Simple Equations Power Carney's Research

OCT images of a rat tumor before and after using Interferometric Synthetic Aperture Microscopy
OCT images of a rat tumor before and after using Interferometric Synthetic Aperture Microscopy

Beckman Institute researcher Scott Carney works at the highest levels of mathematics in order to advance imaging technologies, but his research approach is based on four simple equations that were first postulated more than a century ago.

Like any good theoretical physicist, Scott Carney likes explanations that are simple yet – in his discipline’s most praiseworthy adjective – elegant. For Carney, a Beckman Institute researcher with a focus on theoretical optics, the explanation that best serves his work is Maxwell’s equations, a set of four equations describing the fundamentals of electromagnetism. 

“Your life is dominated by electromagnetism and gravity, and gravity is simple,” Carney explained in his third floor Beckman office, using elements at hand to illustrate the point. “Maxwell’s equations dominate your experience in this world, from the light in this room to the extremely high order, multi-polar interactions between the atoms in my finger and the atoms in this tabletop which keep my finger from passing through it. The seeming diversity of phenomena that we encounter, they all spring from this same basic set of very, very simple equations.”

A Scottish-born physicist, James Clerk Maxwell postulated his famous equations in 1873 (a link to them from Champaign’s Wolfram Research can be found here). They describe the fundamental laws of magnetism and electricity, as well as light, as they work in our world.

Carney, whose main research efforts involve the mathematics underlying imaging modalities, says those equations are just as valuable to a researcher like himself looking to advance modern imaging methods as they were to scientists in the 19th Century.

“That is why it is so significant; it is everywhere,” Carney said. “Now, it’s timely these days because in optics, which is really where I work, we are in the last few years able to make measurements we’ve never been able to make before. New detector technology allows us to make very fast measurements and new laser technology allows us to make very short laser pulses.

“In these new regimes there are new phenomena that, despite the fact that Maxwell’s equations are 140 years old, haven’t thoroughly been investigated because there was no reason to do so. But now the technology is there to actually exploit these phenomena and somebody who is reasonably well-versed in classical electrodynamics can make a living exploiting these new abilities.”

Carney is taking advantage of the power of Maxwell’s equations as he works with Beckman colleagues like Stephen Boppart and Rohit Bhargava from the Bioimaging Science and Technology group to advance imaging modalities such as optical coherence tomography (OCT) and spectroscopy.

“Maxwell’s equations provide us a link between the numbers that come up on the detectors and the structure of the object we are trying to investigate,” Carney said. “They provide a mapping between the two. Once we have the numbers from the detector, we’d like to know what the object’s properties are. Maxwell’s equations provide the bridge between those two things, so when experimenters make measurements with their detectors, I can take the measurements and turn them back into a direct description of the thing we really want to know about.

“I’ve been doing a lot of work in OCT with Stephen Boppart and spectroscopy with Rohit Bhargava and outside collaborators to take this 140-year-old piece of physics, Maxwell’s equations, put a little bit of fancy mathematics around it, and make new predictions about the way the world works.”

One collaboration with Boppart used Carney’s computational approach to take blurry optical microscopy images and turn them into sharp three-dimensional images. The technique, called Interferometric Synthetic Aperture Microscopy or ISAM, reconstructs blurry images into high resolution optical signals by taking advantage of the sample’s light-scattering physics. The method is a huge improvement for optical coherence tomography imaging. 

“It’s one of those things where there were a lot of people working in the field developing the technology, the instruments, but there really weren’t any theorists looking at the problem,” Carney said. “There is a common theme throughout my work here: there is a lot of great technology developed that can be taken to a higher level simply by understanding how it actually works. For example, if we understand optics at the level of rays and trace things through a classical optical system, we can design instruments that have amazing capabilities that can only be realized by understanding the physics beyond simple ray models.”

Carney said that was the case with OCT and the development of ISAM technology.

“Within the OCT community, people built instruments that were much more capable than they realized,” he said. “But take a step back, and see that the simplified straight line beam propagation model that is used to design and understand this instrument really springs from something more fundamental. Let’s take a look at the instrument model within the context of this more fundamental thing, Maxwell’s equations, and see if there is more than meets the eye here.

“In fact that’s what happened with Steve and me and the OCT problem. By taking a step back we were able to realize the full potential of the instrument.”

Carney is an Associate Professor in the Department of Electrical and Computer Engineering at Illinois. A native of New York state, Carney earned his Ph.D. from the University of Rochester in 1999, coming to Illinois in 2001.

As an undergraduate at Illinois, Carney found a mentor at Beckman in former faculty member John Tucker who, Carney says, shone a light on the path he now follows.

“He really opened my eyes to the whole concept that you can do applied physics, study fundamental, beautiful things, and make a living inventing stuff and applying it,” Carney said.

Carney’s Optical Science research group at Beckman studies optical physics, which includes topics such as imaging, near-field microscopy, and mathematical methods in inverse scattering and the propagation of light.

As might be expected, Carney’s teaching approach as an ECE professor also involves the encompassing power of Maxwell’s equations. Carney, who has won outstanding advisor and excellence in teaching awards, teaches three graduate level courses and a senior design class that he says has been a big influence in his approach to teaching. Inherited from ECE colleague Gary Swenson, the senior design class lets students design their own projects, within certain guidelines.

“The students have a sense of ownership of what they’re doing, so there isn’t a sense that here is a textbook and here are a set of homework problems that I’m pushing on you,” Carney said. “There’s no excuse for not performing so they have a self-induced pressure to succeed.

“I also think that because they are picking their own projects with my guidance, they find the thing that really excites them, stimulates them intellectually. I think that’s the most effective way to master material. You have to have a sense of excitement. It absolutely should be thrilling to do what we do, to study things, to understand how the world works and, as an engineer, to understand how to control your own environment.”

With backgrounds and research roles in both theory and engineering, Carney is at a unique intersection when it comes to the science he practices.

“I think there are lots of things I am doing right now that are really important and could have great applications, but will simply vanish and never matter at all,” Carney said with a laugh. “But it’s very hard to tell what those things will be. Some of the more significant stuff I’ve done, some that have proven to be more significant, started on a lark. But I don’t think I have ever worked on a problem of which I thought ‘this is definitely useless and I’ll do it just for the sheer mathematical exercise of doing it.’”

And that means that contributing to advances in practical applications such as imaging methods is a driving force for Carney.

“The application is really very important to me,” he said. “I do take a long view of applications; I am a theorist. But I don’t think I would work on the theory problems that I work on if I didn’t think there were good applications for them and that they might be important in the lives of my fellow citizens.

“It is an enormous privilege to do work that is sort of fun, get paid for it, and think that some of it, someday, might really matter. It’s very satisfying.”