A high-speed super-resolution computational imaging technique is introduced on the basis of classical and quantum correlation functions obtained from photon counts collected from quantum emitters illuminated by spatiotemporally structured illumination. The structured illumination is delocalized—allowing the selective excitation of separate groups of emitters as the modulation of the illumination light advances. A recorded set of photon counts contains rich quantum and classical information. By processing photon counts, multiple orders of Glauber correlation functions are extracted. Combinations of the normalized Glauber correlation functions convert photon counts into signals of increasing order that contain increasing spatial frequency information. However, the amount of information above the noise floor drops at higher correlation orders, causing a loss of accessible information in the finer spatial frequency content that is contained in the higher-order signals. We demonstrate an efficient and robust computational imaging algorithm to fuse the spatial frequencies from the low-spatial-frequency range that is available in the classical information with the spatial frequency content in the quantum signals. Because of the overlap of low spatial frequency information, the higher signal-to-noise ratio (SNR) information concentrated in the low spatial frequencies stabilizes the lower SNR at higher spatial frequencies in the higher-order quantum signals. Robust performance of this joint fusion of classical and quantum computational single-pixel imaging is demonstrated with marked increases in spatial frequency content, leading to super-resolution imaging, along with much better mean squared errors in the reconstructed images.
A high-speed super-resolution computational imaging technique is introduced on the basis of classical and quantum correlation functions obtained from photon counts collected from quantum emitters illuminated by spatiotemporally structured illumination. The structured illumination is delocalized—allowing the selective excitation of separate groups of emitters as the modulation of the illumination light advances. A recorded set of photon counts contains rich quantum and classical information. By processing photon counts, multiple orders of Glauber correlation functions are extracted. Combinations of the normalized Glauber correlation functions convert photon counts into signals of increasing order that contain increasing spatial frequency information. However, the amount of information above the noise floor drops at higher correlation orders, causing a loss of accessible information in the finer spatial frequency content that is contained in the higher-order signals. We demonstrate an efficient and robust computational imaging algorithm to fuse the spatial frequencies from the low-spatial-frequency range that is available in the classical information with the spatial frequency content in the quantum signals. Because of the overlap of low spatial frequency information, the higher signal-to-noise ratio (SNR) information concentrated in the low spatial frequencies stabilizes the lower SNR at higher spatial frequencies in the higher-order quantum signals. Robust performance of this joint fusion of classical and quantum computational single-pixel imaging is demonstrated with marked increases in spatial frequency content, leading to super-resolution imaging, along with much better mean squared errors in the reconstructed images.
Pixelation occurs in many imaging systems and limits the spatial resolution of the acquired images. This effect is notably present in quantum imaging experiments with correlated photons in which the number of pixels used to detect coincidences is often limited by the sensor technology or the acquisition speed. Here, we introduce a pixel super-resolution technique based on measuring the full spatially-resolved joint probability distribution (JPD) of spatially-entangled photons. Without shifting optical elements or using prior information, our technique increases the pixel resolution of the imaging system by a factor two and enables retrieval of spatial information lost due to undersampling. We demonstrate its use in various quantum imaging protocols using photon pairs, including quantum illumination, entanglement-enabled quantum holography, and in a full-field version of N00N-state quantum holography. The JPD pixel super-resolution technique can benefit any full-field imaging system limited by the sensor spatial resolution, including all already established and future photon-correlation-based quantum imaging schemes, bringing these techniques closer to real-world applications.
Techniques of optical superresolution imaging are vital for uncovering the complex dynamics of biochemistry in cellular environments. However the practical resolution for superresolution imaging is limited by the increased photon budget for superresolution, compared with conventional microscopy. For this reason it is important to determine the optimal methods for analysing all of the incoming information. Most approaches to microscopy use only the wave-like properties of light, but the particle-like nature of light provides extra information that is normally inaccessible and can be used to increase imaging resolution. Here we theoretically study the localisation of quantum emitters using higher-order quantum correlation functions to understand the resolution that is practically achievable for bio-imaging tasks. We show explicit imaging results for varying number of emitters as a function of correlation order to illustrate the necessary tradeoffs between imaging resolution and acquisition time.
Quantum imaging emerged quite recently as a breakthrough technology of overcoming the diffraction limit in microscopy and enhancement of optical resolution without the necessity to use hard radiation or perform scanning in the near field [1] , [2] . Both, the quantum imaging itself and the more “classical” techniques inspired by it (for example, super-resolution optical fluctuations imaging – SOFI [3] ), rely on detection and analysis of photon (intensity) correlations. Typically, it is believed that the more correlated illuminating light is used and the higher order of the correlations is measured, the larger super-resolution can be achieved. That conclusion is based on efficient narrowing of the point-spread function, which, however, does not necessarily imply better resolution as the ability to reconstruct smaller features of the investigated object successfully.
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.
Reaching high-resolution imaging of delicate samples at a low-intensity level is a major challenge in microscopy. Here, we present and experimentally implement an advanced quantum super-resolution imaging technique based on photon statistics measurement. Our reconstruction algorithm adapts to any kind of non-Poissonian emitters, outperforming the corresponding classical SOFI method, in particular in low-light conditions. It offers sub-diffraction resolution improvement that scales with the j , where j is the highest-order central moments of the photocounts. More remarkably, we show that in combination with structured illumination, an improvement of j + j can be reached, providing a promising avenue for non-invasive super-resolution microscopy.
Entangled photons have the remarkable ability to be more sensitive to signal and less sensitive to noise than classical light. Joint photons can sample an object collectively, resulting in faster phase accumulation and higher spatial resolution, while common components of noise can be subtracted. Even more, they can accomplish this while physically separate, due to the nonlocal properties of quantum mechanics. Indeed, nearly all quantum optics experiments rely on this separation, using individual point detectors that are scanned to measure coincidence counts and correlations. Scanning, however, is tedious, time consuming, and ill-suited for imaging. Moreover, the separation of beam paths adds complexity to the system while reducing the number of photons available for sampling, and the multiplicity of detectors does not scale well for greater numbers of photons and higher orders of entanglement. We bypass all of these problems here by directly imaging collinear photon pairs with an electron-multiplying CCD camera. We show explicitly the benefits of quantum nonlocality by engineering the spatial entanglement of the illuminating photons and introduce a new method of correlation measurement by converting time-domain coincidence counting into spatial-domain detection of selected pixels. We show that classical transport-of-intensity methods are applicable in the quantum domain and experimentally demonstrate nearly optimal (Heisenberg-limited) phase measurement for the given quantum illumination. The methods show the power of direct imaging and hold much potential for more general types of quantum information processing and control.