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arXiv:2112.05455 · Physical Review A

Quantum-enhanced passive remote sensing

Emre Köse, Gerardo Adesso, Daniel Braun

Published Jul 6, 2022• 7 citations
arXivHTMLPDF

Abstract

We investigate theoretically the ultimate resolution that can be achieved with passive remote sensing in the microwave regime used, e.g., on board of satellites observing Earth, such as the soil moisture and ocean salinity (SMOS) mission. We give a fully quantum mechanical analysis of the problem, starting from thermal distributions of microscopic currents on the surface to be imaged that lead to a mixture of coherent states of the electromagnetic field which are then measured with an array of antennas. We derive the optimal detection modes and measurement schemes that allow one to saturate the quantum Cram\'er-Rao bound for the chosen parameters that determine the distribution of the microscopic currents. For parameters comparable to those of SMOS, a quantum enhancement of the spatial resolution by more than a factor of 20 should be possible with a single measurement and a single detector, and a resolution down to the order of 1 m and less than a $\frac{1}{10}$ K for the theoretically possible maximum number of measurements.

DOI
10.1103/physreva.106.012601

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Proceedings of SPIE, the International Society for Optical Engineering/Proceedings of SPIE•May 13, 2011•0 citations
We investigate theoretically the ultimate resolution that can be achieved with passive remote sensing in the microwave regime used, e.g., on board of satellites observing Earth, such as the soil moisture and ocean salinity (SMOS) mission. We give a fully quantum mechanical analysis of the problem, starting from thermal distributions of microscopic currents on the surface to be imaged that lead to a mixture of coherent states of the electromagnetic field which are then measured with an array of antennas. We derive the optimal detection modes and measurement schemes that allow one to saturate the quantum Cram'er-Rao bound for the chosen parameters that determine the distribution of the microscopic currents. For parameters comparable to those of SMOS, a quantum enhancement of the spatial resolution by more than a factor of 20 should be possible with a single measurement and a single detector, and a resolution down to the order of 1 m and less than a 110\frac{1}{10}101​ K for the theoretically possible maximum number of measurements.
For more than a century, the diffraction limit has defined the resolution achievable by passive optical imaging systems. Although some resolution improvement can be gained through classical data processing of the image, it is limited by the noise arising from quantum nature of light. Minimizing the effect of this noise requires quantum treatment of optical imaging. By reformulating imaging as a problem of quantum measurement and estimation, it becomes possible to identify optimal detection strategies that recover spatial information previously thought inaccessible. This review summarizes the theoretical framework that underpins this development, from the formulation of quantum Cramer-Rao bounds and Chernoff bounds to the construction of receivers that attain them, such as those based on spatial-mode demultiplexing. We show how these methods can beat conventional imaging in the classification, localization, and imaging of sub-Rayleigh incoherent sources. We then discuss extensions to multiparameter and partially coherent scenarios, and highlight the unifying connections between estimation and discrimination tasks. Finally, we survey recent experimental demonstrations that approach quantum-limited resolution and outline emerging applications in microscopy, astronomy, and optical sensing.
We study super-resolution imaging theoretically using a distant nnn-mode interferometer in the microwave regime for passive remote sensing, used, e.g., for satellites like the ``Soil Moisture and Ocean Salinity'' (SMOS) mission to observe the surface of the Earth. We give a complete quantum-mechanical analysis of multiparameter estimation of the temperatures on the source plane. We find the optimal detection modes by combining incoming modes with an optimized unitary that enables the most informative measurement based on photon counting in the detection modes and saturates the quantum Cram\'er-Rao bound from the symmetric logarithmic derivative for the parameter set of temperatures. In our numerical analysis, we achieved a quantum-enhanced super-resolution by reconstructing an image using the maximum likelihood estimator with a pixel size of 3 km, which is ten times smaller than the spatial resolution of SMOS with comparable parameters. Further, we find the optimized unitary for uniform temperature distribution on the source plane, with the temperatures corresponding to the average temperatures of the image. Even though the corresponding unitary was not optimized for the specific image, it still gives a super-resolution compared to local measurement scenarios for the theoretically possible maximum number of measurements.
