Structured Illumination, pt. 2

This is a long post. If you’re in a rush, then just read these first two paragraphs.

One of the early posts on this blog was about structured illumination. Specifically, I spoke about Mats Gustafsson’s version, which yields superresolution imaging, in the wide-field mode. Just recently, JM commented on that post and asked if there was any kind of guide on how to get this set up and running. Besides the usual sources (methods sections, co-authors, etc.), I’m not aware of any such guide. However, I have corresponded a few times with Mats over the years and he was always overwhelmingly helpful.

He passed away earlier this year and there have been a few articles written about his landmark work, his thoroughness, and his kindness (Nature Methods, HHMI). In this post, I want to share some excerpts from his emails to me. They’re not personal (we were just acquaintances), they’re technical. In addition to them being useful to people who may be putting together their own patterned illumination rig, I think they also give a small insight into how kind of a person Mats was. He took the time to write these detailed responses to just some postdoc that he met at a small conference.

Do you use holographic gratings?

MG. No, holographic gratings are usually used to make very tight (sub-micron) line spacings, while we need very coarse periods on the order of 20-30 microns (because the grating period will be demagnified by the objective). We instead use photolithographically patterned transmission gratings, essentially a piece of flat glass with grooves etched into it.

Where do you buy your gratings?

Several companies can make these things. The last time (several years ago now) we used Diffraction Limited. A run will cost a few thousand dollars, but yields a lot of gratings. They patterned one substrate (4″ I think, highly flat and parallel) for us into something like 50 grating chips of three different spacings. So if you can forsee future needs, one run will last you a long time. Other companies like Digital Optics Corporation may be able to do an even better job, for a lot more money.

What elements do you use to keep just the +1 and -1 diffraction orders?

Two answers:
(a) The most useful mode really is 3D structured ilumination, for which we do want the zero-order beam as well as the +-first order ones. For that case we simply use an iris in a pupil plane to exclude higher orders. In order for an accessible pupil plane to exist, the grating can’t be in the primary image plane (directly after the tube lens), but must reside in a re-imaged, secondary image plane. One could rely on the objective aperture itself to exclude higher orders, if one wanted to eliminate the re-imaging lenses, but stray light could be an issue. One might be able to block them right before the objective, as long as they are not expanded in beam size enough to overlap the observation light beam. Some pre-blocking before the first lens after the grating, to keep any light from hitting the edges of lenses or mirrors, helps limit stray light.
(b) If one does want to work in 2D (for high speed on thin samples, or for the nonlinear ultra-high-resolution schemes), then one does need the accessible pupil plane, to be able to exclude the zero order (which will always be present at some residual level evel if the grating is designed to produce no zero order). I simply suspended a small piece of aluminumm foil in the middle of the iris on a thin metal wire (which I pulled out of a piece of thin multi-strand electrical cable), and just make sure that the wire is at an angle that doesn’t interfere with the beams at any of the pattern orientations to be used. (Our light source makes a small spot in the pupil plane (spot diameter ~5-10% of the pupil diameter), which gets turned into three similarly small spots by the grating, so in the linearmode where we only use three pattern orientations there is plenty of unused angle space for the wire.

If you do want to work in 3D, which I assume you do, then you will have to design the grating to generate a zero order beam of appropriate strength. A symmetric (walley width=50% of period) grating design with a step height that corresponds to Pi phase shift (at the design wavelength) is very efficient at producing +-first order beams, and is therefore ideal fro 2D, but generates no zero order beam. To generate a zero order beam, the design has to be modified in either or both of two parameters: the valley fraction, or the phase shift (step height). The latter is more efficient, but makes the zero order (and 1st order) strength depend strongly on the wavelength. If one, like us, wants to use a single grating at amny wavelengths, it is better to paly with the walley fraction (“duty cycle”). Our last design used 29% valley width, and Pi phase shift at some wavelength near the geometric enter of your span of intended illumination wavelengths. That gives a zero order beam ~70% as strong as the first order ones at the design wavelength (and, I think, somewhat stronger relative to the first orders away from the design wavelength).

About illumination…
Yes, we illuminate only a small part of the pupil, but not by just turning down the aperture, and not just to be able to block higher orders. If you just close down the pupil, with a conventional illumination source, you would get very little light through. If you read the previous email again, you’ll note that I talked about our light source illuminating only a small spot in the back focal plane (spot diameter ~5-10% of the pupil diameter). With a 10% spot size, you’d get 10%^2=1% of the light through. Not good. So we need higher brightness than an arc lamp source can supply (we need ~same power but into a much smaller area*solid angle). Therefore we designed a special light source that spatially scrambles laser light into a small multi-mode fiber. Scrambling is done with a rotating holographic diffuser (Physical Optcs Corp). You could use purely coherent light instead (ie.e no scrambling, and use a single-mode fiber if fiber delivery was needed); we like to remove spatial coherence by scrambling because it decreases the problem of stray interference fringes that otherwise are caused by any unintended reflections and by scattering from dust particles, etc. Lower coherence also has some advantages in the 3D mode.

The main reason to use a small spot size is that then we can place it close to the edge of the aperture, and thus get maximal resolution imporovement, and still get all the light through, which you need in order to get maximum pattern contrast, and thus signal-to-noise ratio.