No image is infinitely sharp. No matter how well a microscope or camera is designed, there are always fundamental limits to precision that cannot be exceeded. For example, the position of a particle can never be measured with infinite precision; a certain degree of uncertainty is inevitable. This limit is not the result of technical weaknesses, but of the intrinsic physical properties of light and the transmission of information itself.

Physicists from the Laboratoire interdisciplinaire de physique (LIPhy - CNRS/UGA), the University of Glasgow (United Kingdom) and TU Wien (Austria) asked themselves the following questions: what is the absolute limit of precision that can be achieved with optical measurement methods? And how can we get as close to it as possible? This international team calculated an ultimate limit to the theoretically achievable precision and successfully developed artificial neural networks that approach it once they have been properly trained. This strategy could eventually be used to improve current imaging methods, for example for applications in biomedical imaging.

To illustrate the challenge of this research, imagine that we are observing a small object located behind a translucent shower curtain. Due to the random scattering of light by the curtain, we do not see just an image of the object, but highly distorted light patterns. The question now is: how can we accurately estimate the actual position of the object from this image, and what is the ultimate limit to the accuracy that can be achieved? Such scenarios are particularly important in biophysics and medical imaging. Indeed, when light is scattered by biological tissues, information about the deepest structures of these tissues is necessarily lost. But how much information can we recover in principle? This question goes beyond simple technical limitations, as physics itself imposes a fundamental limit. 


The answer to this question is provided by a theoretical measure called Fisher information. It describes the amount of information contained in a noisy optical signal concerning, for example, the position of an object. If the Fisher information is low, it will not be possible to determine the position accurately, even with very advanced signal analysis methods. Using this concept, the researchers were able to calculate an upper limit on the precision that can theoretically be achieved in optical experiments. 

The experiment designed to validate the method consisted of directing a laser beam at a small reflective object. This object was located behind a cloudy liquid, so that only highly distorted patterns appeared on the recorded images. By presenting numerous images of this type (each with a known object position) to a neural network, the network was able to learn which patterns were associated with which positions. After sufficient training, the network was able to determine the position of the object with high accuracy, even with new and unknown patterns. Remarkably, the accuracy of the network's predictions was only slightly lower than the theoretically achievable accuracy, calculated from Fisher's information, proving that the artificial neural networks implemented in this study are nearly optimal with respect to the laws of physics.

This result is likely to have significant consequences: with the help of intelligent algorithms, optical measurement methods could be improved in many fields such as medical imaging, materials science and quantum technology. As part of future projects, the researchers involved in this project hope to collaborate with departments of applied physics and medicine in order to implement these AI-based methods in practical applications.