Dr. Arthur McCray is a postdoctoral researcher in the materials science department at Stanford University. He studied physics at Carleton College and received his PhD in Applied Physics from Northwestern University in 2023. Arthur grew up near Seattle and attended Lakeside for middle and high school. He loved sports and reading--especially science fiction--as a kid. He knew he wanted to become a scientist when he read, “A Brief History of Time” by Stephen Hawking because it took the scale and epic grandeur of science fiction concepts and turned them into something he could study. He decided to become a physicist in high school because physics helps us to answer the “why” questions we ask about the world, e.g. why is the sky blue? In his free time, he loves getting outdoors. Biking, hiking, and climbing are his main hobbies and he also loves to cook!
Arthur works in a lab that focuses on developing methods for very high resolution imaging. They use transmission electron microscopes (TEMs, like the one further down the page) that use electrons to image a sample rather than photons (which are light particles, and what typical microscopes use). This lets a TEM capture images with enough resolution to see individual atoms!
Crystal structure (left) and TEM images (right) of a material known as Cr2Si2Te6 (CST). Images (a) and (b) show a representation of the crystal structure of CST. Images (c) and (d) show TEM images of CST along two different directions: (c) corresponds to the view shown in (b), and (d) is looking down the x-axis shown in (a). Colored circles are overlaid to depict where the different atoms would sit in each image. Note the scale bar in (c) and (d)! 1 nanometer (nm) is equal to 10-9 meters, that’s 50,000 times smaller than the diameter of a human hair, or 1,000 times smaller than an e-coli bacteria.
Arthur in front of a (quite small) TEM that he used for his PhD work.
Image courtesy of Arthur McCray"I love my job because it lets me do the things that originally inspired me to become a scientist: I get to answer fundamental questions about the world, solve interesting problems, and learn things that nobody knew before."
"Growing up I had many questions about why the world is the way it is. In middle school I realized that the people who actually had answers to my questions were science teachers and scientists, so I decided to become one myself."
A fundamental limitation of transmission electron microscopes (TEMs) is that they operate in a “projection imaging” mode. This is like shining a bright light onto an object and seeing the shadow projected against a wall; the shadow will only show the outline of the object. We lose all the 3D information about the object or, to put it another way, the 3D object is “projected” onto the 2D surface of the wall. The relationship between the object and its shadow can be quite unintuitive! As an example, artists have made fantastic sculptures that look like a tangled mess of wire, but which project the shadow of a human head.
The sculptures of tangled metal to the right cast shadows that look like human heads. If all we could see were the shadows, how could we determine the 3D shapes of the sculptures?
Inverse problems are defined by the fact that it is easy to calculate what happens in one direction, e.g. it is easy to use a 3D shape to calculate a 2D projection, but it is very difficult to go the other way, from a picture of a 2D shadow to the 3D object that cast the shadow. Reconstructing the 3D shape of an object is just one example of an inverse problem, and there are many others that occur when imaging with an electron microscope.
One topic that is particularly exciting to Arthur is how we can use computational tools to solve inverse problems that we encounter when using a TEM (transmission electron microscope). One example is that of reconstructing a 3D structure from 2D projected images. This can’t be done from a single image (the problem is “under-constrained”, meaning there are many solutions that could work), but it can be done by recording lots of images with the sample at different orientations. These images can be used to reconstruct the 3D sample in a process known as tomography.
Diagram of an electron tomography experiment. The nanoparticle sample (left) is rotated within the microscope and images are taken at many tilt angles (center). These are pieced together over and over again (right) to reconstruct the 3D shape of the nanoparticle.
Courtesy of AAAS: https://doi.org/10.1126/science.aaf2157In all cases, inverse problems occur because the images that we collect don’t readily contain the most important information about a sample. This occurs frequently when using a TEM, and it can cause problems both when imaging the atomic structure of a sample and when imaging other things like magnetic fields.
Much of Arthur’s work focuses on developing computation tools, i.e. writing computer programs, that help us solve inverse problems (determining 3D structure from 2D information) and better understand images that are recorded with a TEM. Machine learning is a particularly important tool in his work, as it has greatly expanded the types of tasks that computers can perform. With machine learning, we can train artificial neural networks, which are a type of computer program loosely based on the cell networks that make up our brains. Neural networks can be trained to do lots of useful and otherwise tedious tasks, for example they can be trained to identify specific features in an image more accurately and much, much faster than can be done by hand.
We can also use machine learning to help us solve inverse problems directly. If we can develop a mathematical forward model for a particular problem (eg recognizing the 2D projection of a 3D object), then we can apply a machine learning technique called “backpropagation” to help us directly solve the problem, meaning the program could be trained to determine 3D structure from 2D images. This is not a magic bullet for solving every hard problem, but we have shown it to be a very powerful technique that can be applied to many situations. In many cases we can combine this technique with neural networks and other physics-based computational techniques, and this provides a powerful basis for much of Arthur’s work.