#electron.

A New Look for Atomic Imaging?

When you wish to observe matter on small scales, you typically use a microscope which can magnify an image for you. However, one of the fundamental limitations imposed by Nature is that you can never resolve an image smaller than the wavelength of light you use to "see" it. It is for this reason that the electron microscope is used for nanoscale (0.000000001m) observations.

The De Broglie relationship (λp = h) allows us to assign a wavelength according to the wave-particle duality we use to describe particles. Therefore typically a beam of electrons will have a smaller wavelength associated with it and can achieve imaging resolutions and magnifications which surpass using visible light.

However, whilst the fundamental wavelength resolution is superior to using light, there are limitations owing to the design of electron microscopes. The beams of electrons are focused by magnets which can cause aberrations to form in images. This means there is additional noise added to the image from the equipment. In fact, in 1936 it was shown that this limiting factor reduces the perfect resolution achievable by a factor of 100. It was not until 1997 that different magnetic lens designs were successfully implemented, though still the resolution achievable is still 25 times poorer than the fundamental limit.

A Brief Introduction to Electron Microscopes

At this stage it is probably worth highlighting that there are a couple of different ways to use an electron microscope.

A transmission electron microscope (TEM) works by firing the electron beam through your sample, where it gets scattered as it passes through. The beam which is transmitted through the sample therefore contains spatial information about the sample which can be imaged after magnification.

A scanning electron microscope (SEM) does not need to use a thin sample because it works by scanning an electron beam across the surface of a sample. When the beam interacts with the sample, energy is lost from the beam and detectors are located such as to detect this energy loss (through thermal emissions or backwards scattering of the electrons) to build up an image of the surface the beam is moving across.

So what?

Now there was a paper published on the 7th March 2012 in Nature Communications (see Ptychographic electron microscopy using high-angle dark-field scattering for sub-nanometre resolution imaging) which I had brought to my attention. Whilst on a Science in Media course, there was a very nice lecturer from the Material Science department at Imperial College London who spoke about this paper. Her main concern was that this paper had not been given enough (ie any) publicity, yet she felt that it will lay the groundwork to revolutionise atomic imaging, not only in her field but across the board. That in itself got me quite interested, and the more she explained what it was about the more I could understand why she felt it was important.

The reason being that the description I have given so far about electron microscopy shows that it is good, but has inherent limiting factors particularly coming from the equipment setup. In some cases as well the actual apparatus can be extremely large, requiring vibration proofed and evacuated chambers for them to work properly (though this is more for the TEM if I understand correctly).

This paper details a new method of imaging using a relatively low-energy electron beam in order to image a sample at nanoscale levels, but over an infinitely large region of interest and without the limiting factors from using lenses. In addition to this, it uses the technology of a SEM which is much smaller than a TEM and can attain better image resolutions than either of the other two methods.

It sounds to good to be true as it effectively means it will be able to image at better resolutions at a much cheaper cost than can be done currently!

So how does ptychographic electron microscopy work?

Physicists like to think in many dimensions. A good example of this is Fourier analysis. A Fourier transform will take you from one domain to another. Typically we talk about moving from the time (or spatial) domain to the frequency domain. Often when something is complex in one domain, it is simpler to change to the other domain and apply the equivalent operation within that domain before changing back and seeing what the result it.

The analysis described in the Nature Communications paper uses this technique. Using a SEM, they illuminate the sample with a defocused beam (unlike the SEM which relies upon the sharpness of the beam used). On each illumination they record the diffraction pattern that is formed by the electrons after they travel through (and interact with) the sample. This is similar to the TEM except that the image formed by the TEM is of the object, not of the diffraction pattern. The idea is to then use a Fourier analysis to transform the diffraction pattern into the image of the object.

For those who have worked with computational problems and Fourier transforms, it should be apparent that trying to perform a Fourier inversion when you don't know much about the diffraction pattern will either be computational heavy, or could have multiple solutions. However, to counter this, the group uses the scanning part of the SEM to illuminate overlapping areas of the sample and record the diffraction pattern again. In this way, they build up a number of diffraction patterns which can be combined to hone in on the true solution using the "redundancy" of information coming from the overlap (which to my mind means the information is not redundant as it has a use).

Armed with this additional information, it appears that the solution to the Fourier inversion is relatively straight forward and this allows for the reconstruction of the image of the sample which caused those patterns.

This idea seems extremely simplistic and beautiful in the way that complex mathematics often is. From the results of the paper, it appears that they have successfully imaged samples at a higher resolution than a higher energy TEM could achieve. This in itself looks to be a great achievement! There are some drawbacks they conclude coming from the experimental setup and the requirement to have very thin sample slices as 3D imaging with this method is too complex for now.

It does however look to be a piece of ground breaking research, as it has taken ideas that were already in existence but through new applications in the experimental realm, have been able to achieve impressive results, so this is my way of trying to give this work a bit of public exposure and hopefully impress some people in the way I was impressed when I was told about the work!