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Micro-channel plate (MCP) detectors, when used at pulsed-neutron-source instruments, offer the possibility of high spatial resolution and high contrast imaging with pixel-level spectroscopic information. Here we demonstrate the possibility of multimodal analysis including total neutron cross-section spectra measurements, quantitative material differentiation imaging and texture-sensitive in-line phase imaging, from a single exposure using an MCP detector. This multimodal approach operates in full-field imaging mode, with the neutron transmission spectra acquired at each individual detector pixel. Due to the polychromatic nature of the beam and spectroscopic resolving capability of the detector, no energy scanning is required. Good agreement with the library reference data is demonstrated for neutron cross-section spectra measurements. Two different images corresponding to two selected energy bandwidths are used for elemental differentiation imaging. Moreover, the presence of changes in texture, i.e., preferred grain orientation, in the sample is identified from our phase-retrieval imaging results., Comment: Revised manuscript resubmitted to Physical Review A

A unified method for three-dimensional reconstruction of objects from transmission images collected at multiple illumination directions is described. The method may be applicable to experimental conditions relevant to absorption-based, phase-contrast or diffraction imaging using X-rays, electrons and other forms of penetrating radiation or matter waves. Both the phase retrieval (also known as contrast transfer function correction) and the effect of Ewald sphere curvature (in the cases with a shallow depth of field and significant in-object diffraction) are incorporated in the proposed algorithm and can be taken into account. Multiple scattering is not treated explicitly, but can be mitigated as a result of angular averaging that constitutes an essential feature of the method. The corresponding numerical algorithm is based on three-dimensional gridding which allows for fast computational implementation, including a straightforward parallelization. The algorithm can be used with any scanning geometry involving plane-wave illumination. A software code implementing the proposed algorithm has been developed, tested on simulated and experimental image data and made publicly available., Comment: 16 pages, 3 figures

A new method is developed for three-dimensional (3D) reconstruction of multi-material objects using propagation-based X-ray phase-contrast tomography (PB-CT) with phase retrieval via the contrast transfer function (CTF) formalism. The approach differs from conventional PB-CT algorithms that apply phase retrieval on individual two-dimensional (2D) projections. Instead, this method involves performing phase retrieval to the CT-reconstructed volume in 3D. The CTF formalism is further extended to the cases of partially-coherent illumination and strongly absorbing samples. Simulated results demonstrate that the proposed post-reconstruction CTF method provides fast and stable phase retrieval, producing results equivalent to conventional pre-reconstruction 2D CTF phase retrieval. Moreover, it is shown that application can be highly localised to isolated objects of interest, without a significant loss of quality, thus leading to increased computational efficiency. Combined with the extended validity of the CTF to greater propagation distances, this method provides additional advantages over approaches based on the transport-of-intensity equation., Comment: 11 pages, 5 figures

Propagation-based phase-contrast X-ray imaging (PB-PCXI) generates image contrast by utilizing sample-imposed phase-shifts. This has proven useful when imaging weakly-attenuating samples, as conventional attenuation-based imaging does not always provide adequate contrast. We present a PB-PCXI algorithm capable of extracting the X-ray attenuation, $\beta$, and refraction, $\delta$, components of the complex refractive index of distinct materials within an unknown sample. The method involves curve-fitting an error-function-based model to a phase-retrieved interface in a PB-PCXI tomographic reconstruction, which is obtained when Paganin-type phase-retrieval is applied with incorrect values of $\delta$ and $\beta$. The fit parameters can then be used to calculate true $\delta$ and $\beta$ values for composite materials. This approach requires no a priori sample information, making it broadly applicable. Our PB-PCXI reconstruction is single distance, requiring only one exposure per tomographic angle, which is important for radiosensitive samples. We apply this approach to a breast-tissue sample, recovering the refraction component, $\delta$, with 0.6 - 2.4\% accuracy compared to theoretical values., Comment: 8 pages, 4 figures and 1 table

Imaging is an important means by which information is gathered regarding the physical world. Spatial resolution and signal-to-noise ratio are underpinning concepts. There is a paucity of rigorous definitions for these quantities, which are general enough to be useful in a broad range of imaging problems, while being also sufficiently specific to enable precise quantitative evaluation of the relevant properties of imaging systems. This is particularly true for many modern forms of imaging that include digital processing of the acquired imaging data as an integral step leading to final images presented to an end-user. Here, both the well-known historical definitions of spatial resolution and some more recent approaches suitable for many forms of modern computational imaging are discussed. An intrinsic duality of spatial resolution and signal-to-noise exists in almost all types of imaging, with the related uncertainty relationship determining a trade-off between the two quantities. Examples are presented with applications to super-resolution imaging, inline holography and ghost imaging.

