Green’s Function Retrieval and Passive Imaging from Correlations of Wideband Thermal Radiations
About ten years ago, Weaver and Lobkis showed theoretically and experimentally that the Green’s functions can be retrieved by cross correlating thermal ultrasonic noise in reverberant cavities. This property has later been generalized to other kind of configurations and studies have shown that when noise sources produce a field that is equipartitioned in energy, the time derivative of the noise correlation function at two positions is proportional to the difference between the anticausal and causal Green’s functions. The Green’s function estimation from diffuse noise cross-correlations has paved the way for passive imaging using external noise sources because it is a way to passively estimate the transient response as if one receiver is replaced by a virtual source emitting a short pulse.
In this article we present to our best knowledge the first experimental demonstration of electromagnetic Green’s function retrieval from thermal radiations. The experiment is first conducted in an anechoic room which behave at microwave frequencies as a blackbody because its walls are perfectly absorbing materials. The impulse response between two dipole antennas is estimated by cross correlating milliseconds of ambient thermal radiations and is seen in the attached figure to be in a very good agreement with the impulse response measured actively. We show that the temperature dependence of the cross-correlation amplitude is well predicted by the blackbody theory in the Rayleigh-Jeans limit. The effect of a non-uniform temperature distribution on the cross-correlation time symmetry is also explored. We also cross-correlate thermal radiations in an oven (a reverberant cavity) and we show that more than 10 ns of the impulse response can be reconstructed.
Finally, electromagnetic Green’s function estimation is applied to imaging. We show that not only we retrieve the direct path between antennas but we also accurately detect and localize a metallic cylinder from measurements of ambient thermal radiations. We have therefore created a thermal emission detection and ranging (THEDAR), which consists of an ultrawideband passive radar based on thermal noise diffuse field. This completely differs from narrow band passive radar systems at microwave frequencies which exploit ‘‘illuminators of opportunity,’’ such as broadcast emitters (radio, TV) or wireless networks (GSM, WiFi, Bluetooth, etc.). Here, thanks to the diffuse property of thermal noise, the imaging device only weakly depends on the emission properties of the thermal source.
Davy, M., Fink, M. & de Rosny, J. Green’s Function Retrieval and Passive Imaging from Correlations of Wideband Thermal Radiations. Physical Review Letters 110, 203901 (2013).