Space Situational Awareness

The Rayleigh limit and low Signal-to-Noise Ratio (SNR) scenarios pose significant limitations to optical imaging systems used in remote sensing, infrared thermal imaging, and space domain awareness. In this study, we introduce a Stochastic Sub-Rayleigh Imaging (SSRI) algorithm to localize point objects and estimate their positions, brightnesses, and number in low SNR conditions, even below the Rayleigh limit. Our algorithm adopts a maximum likelihood approach and exploits the Poisson distribution of incoming photons to overcome the Rayleigh limit in low SNR conditions. In our experimental validation, which closely mirrors practical scenarios, we focus on conditions with closely spaced sources within the sub-Rayleigh limit (0.49-1.00R) and weak signals (SNR less than 1.2). We use the Jaccard index and Jaccard efficiency as a figure of merit to quantify imaging performance in the sub-Rayleigh region. Our approach consistently outperforms established algorithms such as Richardson-Lucy and CLEAN by 4X in the low SNR, sub-Rayleigh regime. Our SSRI algorithm allows existing telescope-based optical/infrared imaging systems to overcome the extreme limit of sub-Rayleigh, low SNR source distributions, potentially impacting a wide range of fields, including passive thermal imaging, remote sensing, and space domain awareness.

The growth in space activity has increased the need for Space Domain Awareness (SDA) to ensure safe space operations. Imaging and detecting space targets is, however, challenging due to their dim appearance, small angular size/separation, dense distribution, and atmospheric turbulence. These challenges render space targets in ground-based imaging observations as point-like objects in the sub-Rayleigh regime, with extreme brightness contrast but a low photon budget. Here, we propose to use the recently developed quantum-accelerated imaging (QAI) for the SDA challenge. We mainly focus on three SDA challenges (1) minimal a priori assumptions (2) many-object problem (3) extreme brightness ratio. We also present results on source estimation and localization in the presence of atmospheric turbulence. QAI shows significantly improved estimation in position, brightness, and number of targets for all SDA challenges. In particular, we demonstrate up to 2.5 times better performance in source detection than highly optimized direct imaging in extreme scenarios like stars with a 1000 times brightness ratio. With over 10 000 simulations, we verify the increased resolution of our approach compared to conventional state-of-the-art direct imaging paving the way towards quantum optics approaches for SDA.

Photon statistics of an optical field can be used for quantum optical sensing in low light level scenarios free of bulky optical components. However, photon-number-resolving detection to unravel the photon statistics is challenging. Here, we propose a novel detection approach, that we call 'photon discerning', which uses adaptive photon thresholding for photon statistical estimation without recording exact photon numbers. Our photon discerner is motivated by the field of neural networks where tunable thresholds have proven efficient for information extraction in machine learning tasks. The photon discerner maximizes Fisher information per photon by iteratively choosing the optimal threshold in real-time to approach the shot noise limit. Our proposed scheme of adaptive photon thresholding leads to unique remote-sensing applications of quantum degree of linear polarization camera and quantum LiDAR. We investigate optimal thresholds and show that the optimal photon threshold can be counter-intuitive (not equal to 1) even for weak signals (mean photon number much less than 1), due to the photon bunching effect. We also put forth a superconducting nanowire realization of the photon discerner which can be experimentally implemented in the near-term. We show that the adaptivity of our photon discerner enables it to beat realistic photon-number-resolving detectors with limited photon-number resolution in certain applications. Our work suggests a new class of detectors for information-theory driven, compact, and learning-based quantum optical sensing.

Intensity interferometry based on Hanbury Brown and Twiss’s seminal experiment for determining the radius of the star Sirius formed the basis for developing the quantum theory of light. To date, the principle of this experiment is used in various forms across different fields of quantum optics, imaging, and astronomy. Although the technique is powerful, it has not been generalized for objects at different temperatures. Here, we address this problem using a generating functional formalism by employing the P-function representation of quantum-thermal light. Specifically, we investigate the photon coincidences of a system of two extended objects at different temperatures using this theoretical framework. We show two unique aspects in the second-order quantum coherence function: interference oscillations and a long-baseline asymptotic value that depends on the observation frequency, temperatures, and size of both objects. We apply our approach to the case of binary stars and discuss the advantages of measuring these two features in an experiment. In addition to the estimation of the radii of each star and the distance between them, we also show that the present approach is suitable for the estimation of temperatures as well. To this end, we apply it to the practical case of binary stars Luhman 16 and Spica α Vir. We find that for currently available telescopes, an experimental demonstration is feasible in the near term. Our work contributes to the fundamental understanding of intensity interferometry of quantum-thermal light and can be used as a tool for studying two-body thermal emitters, from binary stars to extended objects.

Imaging point sources with low angular separation near or below the Rayleigh criterion are important in astronomy, e.g., in the search for habitable exoplanets near stars. However, the measurement time required to resolve stars in the sub-Rayleigh region via traditional direct imaging is usually prohibitive. Here we propose quantum-accelerated imaging (QAI) to significantly reduce the measurement time using an information-theoretic approach. QAI achieves quantum acceleration by adaptively learning optimal measurements from data to maximize Fisher information per detected photon. Our approach can be implemented experimentally by linear-projection instruments followed by single-photon detectors. We estimate the position, brightness, and the number of unknown stars 10∼100 times faster than direct imaging with the same aperture. QAI is scalable to a large number of incoherent point sources and can find widespread applicability beyond astronomy to high-speed imaging, fluorescence microscopy, and efficient optical read-out of qubits.