Imaging with X-rays is usually pretty disappointing. The expectation is that, because the wavelength is short—wavelengths of 10nm are about 40 times shorter than those of blue light—you'll see lots of features that you would otherwise have missed. But in reality, mostly you get a blur. This comes down to two problems: X-ray sources are not very bright, and that brightness fluctuates. Researchers are instead forced to compromise. You can either image quickly and cope with the noise of the light source, or you can image slowly and suffer from noise due to the sample shifting about. Either way, you lose.

The second issue is that the optic hardware is pretty poor compared to the optics for visible light, so they simply don't capture the X-rays that carry the finest details in the image. So, you might as well have used a very good visible light imaging system or an electron microscope. But researchers have now figured out how to greatly improve the performance of X-ray imaging. All it takes is careful measurements of your X-ray source, a bit of scattered light, and lots of clever math.

Scattered pictures

Instead of sending X-rays through your imaging target and reading them on the other side, you can recreate an image using light that scatters back toward the source. The light that scatters from an object already carries all the information required to recreate an image of it: the scattering angle, amplitude, and phase of the light can be used to calculate the details of an object. Instead of using poor-quality optics, you can simply put a big detector near the sample and capture the scattered light.

The data you capture is called a diffraction pattern, and, unfortunately, it only contains the scattering angle and intensity. The phase information, which is absolutely critical to calculating the image, is lost.

To get an image, the phase needs to be recovered by clever numerical work. The basic idea is that you kind-of-sort-of know what the object looks like, so you calculate the diffraction pattern that object would produce (so you now have phases and amplitudes for each pixel). Then you use the difference between the calculated and measured diffraction pattern to correct the phases and amplitudes produced by your first guess. The corrected phases and amplitudes are next used to recalculate the diffraction pattern, which is corrected again. This continues until the difference between the calculated pattern and the measured pattern reduces below some acceptable threshold.

At this point, since you have calculated the pattern from the phases and amplitudes of the scattered light, you can also use the calculated phases and amplitudes to construct an image of the object. This process is very common in many fields of physics, and it generally works OK, but the details of the images are sometimes disappointing.

These imaging systems also still have physical limits: the smallest object you can see is given by the range of scattering angles collected by the detector, while the sensitivity of the detector and the size of the pixels also limit image details.

The biggest practical limit is the accuracy with which the phase is recovered. The magic in phase recovery is all in how you use your measured data to correct the calculated data.

Adding magic

To make the magic more... magical, researchers have placed an additional step in the measurement process. They measure the spatial profile of the beam before they scatter it off the object. The amplitude measurements are then corrected by this measurement before the phase estimation.

Now, you might think that this is simply correcting for changes to the power of the X-ray light, but it is more than that. The issue is not just that the beam has some fluctuations in intensity. It also has a spatial profile, meaning that the brightness of the light is not the same everywhere on the sample, so different parts of the sample contribute with greater or lesser intensity. And, finally, any light source is either converging or diverging—the beam width is either increasing or decreasing with distance. That means that light doesn't hit the sample at a single angle, but at a range of angles. The diffraction pattern depends on this angle of incidence, so a beam with a range of angles smears the pattern out and adds uncertainty to the phase estimation.

By measuring the beam profile on a regular basis, the researchers don't just get additional information about the brightness and spatial profile of the beam, but also the range of angles of the light incident on the sample. This information is used to modify the calculated diffraction pattern, which is then corrected via comparison with the measured diffraction pattern.

The researchers compared the performance of imaging with and without the extra step. The new step produced images with a resolution of just under 13nm using a wavelength just over 13nm. Given the setup the researchers used, this is actually right at the physical limit of the imaging system. That's also about a factor of five better than images that are reconstructed without the extra step.

One of the nice aspects of this work is that it also uses equipment that you can obtain off the shelf—no facility-sized free electron lasers required here. And there are a lot of places that might be interested in pulling that hardware off the shelf. The semiconductor manufacturing industry, for example, needs high-speed, wide-area imaging, and this may turn out to be one solution.

Nature Photonics, 2017, DOI: 10.1038/NPHOTON.2017.33