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...