, maybe changing the sampling density and recording more planes. Read more at Recording Beads.

No. The reason here is that the shape of the expected (theoretical) PSF is forced only lightly on the measured PSF. This is done in the form of a bandlimit constraint, and the pinhole size has not much influence on this. If we would impose the theoretical shape on the measured data more strongly it would, for instance, force a non-existent axial symmetry on the measured PSF, exactly what we don't want. Still, from version 2.07 of the Huygens onward the theoretical shape is imposed on the data slightly more strongly.

Yes. Since the wavelength parameter has an effect on the PSF you need to generate or measure a PSF for each different channel. The deconvolution wizard handles multi-channel images for you and the PSF distiller also detect multi-channel beadimages to generate a multi-channel measured PSF. In scripting you process a multi-channel image by first splitting it into a series of one-channel images. Then you deconvolve these images using the measured or generated PSF's for each channel and merge the results.

To obtain a measured PSF the Huygens Software contains a set of tools with which you can derive a PSF from images of fluorescent beads. In principle one would need a very small, point-like bead to measure a 'point' spread function. Since sufficiently small beads are also very dim this is impractical. Huygens solves this by being able to extract PSFs from larger, much brighter beads. A typical size is 200nm radius. To improve accuracy it is also capable of averaging over multiple beads, from single or multiple images.

See also Psf Distiller.

It all greatly depends on the Numerical Aperture (NA), to a lesser degree on WaveLengths. For a 'typical' Confocal Microscope (NA = 1.3) 5 micron is fine, 3 will do. For a Wide Field Microscope the situation is different because the PSF does not stop in Z. For restoration the software needs a PSF which is a bit larger in Z than the image to be restored. Now the problem is that this needed extent can't be known to the software during the measurement, i.e. bead averaging/cleaning + PSF reconstruction.

It turns out that in practice recorded PSFs are often too shallow, so we have fitted out the reconstruct tool with a powerful extrapolator and a manual Z-size setting. Provided the extrapolator has a big enough foothold it can extrapolate to whatever size you need. Rule of thumb for the foothold is 5 micron. Ideally the extrapolator is called as part of the preprocessing phase of the restoration tools, but because it is rather lengthy we put it in the reconstructor. We did put a light-weight extrapolator in the restoration tools to be able to extend a PSFs a little bit.

See also Recording Beads.

What type of beads you need to use for determining a PSF depends on the microscope type. You can find under the section "Pratical beads" on this page links to information for the different microscope types.

Beads with a size close to the width of the PSF half intensity width (HIW, the width of the PSF at 50% of the peak intensity) show up in the image as spots which are slightly wider than the PSF.
To compare a bead image to a theoretical PSF proceed as follows:
  • Open an operation window on the bead or averaged bead image
  • Choose a free destination image
  • Click the PSF button and set Dimensions to Parent
  • Click Run to generate a theoretical PSF of which the size matches the size of the bead image

You can now compare the two images by opening a Slicer window on the PSF destination image. If you find that the beads are much larger than the PSF you might be looking at bead clusters. In that case you might find weak single bead images in the background. Because the clusters are of unknown size you can't use them for PSF measurement. Alternatively there might be large beads in the sample. If these have an unknown size, or if their size is larger than the HIW, best not use them for PSF measurement.

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.

The deconvolution tools are capable of adapting a PSF derived from such bead images to the sampling density of the specimen. Still, it is best to sample at the same density as at which you are going to collect the biological images later, or with densities which differ by a factor of 2 or 3.

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 Nyquist Calculator for determining the ideal sampling values for your experimental conditions.

There are two problems, though:
  • In some microscopes the magnification at high zoom is unreliable, with errors up to 30%.
  • 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.
If you want to obtain confocal-like 3D images from regular epifluorescence microscopy, i.e. widefield microscopy, then you need indeed a series of images recorded at different depth: a so-called stack. To arrive at a result that is comparable to a well-sampled confocal image a typical Z step size (Z sampling distance) is 200nm.

If you'd like to obtain confocal-like single slice images the best procedure is to acquire a short stack of 10-20 slices around the plane of interest and deconvolve that. However, if you lack a z-drive or the time to acquire the stack Huygens-Pro and Huygens Essential also allow you to deconvolve a single 2D widefield image.

Basically it is very simple: beads were brought on a coverslip and left to dry. Then for water type medium simply distilled water was added. For high refractive index Aquatex (Merck) was added, covered with a second coverslip and left to dry for 3-4 weeks. For this last sample 115 nm beads from Molecular probes were used with very good results. For a recipe using glycerol see section "Measuring a PSF" in the recipe booklet that you received in the case you have purchased the software.

