A new theory describes how waves transmit information from the surroundings

Waves collect information from their environment through which they travel. At TU Wien, a theory of information carried by waves has now been developed – with amazing results that can be used for technical applications.

Ultrasound is used to analyze the body, radar systems to study 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. Thanks to this, these waves carry a certain amount of information about their environment, and this information must then be extracted as comprehensively and accurately as possible.

Finding the best way to achieve this has been the subject of research around the world for many years. TU Wien has now succeeded in describing the information transmitted by the wave about its environment with mathematical precision. This made it possible to show how the waves capture information about the object and then transmit it to the measuring device.

This can now be used to generate tailored waveforms to extract the maximum amount of information from the environment – ​​for example for more accurate imaging processes. This theory was confirmed by 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 at an object and the part of the wave that is scattered back from the object is measured by the detector,” says Prof. Stefan Rotter from the Institute of Theoretical Physics at TU Wien.

“The data can then be used to learn something about the object – for example, its exact position, speed or size.” This information about the environment that this wave carries with it is called “Fisher information”.

However, it is often not possible to capture the whole 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 give the detector more information?

“To get to the heart 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 the so-called continuity equation – the information in the wave is preserved as it moves through space, according to laws that are very similar to the laws of conservation of energy, for example.”

An understandable way of information

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

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

“For example, if we want to measure whether an object is a little more to the left or a little more to the right, then the Fisher information is carried precisely by the part of the wave that comes into contact with the right and left edges. object,” says Jakob Hüpfl, a doctoral student who played a key role in the study.

“This information is then expanded, 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, Felix Russo conducted experiments as part of his thesis: A disordered environment was created in a microwave chamber using randomly placed Teflon objects. A metal rectangle was placed between these objects, the position of which was 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 captured by the detector in such a complex 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 propagates: it originates from the respective edges of the rectangle and then moves along with the wave – without any information being lost, just as the newly developed theory predicts.

Possible applications in many areas

“This new mathematical description of Fisher information has the potential to improve the quality of various imaging methods,” says Rotter. If it is possible to quantify where the desired information is located and how it propagates, then it is also possible, for example, to place the detector more appropriately or to calculate tailored waves that will transmit the maximum amount of information to the detector.

“We tested our theory using microwaves, but it is equally valid for a wide range of waves with different wavelengths,” Rotter points out. “We provide simple formulas that can be used to improve both microscopic methods and quantum sensors.”