Point spread functions

One way to characterize the quality of one’s microscope is to measure the point spread function (PSF), that is the image that is created by a point source  (which can be a fluorescent bead smaller than the expected size of the PSF embedded in agarose). I recently spent quite some time aligning my multiphoton microscope, and due to some reasons, it took me not only some hours, but several days (or nights). In the end, the PSF again was symmetric, small, sharp and nice, but the way to go there was crowded with all varieties of bad, strange and extremely ugly PSFs, sometimes at points during the alignment when I didn’t expect it.

In scientific publications, one only gets to see the nicest symmetric ‘typical’ PSFs, so I just want to put some really bad PSFs here. Not all the PSFs were as bad as they look like, because I have adjusted the contrast of the gifs in order to better show the shape of the PSF. All gifs are simple z-stacks acquired with variable z-spacing at the same day on the very same microscope, with only minor and rarely predictable changes to the beam path.

Here comes the classical stone in the water-PSF, thrown from the lower right:


This one is thrown from the top right:


This is the bathing in a sea of other beads-PSF. Or, rather than bathing, swimming, because there is a clearly visible upwards direction. This happens when you have to many beads in your agarose:


This astigmatic PSF, on the other hand, is rather indecisive, first going to the right and then upwards.


Here an even more advanced indecisive right-up-goer-PSF:


This one is so undecided that it decides to almost split in two halves. Let’s call it the bifurcating PSF:


This is the banana-PSF, coming from the left and going back again:


And finally, you would not guess this to be a PSF, here comes the flying eagle-PSF. I created it simply by tightening too much one of the screws that held the dichroic beam splitter, the back aperture of the objective still seemed to be properly filled:



Sidenote: In some of these pictures in one or two planes, one can see a diagonal striping pattern. This comes from the pulsing laser, which was unstable during these days, being modulated to the microsecond-timescale. Fortunately, nowadays I have a nice PSF and a stable laser again …

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4 Responses to Point spread functions

  1. E says:

    just came across your blog, looking for banana shaped PSFs. Can you comment what kind of adjustment you did to get these PSFs? Or more importantly what changes did you do to get to a nice PSF?

  2. Hi Enno,

    The short answer to both of your questions is that I don’t know. When I did these adjustments, I was mainly adjusting two mirrors forming a periscope, located between tube lens and objective of the 2P microscope. From time to time I had to change the angle of a scanning mirror’s resting position for some obscure reasons. Of course, I tried to center the beam such that it hits the back focal plane of the objective, overfills it nicely and is mostly collimated in front of the objective. In my case, I had to make some compromises due to some imperfect lenses and mirrors (lenses used for seven years in a wet lab …). These details led to workaround solutions that compensated imperfections by other imperfections. In short, it’s complicated, and – as in every chaotic situation – small modifications can change the outcome in unpredictable ways. This is certainly not the answer you wanted to have.

    From my experience: I’ve seen similar-shaped PSFs created by a seemingly diverse set of misalignments. One of the easiest-to-recognize shapes of PSFs is caused by astigmatism. You can recognize this when the foci in x- and y-directions occur at different points in z, as in quite some from the above PSFs. This can be due to the dichroic mirror, which is an optic element that is seen differently by the x- and a y-projection of the beam – but many other reasons are also possible. Sometimes a mirror is attached with too much force, causing it to be less flat in one direction than the other. More often, it’s a combination of small misalignments or material imperfections that causes the problems. One of the problems is that some misalignments cannot always be traced back to its causes, and therefore fine alignment often is just an hour-long frustrating random walk in parameter space.

    The best collection of general advice on optical alignment that I have found has been written down by Rainer Heintzmann: see http://labrigger.com/blog/2015/01/07/practical-guide-to-optical-alignment/

    For my own work, I never used shear plates (not available in my lab). Pinholes are often key for re-alignment. If you cannot insert a pinhole or at least a sheet of paper/a credit card in front of an important lens, this will make alignment more difficult than otherwise. And then it is often useful to custom-build your own tools that help you center the beam for tube lens, scan lens or objective back focal plane. Another nice tool that I’m using is a reflective grating – some people use mirrors to back-reflect the beam (in order to see whether the whole path is collimated), but the grating creates a symmetric pattern that is simply bigger, which helps to see it.

    If you have a concrete problem with your PSF, it also depends on your system (custom-built or commercial vendor? confocal or two-photon?). If I can help you somehow, let me know.

    If you need help from a community, you can also consider writing an email to the confocal microscopy mailing list. The list has given help in some previous cases (e.g., http://confocal-microscopy-list.588098.n2.nabble.com/4f-system-alignment-with-fluorescent-light-td7583200.html) and is crowded with competent people.

    • E says:

      thanks for your answer! This points me to a few things, I will try. We actually have a commercial Nikon Ti-E microscope, so I cannot access a lot of the optical elements, but your text was a great reminder that the PSF is not just a property of the objective, but the entire optical system. The banana shaped PSF I observed was actually measured in epi-fluorescence mode and the beads were excited using LEDs, not a laser.
      Thanks again! Really appreciate your reply.

  3. There is an interesting discussion on Twitter brought up by Jonathan Taylor, pointing out the potential aberration behind a “bifurcating PSF”: https://twitter.com/jtimaging/status/1623348707553943553

    The underlying aberration seems to be a combination of astigmatism (maybe due to non-flat dichroic) and some additional spherical aberration (which could come from anywhere).

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