New theory describes how waves convey information from the environment

Waves pick up information from their environment, causing them to propagate. A theory of information transmitted by waves has now been developed at TU Wien, with astonishing results that can be used for technical applications.

Ultrasound is used to analyze the body, radar systems to study the airspace or seismic waves to study the interior of our planet. Many areas of research deal with waves that are deflected, scattered or reflected by their surroundings. As a result, these waves carry a certain amount of information about their environment, and this information must then be extracted as completely and accurately as possible.

The search for the best way to do this has been the subject of research around the world for years. TU Wien has now succeeded in describing the information that a wave carries about its environment with mathematical precision. This has made it possible to show how waves pick up information about an object and then transport it to a measuring device.

This can now be used to generate customized waves to extract the maximum amount of information from the environment, for example for more accurate imaging processes. This theory was confirmed with microwave experiments. The results were published in the journal Natural physics.

Where exactly is the information located?

“The basic idea is quite simple: you send a wave to an object and the part of the wave that is reflected from the object is measured by a detector,” says Prof. Stefan Rotter from the Institute for Theoretical Physics of TU Wien.

“The data can then be used to learn something about the object, for example its precise position, speed or size.” This information about the environment that this wave brings is known as ‘Fisher information’.

However, it is often not possible to capture the entire wave. Usually only part of the wave reaches the detector. This begs the question: where exactly is this information located in the wave? Are there parts of the wave that can be safely ignored? Could a different waveform perhaps provide more information to the detector?

“To get to the bottom of these questions, we took a closer look at the mathematical properties of this Fisher information and came up with some amazing results,” says Rotter.

“The information satisfies a so-called continuity equation: the information in the wave is preserved as it moves through space, according to laws very similar to laws for the conservation of energy, for example.”

An understandable information path

Using the newly developed formalism, the research team has now been able to calculate exactly at which point in space the wave actually contains how much information about the object. It turns out that information about different properties of the object (such as position, speed and size) can be hidden in completely different parts of the wave.

As the theoretical calculations show, the information content of the wave depends precisely on how strongly the wave is influenced by certain properties of the object under investigation.

“For example, if we want to measure whether an object is a little further to the left or a little further to the right, then the Fisher information is carried exactly by the part of the wave that contacts the right and left edges. of the object,” says Jakob Hüpfl, the PhD student who played a key role in the research.

“This information then spreads out, and the more of this information reaches the detector, the more accurately the position of the object can be read from it.”

Microwave experiments confirm the theory

In Ulrich Kuhl’s group at the University of Cote d’Azur in Nice, experiments were carried out by Felix Russo as part of his master’s thesis: A disorderly environment was created in a microwave chamber using randomly positioned Teflon objects. A metal rectangle was placed between these objects, the position of which had to be determined.

Microwaves were sent through the system and then picked up by a detector. The question now was: how well can the position of the metal rectangle be deduced from the waves received in the detector in such a complicated physical situation and how does the information flow from the rectangle to the detector?

By accurately measuring the microwave field, it was possible to show exactly how the information about the horizontal and vertical position of the rectangle spreads: it emanates from the respective edges of the rectangle and then moves with the wave – without information is lost. exactly as predicted by the newly developed theory.

Possible applications in many areas

“This new mathematical description of Fisher information has the potential to improve the quality of a variety of imaging methods,” says Rotter. If it is possible to quantify where the desired information is located and how it propagates, then it also becomes possible, for example, to better position the detector or to calculate adapted waves that transport the maximum amount of information to the detector.

“We tested our theory with microwaves, but it also applies to a wide variety of waves with different wavelengths,” Rotter emphasizes. “We provide simple formulas that can be used to improve both microscopy methods and quantum sensors.”