Remarkable resolution improvement has been achieved in super-resolution imaging [1]–[4], but all of the techniques possess the shortcoming of not being able to passively image the sample. In 2015 Tsang et al. [5]–[7] showed that the diffraction limit can be overcome for estimating the distance between two incoherent point sources. Our group extended his framework into complete far-field, linear-optical, and passive 2D imaging, deemed Hermite-Gaussian imaging (HGI), by measuring Hermite-Gaussian (HG) modes in the image plane and shown a two-fold resolution improvement for reconstructing coherent objects [8]–[9].
Remarkable resolution improvement has been achieved in super-resolution imaging [1]–[4], but all of the techniques possess the shortcoming of not being able to passively image the sample. In 2015 Tsang et al. [5]–[7] showed that the diffraction limit can be overcome for estimating the distance between two incoherent point sources. Our group extended his framework into complete far-field, linear-optical, and passive 2D imaging, deemed Hermite-Gaussian imaging (HGI), by measuring Hermite-Gaussian (HG) modes in the image plane and shown a two-fold resolution improvement for reconstructing coherent objects [8]–[9].
The resolution of optical imaging devices is ultimately limited by the diffraction of light. To circumvent this limit, modern superresolution microscopy techniques employ active interaction with the object by exploiting its optical nonlinearities, nonclassical properties of the illumination beam, or near field probing. Thus, they are not applicable whenever such interaction is not possible, for example, in astronomy or noninvasive biological imaging. Far field, linear optical superresolution techniques based on passive analysis of light coming from the object would cover these gaps. In this Letter, we present the first proof-of-principle demonstration of such a technique for 2D imaging. It works by accessing information about spatial correlations of the image optical field and, hence, about the object itself via measuring projections onto Hermite-Gaussian transverse spatial modes. With a basis of 21 spatial modes in both transverse dimensions, we perform two-dimensional imaging with twofold resolution enhancement beyond the diffraction limit.
The resolution of imaging devices is ultimately limited by the diffraction of light. This limit can be circumvented by exploiting near-field phenomena, non-linearities of the sample or specific illumination schemes, which led to the recent explosion of optical super-resolution techniques. However, it would be desirable to reach the nanoscale in the most general way possible, with far-field linear imaging of uniformly illuminated samples. In the last few years, the answer to that came with the field of quantum-inspired super-resolution (QISR), where quantum metrological techniques were used to find novel measurement schemes that, beyond the conventional direct imaging of light, would achieve higher precisions. Interestingly, these ideas would always in some way or another involve transverse spatial modes of light. This thesis presents our work on the subject, with novel theoretical and experimental results. Firstly, we develop the traditional theory of QISR, with has mostly focused on either the estimation of separation of two point sources or on geometric moments of samples. Then, we introduce our own results on optical imaging of general distributions of point sources, in a step to take QISR from toy examples to real imaging scenarios. Secondly, we apply all the concepts studied on a experimental, proof-of-principle implementation of a QISR scheme dubbed Hermite-Gaussian Microscopy (HGM), which uses heterodyne detection with several Hermite-Gaussian modes as local oscillator in order to reconstruct the object sample and achieve super-resolution. We report the techniques necessary for the manipulation of spatial modes of light, as well as our results, where we demonstrated 2D imaging with twofold resolution enhancement beyond the diffraction limit.
The resolution of direct imaging, the most common method for remote observation in the optical domain, is inherently constrained by diffraction. Recent studies have demonstrated that this diffraction limit can be surpassed, even with passive optics, through interferometric far-field techniques such as spatial mode demultiplexing (SPADE) or super localization by image inversion interferometry (SLIVER). We share our findings on sub-diffraction imaging of two incoherent point-like sources using SPADE and SLIVER.
The diffraction, or Rayleigh, limit was long thought to determine the ultimate resolving power of optical imaging devices. Using techniques from quantum statistical inference, Tsang et al. [1] demonstrated that this limit can be circumvented, and derived an alternative measurement strategy capable of resolving two incoherent point sources no matter how arbitrarily small their separation is. However, these measurements require perfect knowledge of the sources centroid position, and are extremely sensitive to any source of misalignment about this position [2] , [3] . In this work, we study the problem of super-resolution from a more global point of view.
Resolving sources beyond the diffraction limit is important in imaging, communications, and metrology. Current image-based methods of super-resolution require phase information (either of the source points or an added filter) and perfect alignment with the centroid of the object. Both inhibit the practical application of these methods, as uniform motion and/or relative jitter destroy their assumptions. Here, we show that measuring intensity in the Fourier plane enables super-resolution without any of the issues of image-based methods. We start with the shift-invariance of the Fourier transform and the observation that the two-point position problem x1,x2 in the near field corresponds to the single-point wavenumber problem k=2π/(x2−x1) in the far field. We consider the full range of mutual coherence and show that for fully coherent sources, the Fourier method saturates the quantum limit, i.e. it gives the best possible measurement. Similar results hold for sub-Rayleigh constellations of N sources, which can act collectively as a spatially averaged metasurface and/or individually as elements of a phased-array antenna. The theory paves the way to merge Fourier optics with super-resolution techniques, enabling experimental devices that are both simpler and more robust than previous designs.
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.