Established x-ray diffraction methods allow for high-resolution structure determination of crystals, crystallized protein structures, or even single molecules. While these techniques rely on coherent scattering, incoherent processes like fluorescence emission-often the predominant scattering mechanism-are generally considered detrimental for imaging applications. Here, we show that intensity correlations of incoherently scattered x-ray radiation can be used to image the full 3D arrangement of the scattering atoms with significantly higher resolution compared to conventional coherent diffraction imaging and crystallography, including additional three-dimensional information in Fourier space for a single sample orientation. We present a number of properties of incoherent diffractive imaging that are conceptually superior to those of coherent methods. DOI: 10.1103/PhysRevLett.119.053401 The advent of accelerator-driven x-ray free-electron lasers (FEL) has opened new avenues for high-resolution x-ray structure determination via coherent diffractive imaging (CDI) methods that go far beyond conventional x-ray crystallography [1][2][3][4][5][6][7][8][9][10][11]. In these methods, it is assumed that a fixed phase relation between the incoming and scattered photons exists and the first-order coherence of the radiation field is maintained throughout the imaging procedure. This produces a stationary interference pattern upon measurement of large numbers of photons, a central paradigm of the field since its foundation more than one hundred years ago. Incoherence induced by, e.g., time-varying wavefront distortions or incoherent scattering processes like fluorescence emission or Compton scattering, is generally considered detrimental in this approach, as the scattered photons on average generate a constant intensity distribution producing a background that reduces the fidelity of CDI measurements [12][13][14].The situation is fundamentally altered if the photons are recorded within their coherence time τ c , i.e., a time interval short with respect to the temporal phase fluctuations of the radiation field. Over such short times, the relative phases of the scattered photons can be considered as stable, allowing the observation of a stationary fringe pattern. The pattern will fluctuate and spatially vary over times longer than τ c , yet the autocorrelation of the intensity distribution calculated for each short exposure is insensitive to the spatial pattern variations and will continuously build up when averaging over many short measurements.It was this approach that led Hanbury Brown and Twiss (HBT) to their landmark experiment in stellar interferometry to overcome atmospheric fluctuations and determine the diameter of stars via intensity correlations [15]. Based on the discovery of photon bunching of thermal light [16], the HBT experiment initiated a paradigm shift towards a quantum statistical description of light and is nowadays regarded as one of the founding pillars for the development of modern quantum optics [17]. T...

Intensity correlation microscopy (ICM), which is prominently known through antibunching microscopy or super-resolution optical fluctuation imaging (SOFI), provides superresolution through a correlation analysis of antibunching of independent quantum emitters or temporal fluctuations of blinking fluorophores. For correlation order m the PSF in the signal is effectively taken to the mth power, and is thus directly shrunk by the factor √ m. Combined with deconvolution a close to linear resolution improvement of factor m can be obtained. Yet, analysis of high correlation orders is challenging, what limits the achievable resolutions. Here we propose to use three dimensional structured illumination along with mth-order correlation analysis to obtain an enhanced scaling of up to m + m = 2m. Including the stokes shift or plasmonic sub-wavelength illumination enhancements beyond 2m can be achieved. Hence, resolutions far below the diffraction limit in full 3D imaging can potentially be achieved already with low correlation orders. Since ICM operates in the linear regime our approach may be particularly promising for enhancing the resolution in biological imaging at low illumination levels.

