麻豆淫院

No image is infinitely sharp. For 150 years, it has been known that no matter how ingeniously you build a microscope or a camera, there are always fundamental resolution limits that cannot be exceeded in principle. The position of a particle can never be measured with infinite precision; a certain amount of blurring is unavoidable. This limit does not result from technical weaknesses, but from the physical properties of light and the transmission of information itself.

TU Wien (Vienna), the University of Glasgow and the University of Grenoble therefore posed the question: Where is the absolute limit of precision that is possible with optical methods? And how can this limit be approached as closely as possible?

And indeed, the international team succeeded in specifying a lowest limit for the theoretically achievable precision and in developing AI algorithms for neural networks that come very close to this limit after appropriate training. This strategy is now set to be employed in imaging procedures, such as those used in medicine. The study is in the journal Nature Photonics.

An absolute limit to precision

"Let's imagine we are looking at a small object behind an irregular, cloudy pane of glass," says Prof Stefan Rotter from the Institute of Theoretical 麻豆淫院ics at TU Wien. "We don't just see an image of the object, but a complicated light pattern consisting of many lighter and darker patches of light. The question now is: how precisely can we estimate where the object actually is based on this image鈥攁nd where is the absolute limit of this precision?"

Such scenarios are important in biophysics or medical imaging, for example. When light is scattered by biological tissue, it appears to lose information about deeper tissue structures. But how much of this information can be recovered in principle? This question is not only of technical nature, but physics itself sets fundamental limits here.

The answer to this question is provided by a theoretical measure: the so-called Fisher information. This measure describes how much information an optical signal contains about an unknown parameter鈥攕uch as the object position. If the Fisher information is low, precise determination is no longer possible, no matter how sophisticatedly the signal is analyzed. Based on this Fisher information concept, the team was able to calculate an upper limit for the theoretically achievable precision in different experimental scenarios.

Neural networks learn from chaotic light patterns

While the team at TU Wien was providing theoretical input, a corresponding experiment was designed and implemented by Dorian Bouchet from the University of Grenoble (F) together with Ilya Starshynov and Daniele Faccio from the University of Glasgow (U.K.). In this experiment, a laser beam was directed at a small, reflective object located behind a turbid liquid, so that the recorded images only showed highly distorted light patterns. The measurement conditions varied depending on the turbidity鈥攁nd therefore also the difficulty of obtaining precise position information from the signal.

"To the human eye, these images look like random patterns," says Maximilian Weimar (TU Wien), one of the authors of the study. "But if we feed many such images鈥攅ach with a known object position鈥攊nto a neural network, the network can learn which patterns are associated with which positions." After sufficient training, the network was able to determine the object position very precisely, even with new, unknown patterns.

Almost at the physical limit

Particularly noteworthy in the research was the finding that the precision of the prediction was only minimally worse than the theoretically achievable maximum, calculated using Fisher information. "This means that our AI-supported algorithm is not only effective, but almost optimal," says Stefan Rotter. "It achieves almost exactly the precision that is permitted by the laws of physics."

This realization has far-reaching consequences: With the help of intelligent algorithms, optical measurement methods could be significantly improved in a wide range of areas鈥攆rom medical diagnostics to materials research and quantum technology. In future projects, the research team wants to work with partners from applied physics and medicine to investigate how these AI-supported methods can be used in specific systems.