A 1micron bead is too large for a PSF measurement because it lacks sufficient high spatial frequency components. In other words: a large bead has a lower surface/volume ratio than a small bead. Therefore it has reduced 'edge energy' per unit of total signal strength. In addition, beads as large as 1 mu are often not stained homogeneously and are likely to distort the PSF due to their high refractive index. All these factors render 1 micron beads unsuitable for PSF measurement.

One could argue that very small beads(<25nm) have ideal spectral content, but up to now such small objects lack signal strength. Averaging small beads doesn't work either since the limited signal strength limits the precision of alignment procedure. This situation might change when quantum dots become available for PSF measurement.

The alignment procedure in the Huygens System is based on determination of the Center of Mass (CM) of the beads. This allows bead alignment with sub-pixel accuracy. We found that with 150-230nm diameter beads the right balance is struck between spectral content and alignment accuracy. However, when the fluorescence yield of beads can be increased by better dyes or better anti bleaching agents the optimal size will be reduced. Good results have also been obtained with 110nm beads.

Measuring both the PSF and the sample with the Ideal Sampling is always nice, but not strictly necessary. If required, the deconvolution functions in the Huygens Software will automatically scale the measured PSF to adapt it to the image sampling. However, the PSF should always be ideally sampled or better. In order to do deconvolution, a slight undersampling can occur in the sample image but only to a certain extent.

Why is the Nyquist Rate 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 Ideal Sampling for more details. Therefore, in any case, the beads for PSF acquisition should be imaged with a Sampling Density at least according to the Nyquist Rate, 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. See also the FAQ What is the maximal voxel size at which Huygens can still do a good job?.

PSF measurement

The Huygens Software will reject beads that are severely undersampled if you try to distill a PSF from them, because in that case they do not contain the necessary information to do it! The Nyquist Rate is the minimum sampling required for a proper PSF measurement. Oversampling the bead image can be a good idea (it increases the Signal To Noise Ratio 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.

In practice (and with good signal) it is not necessary to sample finer than 25 nm lateral and 100 nm axial for confocal systems or 50 nm lateral and 100 nm axial for widefield systems. Fair numbers in a typical confocal case are 50 nm lateral and 150 nm axial.

Caveat: at high zoom factors the magnification as reported by the microscope is not always reliable.

In the widefield case best record with no Pixel Binning. This usually results in a lateral sampling density in the 67-100 nm range. Axial sampling should match the sampling of the specimen if it is below 250 nm.

For more information see Recording Beads and Parameter Variation.

Indeed, the better your PSF, the better the resolution to which you can deconvole the object and the fewer artifacts. But as to the resolution, there is a limit. Signal To Noise Ratio (SNR) plays a crucial role there.

The Nyquist Rate (similar to the Shannon theorem) says that IF a signal is bandlimited (see our FAQ What's a bandlimited system?), 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 Aliasing Artifacts (moire patterns, straircasing).

One more reason to oversample is that with sparse objects and good SNR it is often possible to achieve a Half Intensity Width resolution on the objects corresponding with a Band Width in excess of the microscope's bandwidth. The objects are then said to be super resolved. The Shannon theorem says it doesn't matter whether you get the supersampled image during sampling or afterwards by interpolation, but it is more practical to get it during sampling, if only to improve the SNR situation.

A different matter is two-point Spatial Resolution: 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 Nyquist Calculator.

If the PSF is not centered deconvolution will also shift the image. Usually this is unwanted, so the PSF generator and current PSF measurement tools always center the PSF. In previous versions of Huygens this was not always the case, so for example the ICTM has an option to center the PSF.

In multi-channel images the different channels are often shifted with respect to each other. By NOT centering the PSF this shift can be automatically undone by the deconvoluttion, and with sub-pixel accuracy. On the other hand, the shift can be just as well done manually with by the shift tool, also with sub-pixel accuracy. This is perhaps the most practical method.

Since Huygens 3.7 there is a specific option available that measures and corrects for shifts between channels. See Chromatic Shift Corrector.

With large beads the software has a much harder job extracting a PSF than from images of small beads. However, small beads are noisier and will need some averaging to reach a sufficient Signal to Noise Ratio (SNR). Very small low signal beads can't be averaged because their position cannot be measured with sufficient accuracy. As a rule 175 nm diameter beads yield sufficient signal while being small enough. We have seen good results with 110nm beads, but we do not think these can be imaged with sufficient SNR by all microscopes. For high NA microscopes (NA > 1.2) we do not recommend beads as large as 260nm.