We propose to use multiphoton interferences of photons emitted from statistically independent thermal light sources in combination with linear optical detection techniques to reconstruct, i.e., image, arbitrary source geometries in one dimension with subclassical resolution. The scheme is an extension of earlier work [Phys. Rev. Lett. 109, 233603 (2012)] where N regularly spaced sources in one dimension were imaged by use of the N th-order intensity correlation function. Here, we generalize the scheme to reconstruct any number of independent thermal light sources at arbitrary separations in one dimension exploiting intensity correlation functions of order m ≥ 3. We present experimental results confirming the imaging protocol and provide a rigorous mathematical proof for the obtained subclassical resolution.Higher order interferences with photons emitted by statistically independent light sources are an active field of research with the potential to increase the resolution in spectroscopy, lithography and interferometry [1][2][3][4][5][6], as well as in imaging and microscopy [7][8][9][10][11][12][13][14][15][16][17]. So far, subclassical resolution has been achieved by using entangled photons [3,8], but it was also shown that initially uncorrelated light fields -non-classical as well as classical -can be employed for that purpose [13][14][15][16][17]. Recently, Oppel et al. presented a detection scheme that allows to determine the source distance d for an array of N equidistant thermal light sources (TLS) with subclassical resolution by measuring the N th-order spatial intensity correlation function [14].Here, we show that the scheme presented in [14] can be generalized to reconstruct, i.e., image, any number of independent TLS at arbitrary separations in one dimension by exploiting photon correlation functions of order m ≥ 3. Measuring higher order correlations enables to isolate the spatial frequencies of the setup allowing to determine the source distribution with a resolution below the classical Abbe limit. We outline the imaging protocol and present experimental results verifying the theoretical predictions. A physical explanation and rigorous mathematical proof of the protocol and the spatial frequency filtering process is given in the Supplemental Material.We assume N TLS aligned on a grid in one dimension with lattice constant d at arbitrary separations, such that |R l+1 − R l | = x l · d, with x l ∈ N, l = 1, . . . , N − 1. The source geometry is thus determined by the lattice constant d and the N − 1 adjacent source distances x = (x 1 , x 2 , . . . , x N −1 ), whereas the spatial frequencies of the system are given by the tuple of source pair distances {ξ} ≡ {(x 1 ); (x 1 + x 2 ); . . . ; (x l1 + · · · + x l2 ); . . . ; (x 1 + · · · + x N −1 )} (see Fig. 1).To access the set of spatial frequencies {ξ} we make use of the normalized spatial mth-order intensity correlation function g Here, : · : ρ denotes the (normally ordered) quantum mechanical expectation value for a system in the state ρ andÊ (−) (r j...

The advent of accelerator-driven free-electron lasers (FEL) has opened new avenues for high-resolution structure determination via di raction methods that go far beyond conventional X-ray crystallography methods 1-10 . These techniques rely on coherent scattering processes that require the maintenance of first-order coherence of the radiation field throughout the imaging procedure. Here we show that higher-order degrees of coherence, displayed in the intensity correlations of incoherently scattered X-rays from an FEL, can be used to image two-dimensional objects with a spatial resolution close to or even below the Abbe limit. This constitutes a new approach towards structure determination based on incoherent processes 11,12 , including fluorescence emission or wavefront distortions, generally considered detrimental for imaging applications. Our method is an extension of the landmark intensity correlation measurements of Hanbury Brown and Twiss 13 to higher than second order, paving the way towards determination of structure and dynamics of matter in regimes where coherent imaging methods have intrinsic limitations 14 .The discovery by Hanbury Brown and Twiss of photon bunching of thermal light 15 and its application in astronomy to determine the angular diameter of stars by measuring spatial photon correlations 13 was a hallmark experiment for the development of modern quantum optics 16 . The subsequent quantum mechanical description of photon correlations by Glauber paved the way for a generalized concept of optical coherence 17 that is founded on the analysis of correlation functions of order m rather than the first-order coherence. For example, the spatial second-order photon correlation function g (2) (r 1 , r 2 ) expresses the probability to detect a photon at position r 1 given that a photon is recorded at position r 2 . In the case of two incoherent sources, g (2) (r 1 , r 2 ) displays a cosine modulation which oscillates at a spatial frequency depending on the source separation 18,19 . In this way interference fringes show up even in the complete absence of first-order coherence, allowing the extraction of structural information from incoherently emitting objects. This has been applied in Earth-bound stellar interferometry to measure the angular diameter of stars with 100-fold increased resolution 13 or to reveal the spatial and statistical properties of pulsed FEL sources 20,21 .Extending this concept to arbitrary arrangements of incoherently scattering emitters enables one to use intensity correlations for imaging applications. This has been demonstrated recently for one-dimensional arrays of emitters in the visible range of the spectrum [22][23][24] , where a spatial resolution even below the canonical Abbe limit has been achieved. Here we go still further and employ the method to image arbitrary two-dimensional incoherently scattering objects radiating in the vacuum ultraviolet. The extension from one dimension 24 to two dimensions is non-trivial and even unexpected in view of the tremendously enlarg...

Two-photon absorption (TPA) fluorescence of biomarkers has been decisive in advancing the fields of biosensing and deep-tissue in vivo imaging of live specimens. However, due to the extremely small TPA cross section and the quadratic dependence on the input photon flux, extremely high peak-intensity pulsed lasers are imperative, which can result in significant photo- and thermal damage. Previous works on entangled TPA with spontaneous parametric downconversion light sources found a linear dependence on the input photon-pair flux, but are limited by low optical powers, along with a very broad spectrum. We report that by using a high-flux squeezed light source for TPA, a fluorescence enhancement of ∼47 is achieved in fluorescein biomarkers as compared to classical TPA. Moreover, a polynomial behavior of the TPA rate is observed in the the laser dye 4-dicyanomethylene-2-methyl-6-(p(dimethylamino)styryl)-4H-pyran in dimethyl sulphoxide.