It is proved that the width of a function and the width of the distribution of its values cannot be made arbitrarily small simultaneously. In the case of ergodic stochastic processes, an ensuing uncertainty relationship is demonstrated for the product of correlation length and variance. A closely related uncertainty principle is also established for the average degree of fourth-order coherence and the spatial width of modes of bosonic quantum fields. However, it is shown that, in the case of stochastic and quantum observables, certain non-classical states with sub-Poissonian statistics, such as for example photon number squeezed states in quantum optics, can overcome the "classical" noise-resolution uncertainty limit. The described uncertainty relationship, which is fundamentally different from the Heisenberg and related uncertainty principles, can define an upper limit for the information capacity of communication and imaging systems. It is expected to be useful in a variety of problems in classical and quantum physics., Comment: 12 pages, 1 figure, to be submitted to a journal

A reciprocal relationship between the autocovariance of the light intensity in the source plane and in the far-field detector plane is presented in a form analogous to the classical van Cittert - Zernike theorem, but involving intensity correlation functions. A "classical" version of the reciprocity relationship is considered first, based on the assumption of circular Gaussian statistics of the complex amplitudes in the source plane. The result is consistent with the theory of Hanbury Brown - Twiss interferometry, but it is shown to be also applicable to estimation of the source size or the spatial resolution of the detector from the noise power spectrum of flat-field images. An alternative version of the van Cittert - Zernike theorem for intensity correlations is then derived for a quantized electromagnetic beam in a coherent state, which leads to Poisson statistics for the intrinsic intensity of the beam.

Phase-contrast X-ray imaging can improve the visibility of weakly absorbing objects (e.g. soft tissues) by an order of magnitude or more compared to conventional radiographs. Previously, it has been shown that combining phase retrieval with computed tomography (CT) can increase the signal-to-noise ratio (SNR) by up to two orders of magnitude over conventional CT at the same radiation dose, without loss of image quality. Our experiments reveal that as radiation dose decreases, the relative improvement in SNR increases. We discovered this enhancement can be traded for a reduction in dose greater than the square of the gain in SNR. Upon reducing the dose 300 fold, the phase-retrieved SNR was still almost 10 times larger than the absorption contrast data. This reveals the potential for dose reduction factors in the tens of thousands without loss in image quality, which would have a profound impact on medical and industrial imaging applications.

An uncertainty inequality is presented that establishes a lower limit for the product of the variance of the time-averaged intensity of a mode of a quantized electromagnetic field and the degree of its spatial localization. The lower limit is determined by the vacuum fluctuations within the volume corresponding to the width of the mode. This result also leads to a generalized form of the Heisenberg uncertainty principle for boson fields in which the lower limit for the product of uncertainties in the spatial and momentum localization of a mode is equal to the product of Planck's constant and a dimensionless functional which reflects the joint signal-to-noise ratio of the position and momentum of vacuum fluctuations in the region of the phase space occupied by the mode. Experimental X-ray synchrotron measurements provide an initial verification of the proposed theory in the case of Poisson statistics.

Electroencephalography (EEG) has enjoyed considerable attention over the past century and has been applied for diagnosis of epilepsy, stroke, traumatic brain injury and other disorders where 3D localization of electrical activity in the brain is potentially of great diagnostic value. In this study we evaluate the precision and accuracy of spatial localization of electrical activity in the brain delivered by a popular reconstruction technique sLORETA applied to EEG data collected by two commonly used low-density headsets with 14 and 19 measurement channels, respectively. Numerical experiments were performed for a realistic head model obtained by segmentation of MRI images. The EEG source localization study was conducted with a simulated single active dipole, as well as with two spatially separated simultaneously active dipoles, as a function of dipole positions across the neocortex, with several different noise levels in the EEG signals registered on the scalp. The results indicate that while the reconstruction accuracy and precision of the sLORETA method are consistently high in the case of a single active dipole, even with the low-resolution EEG configurations considered in the present study, successful localization is much more problematic in the case of two simultaneously active dipoles. The quantitative analysis of the width of the reconstructed distributions of the electrical activity allows us to specify the lower bound for the spatial resolution of the sLORETA-based 3D source localization in the considered cases., Comment: 13 pages