What fundamentally limits our ability to see planets, stars, and galaxies through a telescope? To differentiate between one star and a galaxy that contains 100 thousand million stars?
“Quantum mechanics,” says Mankei Tsang, a researcher at the National University of Singapore.
This quantum mechanical limit is the subject of two new research efforts that will soon be published in the American Physical Society’s journal Physical Review A—one by Tsang and one by Yale University’s Sisi Zhou and Liang Jiang. Working independently and using different approaches, Tsang and the Yale team reached similar conclusions about what the limit actually is, and both show that we haven’t reached the limit yet. This means that, with clever approaches and state-of-the-art tools, we should be able to create more detailed images of the night sky than ever before.
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| Mauna Kea Observatory in Hawaii. Image Credit: Photo by Conner Baker on Unsplash. |
Imagine that you’re taking a picture of the sky through a telescope. At a basic level, the image depends on the intensity of light that hits each pixel in the camera’s detector. Even with the best possible camera, our ability to distinguish between two stars or galaxies that appear close together is pretty set by something called the Rayleigh criterion. “Rayleigh’s criterion describes the phenomenon that it is difficult to resolve two optical sources when the distance between their centers is too small, compared to the width of the sources,” explains Zhou.
The good news is: there’s a way around this limit.
Two years ago, Tsang and his colleagues Ranjith Nair and Xiao-Ming Lu showed that we can extract even more information from starlight than previously thought, using measurement techniques based on quantum mechanics. With this information, they showed, researchers can differentiate between two stars (or other point sources) so close together that they would normally be indistinguishable, thanks to Rayleigh’s criterion. You can read more about this research in our 2016 post Resolving Starlight with Quantum Technology.
Tsang’s analysis was restricted to two point sources, so the next step was to see if this technique could be generalized to cases of three or more, or even an unknown number of sources.
This was a much harder problem. “The process was quite excruciating,” Tsang says. As any physicist will tell you, problems get difficult quickly when you go from looking at how two objects interact to three or more—not to mention an unknown number. He wanted to solve this problem rigorously and completely, and that required learning math that few people have ever used and diving deep into the fundamental laws of quantum mechanics.
We don’t usually think of galaxies and stars as quantum objects, but remember that we “see” them one tiny bit of light at a time through a telescope. Light is a wave and a particle, and both of these properties work against us when it comes to resolving bright objects on an image. Explains Tsang, “the wave nature introduces blurring to an image, while the random arrival of photons on a camera introduces noise.”
Zhou and Jiang started out hoping that the measurement technique introduced by Tsang would bypass Rayleigh’s criterion for arbitrary imaging situations, but that didn’t go very well. “After we tried some examples and failed, we realized that instead of completely overcoming Rayleigh’s criterion, the new technique also has a resolution limit,” says Zhou. In other words, they realized there was still a limit to how close sources can be in order to be resolvable, but it has to do with quantum mechanics, not Rayleigh’s criterion. Their work described this limit and presented what they call “a modern description of Rayleigh’s criterion.”
When this result came out, Tsang was still elbow-deep in a thorough exploration of the topic. “Seeing their work just motivated me to work harder to reach the result using my method,” he explains. A few months later, he arrived at what he calls a more refined version of their result—a similar finding by way of a different approach.
In the last few decades, better equipment and clever designs have allowed us to dramatically reduce the noise and blurriness in optical images, but the limit reported by Tsang, Zhou, and Jiang tells us that we can never completely eliminate those features, no matter how good our equipment is. Perhaps more importantly, it gives us something to strive for. “The good news is that current imaging systems are nowhere near the limit, and researchers have recently invented techniques that can reach it,” says Tsang.
So, what is the limit?
Rather than a value like the speed of light, the limit is a set of equations that take into account the quantum mechanical nature of light. To most people the equations looks like a code written in Greek letters and symbols, but to the trained eye, they inspire a path toward real technology with practical applications. Such tools could reveal details about the universe that have been there all along, but that we’ve never been able to resolve before.