If you know me, you know that I tend to get obsessive about imaging. I usually stick to optical microscopes, but occasionally the folks who play with electrons and ions do something exciting, too. A recently published paper on ion microscopy has me pretty excited at the moment, which is about all the excuse I need to dig in.

Ion microscopy is similar to electron microscopy. In a typical electron microscope, you fire a beam of electrons at a sample and examine the angles at which the electrons scatter. These angles are directly related to the surface of the sample, so with a few optics (magnetic lenses, in the case of electrons), you get an image. Because electrons are heavy and energetic, they have a very short wavelength, so smaller features can be imaged.

After the development of the electron microscope, scientists realized that you can do similar things with ions—the nucleus of an atom with some or all of the electrons stripped off it. Hence, ion microscopy.

All forms of imaging are subject to the laws of physics, which limit the size of the features that can be seen. Once you eliminate all the imperfections in an imaging system, you're still left with noise. Even if you had optics that magically overcome physical limits, the noise in the illumination system will prevent you from seeing very fine features. In other words, nature hates you and your microscope, too.

Stop the noise

Since we're talking about imaging using an ion source, we need to discuss the noise of an ion source (they're actually the same for electrons and light). Imagine you have a source of ions that emits 100 ions per second on average. That average is subject to an expected variation of about ten ions in any one-second period. To put it simply, if you image by scanning an ion beam along a sample, at some level, you can't tell if a darker patch is due to a feature on the sample or the source emitting slightly fewer ions at that particular time.

The nice thing about these sources is that averaging wins. Consider our source above—its fluctuations scale as the square root of the average. In 0.1 seconds, the average is 10 and the fluctuations are about three. So the noise is nearly as big as the signal. At one second, the noise is at the 10 percent level, and at ten seconds, the noise is down to 3 percent.

Averaging is not ideal, however. Typically, imaging a sample changes it, so the longer it takes to acquire an image, the more likely it is that the feature you're imaging is modified by the ions you are shooting at the sample. And if you are interested in how the sample changes due to some externally applied control, averaging is not your friend.

The short story is that you can't avoid these fluctuations easily. At least not unless you know exactly when an ion is coming. And figuring this out is exactly what researchers in Germany have done.

Old tools get a new job

Over the past three decades, researchers have developed something called cold ion traps. These traps essentially use a bunch of lasers and electric fields to confine ions like beads on a string. Once trapped, they sit there, gently jiggling back and forth. Normally, researchers use the trapped ions for quantum physics experiments, quantum computer gates, or something like that. But our intrepid scientists realized that with the appropriate application of an electric field, they could extract a single ion from the trap. That ion would exit the trap at a well-defined time and have a well-defined energy.

That situation changes the statistics entirely. What is the average number of ions in the beam? It's the number of times the gating field (used to eject ions) is applied per second. What are the fluctuations in the number of ions per second? That's a trick question—the answer is none. As long as there are ions in the trap, the researchers can eject an ion with every switch of the field. There is always one ion and no fluctuations.

There is a subtle point, though: the precise moment the ion leaves the trap changes with each ejection, so the fluctuations are not zero at very high-temporal resolution. But as long as the detector averages over a period that is greater than those tiny fluctuations, there are no fluctuations. This is exactly what the researchers do.

In principle, this would mean that an image should be noiseless. But it isn't—there are several factors that degrade the image. An unavoidable one is that the detector isn't perfect. For every 100 ions incident on the detector, only 96 are detected. This introduces a small amount of unavoidable noise.

Another problem is that the detector will sometimes report an ion when there isn't one (called a "dark count"). Because the ion source only produces ions within a fixed window of time (e.g., just a few moments after the gate field is switched on), the researchers got rid of the vast majority of dark counts by throwing out all detections that occur outside that window. This gating technique allowed them to reduce this noise by a factor of a million.

The biggest problem comes from the environment: vibrations. Vibrations can be eliminated, but that's actually a real engineering challenge. The vibrations limit the focus of the ions to about six nanometers in diameter, which is nothing special in the world of ion microscopy. And because the trap only emits three ions every second, the amount of signal to work with is still very small.

Indeed, in one of the researchers' demonstration images, each pixel is obtained by releasing one ion from the trap and either detecting it or not. Amazingly, the system works quite well. And just to show that this process is much better than a traditional source with the same average number of ions per second, the researchers made their gated source emit at random times (so that it behaves exactly like a classical ion source). The image obtained from randomly emitted ions was much blurrier and missed many features.

Superresolution

Normally, if the diameter of the ion beam was six nanometers, seeing features significantly smaller than six nanometers is very difficult. But this is where the power of a deterministic source (it only emits an ion when you ask it to) comes in. It opens up statistical techniques that can't be readily applied to random sources. The researchers demonstrated the power of these statistical techniques by showing that they could determine diameters of holes much more accurately than the native resolution of the ion microscope would allow. Essentially, if you have an ion source that only provides a single ion per pixel, edge detection becomes very noisy. But the use of statistics allows the edge to be resolved with higher precision.

Even with the power of statistics, the imaging results are not stellar. That should not be your takeaway message, though. This is the first microscope of its type, and the researchers have improvements in mind. For instance, the trap design can be changed so that it automatically loads ions at the same time that it ejects them, allowing a higher ion flux overall (the researchers estimate that they could exceed 100 ions per second). Second, because these are ultra-cold ions, their state can be manipulated with lasers. This means you can imagine doing polarized spin microscopy so that the microscope is directly sensitive to the magnetic properties of the sample. Or you could put the ion in an excited state and examine the end state to determine more about the ion-sample interactions.

One really cool idea is that because the ion flux is directly under the control of the researcher, things like stroboscopic imaging with picosecond time resolution might be possible. Finally, just to make this really exciting, you can use the time it takes for the ions to go from the trap to the detector to correct the lens and obtain even more detailed images.

In other words, this is a first step on a very interesting journey.

Physical Review Letters, 2016, DOI: 10.1103/PhysRevLett.117.043001