When generating a PSF some choice must be made about the size. In most of the cases a border is added to avoid edge artifacts (padding). Depending on the purpose a choice can be made.
  1. Ideal: The size (in microns) of the generated PSF is determined from the physical size. Since the fringes of a PSF go on forever it is in theory not spatially limited, but in practice a volume can be chosen beyond which there is a negligible amount of energy from the PSF. The exception is the widefield PSF: there the amount of energy outside a volume around the focus is always infinite... As the intensity goes down locally it is possible to find a point at which the intensity of the PSF is well below the accuracy of any camera. Still, ideal WF PSFs are much larger than confocal or 2-photon ones.
  2. Parent/Padded Parent/Full Padded Parent: The size is derived from the Parent image: either exactly the same as the parent in fact no padding is made here, or as large as if the parent was 'padded'. The extra volume computed by the software is a trade-off between FFT (Fast Fourier Transform) compute efficiency and the size of the original image. For example If you have 31 layers in your image, adding one layer would optimize the Fourier Transform process. But adding one layer is not enough to prevent wrap around effects. The software will find out how many layers extra is a good compromise. The Fully padded parent mode is relevant for widefield images, for other microscope types this is equivalent to Padded Parent. If PSFs are to be compared it is best to use 'Parent' because that will fix the size.
  3. Automatic: A tradeoff is made between the physical size of the PSF and the memory requirement. In practice confocal or 2-photon ones are ideally sized; WF PSFs are smaller than ideal but at least as large as the padded parent.
  4. Manual: You can manual set the number of Z-slices in this mode using the input field "Min XY-slices (Manual)". Widefield images should never be padded manually.
Full question: We tried to reconstruct PSFs from beads taken in wide-field mode. The problem is that Huygens excludes all the beads from the calculation because of different reasons: too close to an edge or too close to each other. Even taking 100 slices did not improve the situation. We know that the image of the bead in widefield mode can be extremely large even if the cut-off is high.

Yes, this is the problem. Even worse: the thicker you make the stack the wider they become so the tops of the cones will tangle. That will really mess up the PSF. Best way to go is to set 'reduce PSF size', for instance to 2 (=high), and reduce the number of beads to a couple, even just one should be ok for widefield. Starting from Huygens version 2.16 it is less a problem if the PSF is somewhat truncated because of the build-in PSF extrapolation. This is also true for confocal PSFs which tend to be truncated always.

Am I right in assuming, that because microspheres are spherical, a mismatch between the refractive index of the bead and the surrounding medium is of no significance?

What happens when you use a small bead with slightly higher r.i. than the surrounding medium to measure the PSF that it will be not quite homogeneously excited. I think this effect on beads with a size approximately equal to the size of the diffraction spot in XY and so much smaller than the diffraction spot in Z can be neglected. The emitted light from within the sphere might seem to come from outside the sphere because of the sphere acting as a lens, but this is at most something in the order of diameter*( RI_bead/RI_lens -1) outside the sphere, so something like 10nm, also neglectable.

This is what you can do:
  1. Close images you are not immediately working on and turn off the Undo system.
  2. Use the crop tool to crop the data as much as possible, especially in the Z direction.
  3. Use either QMLE or CMLE to deconvolve the image. If possible both will split the data into bricks and generate PSFs matching the bricks. In this way the computation of a single huge PSF is avoided. Currently, widefield images can only be processed brick wise if the data is sufficiently shallow compared to the NA. This is the case when the base of the aperture cone as truncated by the upper and lower planes is far smaller than the lateral extent of the data. This is often true, but overestimated NAs can spoil it. It helps to cut off as many z-planes as possible since this not only reduces the data size, but also allows more efficient brick cutting.
  4. Lastly, make sure your system has sufficient swap space.
Dr. Markus Duerrenberger designed a confocal calibration kit, now available from Polysciences. This kit contains three different sizes of latex beads 0.2mu, 0.5mu and 1mu (all +/- 0.001mu), fluorescent in the whole range of wavelength from 280nm up to 647nm. These beads work extremely well for the Huygens Pro, but also all kinds of alignments and adjustments of the microscope can be done in a highly precise way.

Also Invitrogen and Thermo Scientific have good beads available. See also under "Practical Beads" on this wiki page RecordingBeads to find a list of available beads.

The gensphere command generates a so called "bandlimited sphere", i.e. a geometrical sphere with no spatial frequencies above half of the sampling rate that you intent to use. If a perfect sphere should be used an unlimited number of spatial frequencies is involved and aliasing artifacts are generated due to Nyquist sampling violation. The ringing is a result of the sphere being bandlimited, i.e. perfectly antialiased. Removing the rings would mean corrupting the spatial frequency content which in turn would lead to a sub-optimal measured PSF. Because it is later convolved with a similarly bandlimited but smoothly rolling off PSF it is doesn't matter.

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