Abstract To obtain spatial information about an arbitrary atomic distribution in x-ray structure analysis, e.g., in molecules or proteins, the standard method is to measure the intensity in the far field, i.e., the first-order photon correlation function of the coherently scattered x-ray photons (coherent diffractive imaging). Recently, it was suggested to record alternatively the incoherently scattered photons and measure the second-order photon correlation function to reconstruct the geometry of the unknown atomic distribution (incoherent diffractive imaging). Yet, besides various advantages of the latter method, both techniques suffer from the so-called phase retrieval problem. Lately, an ab-initio phase retrieval algorithm to reconstruct the phase of the so-called structure factor of the scattering objects based on the third-order photon correlation function was reported. The algorithm makes use of the closure phase, which contains important, yet incomplete phase information, well-known from triple correlations and their bispectrum in speckle masking and astronomy applications. Here, we provide a detailed analysis of the underlying scheme and quantities in the context of x-ray structure analysis. In particular, we explicitly calculate for the first time the third-order photon correlation&amp;#xD;function for single photon emitters in a full quantum mechanical treatment and discuss the uniqueness of the closure phase equations constructed from. In this context, we recapitulate the sign problem of the closure phase and how it can be lifted using redundant information. We further show how the algorithm can be improved using even higher-order photon correlation functions produced by single photon emitters, e.g., the fourth-order correlation function, delivering new phase relations appearing in the four-point correlations. 

Phase Retrieval in Incoherent Diffractive Imaging using higher-order photon correlation functions

: Second-order intensity correlations from incoherent emitters can reveal the Fourier transform modulus of their spatial distribution, but retrieving the phase to enable completely general Fourier inversion to real space remains challenging. Phase retrieval via the third-order intensity correlations has relied on special emitter conﬁgurations which simpliﬁed an unaddressed sign problem in the computation. Without a complete treatment of this sign problem, the general case of retrieving the Fourier phase from a truly arbitrary conﬁguration of emitters is not possible. In this paper, a general method for ab initio phase retrieval via the intensity triple correlations is described. Simulations demonstrate accurate phase retrieval for clusters of incoherent emitters which could be applied to imaging stars or ﬂuorescent atoms and molecules. With this work, it is now ﬁnally tractable to perform Fourier inversion directly and reconstruct images of arbitrary arrays of independent emitters via far-ﬁeld intensity correlations alone.

pdf/ab-initio-spatial-phase-retrieval-via-intensity-triple-3cyxxaqt.pdf

Ab Initio Spatial Phase Retrieval via Intensity Triple Correlations

: All-optical ultrasound (OpUS) has emerged as an imaging paradigm well-suited to minimally invasive imaging due to its ability to provide high resolution imaging from miniaturised fibre optic devices. Here, we report a fibre optic device capable of concurrent laser interstitial thermal therapy (LITT) and real-time in situ all-optical ultrasound imaging for lesion monitoring. The device comprised three optical fibres: one each for ultrasound transmission, reception and thermal therapy light delivery. This device had a total lateral dimension of < 1 mm and was integrated into a medical needle. Simultaneous LITT and monitoring were performed on ex vivo lamb kidney with lesion depth tracked using M-mode OpUS imaging. Using one set of laser energy parameters for LITT (5 W, 60 s), the lesion depth varied from 3.3 mm to 8.3 mm. In all cases, the full lesion depth could be visualised and measured with the OpUS images and there was a good statistical agreement with stereomicroscope images acquired after ablation (t = 1.36, p = 0.18). This work demonstrates the feasibility and potential of OpUS to guide LITT in tumour resection.

Miniaturised dual-modality all-optical ultrasound probe for laser interstitial thermal therapy (LITT) monitoring

: Photoacoustic (PA) endoscopy has shown significant potential for clinical diagnosis and surgical guidance. Multimode fibres (MMFs) are becoming increasingly attractive for the development of miniature endoscopy probes owing to their ultrathin size, low cost and diffraction-limited spatial resolution enabled by wavefront shaping. However, current MMF-based PA endomicroscopy probes are either limited by a bulky ultrasound detector or a low imaging speed that hindered their usability. In this work, we report the development of a highly miniaturised and high-speed PA endomicroscopy probe that is integrated within the cannula of a 20 gauge medical needle. This probe comprises a MMF for delivering the PA excitation light and a single-mode optical fibre with a plano-concave microresonator for ultrasound detection. Wavefront shaping with a digital micromirror device enabled rapid raster-scanning of a focused light spot at the distal end of the MMF for tissue interrogation. High-resolution PA imaging of mouse red blood cells covering an area 100 µ m in diameter was achieved with the needle probe at ∼ 3 frames per second. Mosaicing imaging was performed after fibre characterisation by translating the needle probe to enlarge the field-of-view in real-time. The developed ultrathin PA endomicroscopy probe is promising for guiding minimally invasive surgery by providing functional, molecular and microstructural information of tissue in real-time.

Ultrathin, high-speed, all-optical photoacoustic endomicroscopy probe for guiding minimally invasive surgery

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Ab Initio Spatial Phase Retrieval via Intensity Triple Correlations

Miniaturised dual-modality all-optical ultrasound probe for laser interstitial thermal therapy (LITT) monitoring

Ultrathin, high-speed, all-optical photoacoustic endomicroscopy probe for guiding minimally invasive surgery