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Laser Physics

High-order correlation of non-Rayleigh speckle fields and its application in super-resolution imaging

Suzhen Zhang, Wei Wang, Rong Yu, Xiaoxue Yang

Published Apr 13, 2016• 17 citations
Publisher

Abstract

Abstract Classical correlation of Rayleigh speckle fields E ( x ) can only mimic second-order correlation in quantum imaging. Here, we propose a method to explore the high-order correlation of non-Rayleigh speckle fields E N ( x ) which shows a totally different property from the Rayleigh speckle fields. As a specific example, we illustrate and analyze in detail the third-order speckle scanning imaging which overcomes the diffraction barrier by a factor of 3 . The influences of diffractions in the illumination path and the detection path are also discussed. This investigation may pave the way for applications in super-resolution imaging.

DOI
10.1088/1054-660x/26/5/055007

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Abstract Classical correlation of Rayleigh speckle fields E ( x ) can only mimic second-order correlation in quantum imaging. Here, we propose a method to explore the high-order correlation of non-Rayleigh speckle fields E N ( x ) which shows a totally different property from the Rayleigh speckle fields. As a specific example, we illustrate and analyze in detail the third-order speckle scanning imaging which overcomes the diffraction barrier by a factor of 3 . The influences of diffractions in the illumination path and the detection path are also discussed. This investigation may pave the way for applications in super-resolution imaging.
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.
Quantum super-resolution imaging provides a nonlabeling method to surpass the diffraction limit of imaging systems. This technique relies on measurement of the second-order correlation function and usually employs spatially entangled photon sources. We introduce recent methods that achieve spatial resolution enhancement through quantum approaches, particularly the imaging techniques utilizing biphoton states. The fundamental mechanisms are discussed in detail to explain why biphoton states enable super-resolution. Additionally, we introduce multiple algorithms that extract the correlation function from the readings of two-dimensional detectors. Several cases are reviewed to evaluate the advantages and prospects of quantum imaging, along with a discussion of practical developments and potential applications.
The optical diffraction limit, formulated by Abbe 140 years ago, imposes a bound on imaging resolution in classical optics. Over the last twenty years, many theoretical schemes have been presented for overcoming the diffraction barrier in optical imaging using quantum properties of light. An experimental realization of sub-diffraction limited quantum imaging has, however, remained elusive. Here, we demonstrate a quantum imaging method taking advantage of non-classical light naturally produced in fluorescence microscopy due to photon antibunching, a fundamentally quantum phenomenon prohibiting simultaneous emission of multiple photons. Using a photon counting digital camera, we detect antibunching-induced second and third order intensity correlations and perform sub-diffraction limited quantum imaging in a standard wide-field fluorescence microscope.
High-precision measurements implemented with light are desired in all fields of science. However, light acts as a wave, and the Rayleigh criterion in classical optics yields a diffraction limit that prevents obtaining a resolution smaller than the wavelength. Sub-wavelength interference has potential application in lithography because it beats the classical Rayleigh resolution limit. Here, we carefully study second-order correlation theory to establish the physics behind sub-wavelength interference in photon coincidence detection. A Young's double slit experiment with pseudo-thermal light is performed to test the second-order correlation pattern. The results show that when two point detectors are scanned in different ways, super sub-wavelength interference patterns can be obtained. We then provide a theoretical explanation for this surprising result, and demonstrate that this explanation is also suitable for the results found for entangled light. Furthermore, we discuss the limitations of these types of super sub-wavelength interference patterns in quantum lithography.
Resolution is crucially important for optical imaging, which defines the smallest spatial feature of object that can be delivered by light wave. However, due to the wave nature of light, optical imaging is of limited resolution, widely known as Rayleigh limit or Abbe limit. Nevertheless, this limit can be overcome by considering the loopholes in the derivation of the Rayleigh limit, such as light–matter interaction, structured illumination, and near-field interference. In contrast to the conventional single-photon interference, multi-photon amplitudes responsible for optical high-order interference could be designed to possess a reduced effective wavelength, enabling the breakthrough of the Rayleigh limit. In this review, we will present recently developed super-resolution imaging schemes based on optical high-order interference, and discuss future perspectives.
Random illumination microscopy (RIM) could surpass the diffraction barrier in fluorescence microscopy by illuminating an object with unknown speckle patterns. It has been demonstrated that the resolution in RIM using second-order statistics is as good as that of conventional structured illumination microscopy (SIM) from the asymptotic point of view. Compared to classical SIM, RIM is more robust to optical aberrations and scattering introduced by thick samples. In this work, I show that the quantum correlations could further improve the resolution in random illumination microscopy due to the photon antibunching property of fluorophore emitters. In theory, the super-resolution capacity of this quantum-enhanced version of RIM corresponds to the fourth power of the point spread function under the general epi-illumination geometry.