Super-resolution optical classifier with high photon efficiency

Robust super-resolution classifier by nonlinear optics

Spatial-mode projective measurements could achieve super-resolution in remote sensing and imaging, yet their performance is usually sensitive to the parameters of the target scenes. We propose and demonstrate a robust classifier of close-by light sources using optimized mode projection via nonlinear optics. Contrary to linear-optics based methods using the first few Hermite-Gaussian (HG) modes for the projection, here the projection modes are optimally tailored by shaping the pump wave to drive the nonlinear-optical process. This minimizes modulation losses and allows high flexibility in designing those modes for robust and efficient measurements. We test this classifier by discriminating one light source and two sources separated well within the Rayleigh limit without prior knowledge of the exact centroid or brightness. Our results show a classification fidelity of over 80% even when the centroid is misaligned by half the source separation, or when one source is four times stronger than the other.

Experimental demonstration of quantum-inspired optical symmetric hypothesis testing

We use a phase-sensitive measurement to perform a binary hypothesis testing, i.e., distinguish between one on-axis and two symmetrically displaced Gaussian point spread functions. In the sub-Rayleigh regime, we measure a total error rate lower than allowed by direct imaging. Our results experimentally demonstrate that linear-optical spatial mode transformations can provide useful advantages for object detection compared with conventional measurements, even in the presence of realistic experimental cross talk, paving the way for meaningful improvements in identifying, detecting, and monitoring real-world, diffraction-limited scenes.

Identifying Objects at the Quantum Limit for Superresolution Imaging

We consider passive imaging tasks involving discrimination between known candidate objects and investigate the best possible accuracy with which the correct object can be identified. We analytically compute quantum-limited error bounds for hypothesis tests on any library of incoherent, quasimonochromatic objects when the imaging system is dominated by optical diffraction. We further show that object-independent linear-optical spatial processing of the collected light exactly achieves these ultimate error rates, exhibiting scaling superior to spatially resolved direct imaging as the scene becomes more severely diffraction limited. We apply our results to example imaging scenarios and find conditions under which superresolution object discrimination can be physically realized.

Imaging arbitrary incoherent source distributions with near quantum-limited resolution

We demonstrate an approach to obtaining near quantum-limited far-field imaging resolution of incoherent sources with arbitrary distributions. Our method assumes no prior knowledge of the source distribution, but rather uses an adaptive approach to imaging via spatial mode demultiplexing that iteratively updates both the form of the spatial imaging modes and the estimate of the source distribution. The optimal imaging modes are determined by minimizing the estimated Cramér-Rao bound over the manifold of all possible sets of orthogonal imaging modes. We have observed through Monte Carlo simulations that the manifold-optimized spatial mode demultiplexing measurement consistently outperforms standard imaging techniques in the accuracy of source reconstructions and comes within a factor of 2 of the absolute quantum limit as set by the quantum Cramér-Rao bound. The adaptive framework presented here allows for a consistent approach to achieving near quantum-limited imaging resolution of arbitrarily distributed sources through spatial mode imaging techniques.

Quantum-accelerated imaging of N stars

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.

Single-pixel pattern recognition with coherent nonlinear optics

In this Letter, we propose and experimentally demonstrate a nonlinear-optics approach to pattern recognition with single-pixel imaging and a deep neural network. It employs mode-selective image up-conversion to project a raw image onto a set of coherent spatial modes, whereby its signature features are extracted optically in a nonlinear manner. With 40 projection modes, the classification accuracy reaches a high value of 99.49% for the modified national institute of standards and technology handwritten digit images, and up to 95.32%, even when they are mixed with strong noise. Our experiment harnesses rich coherent processes in nonlinear optics for efficient machine learning, with potential applications in online classification of large-size images, fast lidar data analyses, complex pattern recognition, and so on.