Spaceborne radar remote sensing of the earth system is essential to study natural and man-made changes in the ecosystem, water and energy cycles, weather and air quality, sea level, and surface dynamics. A major challenge with current approaches is the lack of broad spectrum tunability due to narrow band microwave electronics, that limit systems to specific science variable retrievals. This results in a significant limitation in studying dynamic coupled earth system processes such as surface and subsurface hydrology, where broad spectrum radar remote sensing is needed to sense multiple variables simultaneously. Rydberg atomic sensors are highly sensitive broad-spectrum quantum detectors that can be dynamically tuned to cover micro-to-millimeter waves with no requirement for band-specific electronics. Rydberg atomic sensors can use existing transmitted signals such as navigation and communication satellites to enable remote sensing. We demonstrate remote sensing of soil moisture, an important earth system variable, via ground-based radar reflectometry with Rydberg atomic systems. To do this, we sensitize the atoms to XM satellite radio signals and use signal correlations to demonstrate use of these satellite signals for remote sensing of soil moisture. Our approach provides a step towards satellite-based broad-spectrum Rydberg atomic remote sensing.
We develop a quantum statistical framework for passive optical surface metrology. Modelling a surface as an incoherent ensemble of point emitters imaged through a diffraction-limited system, we employ techniques from quantum parameter estimation and hypothesis testing to derive ultimate bounds for jointly estimating geometrical features and for deciding the presence or absence of surface defects, and we identify optimal measurements from the geometry of the point-spread-function manifold. As a representative application, we analyse a minimal surface crack model based on three point sources and show that spatial mode sorting can simultaneously enable near-quantum-limited estimation of crack width and depth and markedly enhanced detectability of the crack, compared with direct imaging. Our results pave the way towards enhanced optical inspection and characterisation of sub-diffraction surface features by probing a limited number of spatial modes without any illumination control.
Far-field optical imaging inevitably involves low-pass spatial filtering, limiting the resolution. Moreover, conventional imaging suppresses high spatial frequency components close to the cutoff, making them invisible under noise, particularly the shot noise arising from discrete and random nature of quantum light. Here we propose and implement a method for reducing the effect of this noise by optically pre-processing the incoming light prior to detection, thereby optimizing the quantum measurement performed on it. Our scheme, termed Fourier Domain Division (FDD), partitions the Fourier plane into multiple regions for independent detection and subsequent post-processing for image reconstruction. By analyzing the quantum and classical Fisher information, we show that our method is advantageous with respect to direct imaging for high spatial-frequency components. As a result, the number of photons required to achieve a certain signal-to-noise-ratio in the Fourier domain is reduced, thus enhancing the overall resolution in the photon-starved regime. We demonstrate our method in microscopy, achieving 5-fold improvement of Fisher information on high spatial-frequency components. Unlike active super-resolution methods, FDD is passive, making it broadly applicable in microscopy and other imaging scenarios where active illumination is impractical, including astronomy and remote sensing. Our work establishes a general strategy for designing quantum optimized superresolution imaging systems, bridging fundamental quantum limits, practical image analysis and computer vision applications.
A novel quantum phase amplification (QPA) technique is proposed to enhance the spatial resolution of passive imaging systems, without the commensurate increase of the aperture size. The key component of this approach is the production of phase-amplified light, a squeezed state of the electromagnetic field that can be generated in phase-sensitive three-wave mixing (PSTWM). We have established the theoretical basis for QPA using PSTWM and theoretically derived the conditions for the operation of the ubiquitous PSTWM realized by using standard laser technology. In our approach sub-Rayleigh imaging can be explored to perform the super-resolution enhancement of remotely sensed data. We applied the PSTWM to improve the distinguishability of two point sources in several scenarios. In addition, detector segmentation was modeled to optimize the signal-to-noise ratio.