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PURPOSE: Energy discriminating photon counting x-ray detectors can be subject to a wide range of flux rates if applied in clinical settings. Even when the incident rate is a small fraction of the detector's maximum periodic rate No, pulse pileup leads to count rate losses and spectral distortion. Although the deterministic effects can be corrected, the detrimental effect of pileup on image noise is not well understood and may limit the performance of photon counting systems. Therefore, the authors devise a method to determine the detector count statistics and imaging performance. METHODS: The detector count statistics are derived analytically for an idealized pileup model with delta pulses of a nonparalyzable detector. These statistics are then used to compute the performance (e.g., contrast-to-noise ratio) for both single material and material decomposition contrast detection tasks via the Cramdr-Rao lower bound (CRLB) as a function of the detector input count rate. With more realistic unipolar and bipolar pulse pileup models of a nonparalyzable detector, the imaging task performance is determined by Monte Carlo simulations and also approximated by a multinomial method based solely on the mean detected output spectrum. Photon counting performance at different count rates is compared with ideal energy integration, which is unaffected by count rate. RESULTS: The authors found that an ideal photon counting detector with perfect energy resolution outperforms energy integration for our contrast detection tasks, but when the input count rate exceeds 20% N0, many of these benefits disappear. The benefit with iodine contrast falls rapidly with increased count rate while water contrast is not as sensitive to count rates. The performance with a delta pulse model is overoptimistic when compared to the more realistic bipolar pulse model. The multinomial approximation predicts imaging performance very close to the prediction from Monte Carlo simulations. The monoenergetic image with maximum contrast-to-noise ratio from dual energy imaging with ideal photon counting is only slightly better than with dual kVp energy integration, and with a bipolar pulse model, energy integration outperforms photon counting for this particular metric because of the count rate losses. However, the material resolving capability of photon counting can be superior to energy integration with dual kVp even in the presence of pileup because of the energy information available to photon counting. CONCLUSIONS: A computationally efficient multinomial approximation of the count statistics that is based on the mean output spectrum can accurately predict imaging performance. This enables photon counting system designers to directly relate the effect of pileup to its impact on imaging statistics and how to best take advantage of the benefits of energy discriminating photon counting detectors, such as material separation with spectral imaging.

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Four-dimensional (4D) imaging during structural changes are reported here using ultrafast electron microscopy (UEM). For nanostructures, the phase transition in the strongly correlated material vanadium dioxide is our case study. The transition is initiated and probed in situ, in the microscope, by a femtosecond near-infrared and electron pulses (at 120 keV). Real-space imaging and Fourier-space diffraction patterns show that the transition from the monoclinic (P21/c) to tetragonal (P42/mnm) structure is induced in 3 +/- 1 ps, but there exists a nonequilibrium (metastable) structure whose nature is determined by electronic, carrier-induced, structural changes. For the particles studied, the subsequent recovery occurs in about 1 ns. Because of the selectivity of excitation from the 3d parallel-band, and the relatively low fluence used, these results show the critical role of carriers in weakening the V4+-V4+ bonding in the monoclinic phase and the origin of the nonequilibrium phase. A theoretical two-dimensional (2D) diffusion model for nanoscale materials is presented, and its results account for the observed behavior.

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Reported here is direct imaging (and diffraction) by using 4D ultrafast electron microscopy (UEM) with combined spatial and temporal resolutions. In the first phase of UEM, it was possible to obtain snapshot images by using timed, single-electron packets; each packet is free of space-charge effects. Here, we demonstrate the ability to obtain sequences of snapshots ("movies") with atomic-scale spatial resolution and ultrashort temporal resolution. Specifically, it is shown that ultrafast metal-insulator phase transitions can be studied with these achieved spatial and temporal resolutions. The diffraction (atomic scale) and images (nanometer scale) we obtained manifest the structural phase transition with its characteristic hysteresis, and the time scale involved (100 fs) is now studied by directly monitoring coordinates of the atoms themselves.

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Electron microscopy is arguably the most powerful tool for spatial imaging of structures. As such, 2D and 3D microscopies provide static structures with subnanometer and increasingly with angstrom-scale spatial resolution. Here we report the development of 4D ultrafast electron microscopy, whose capability imparts another dimension to imaging in general and to dynamics in particular. We demonstrate its versatility by recording images and diffraction patterns of crystalline and amorphous materials and images of biological cells. The electron packets, which were generated with femtosecond laser pulses, have a de Broglie wavelength of 0.0335 angstroms at 120 keV and have as low as one electron per pulse. With such few particles, doses of few electrons per square ångstrom, and ultrafast temporal duration, the long sought after but hitherto unrealized quest for ultrafast electron microscopy has been realized. Ultrafast electron microscopy should have an impact on all areas of microscopy, including biological imaging.

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We report direct determination of the structures and dynamics of interfacial water on a hydrophilic surface with atomic-scale resolution using ultrafast electron crystallography. On the nanometer scale, we observed the coexistence of ordered surface water and crystallite-like ice structures, evident in the superposition of Bragg spots and Debye-Scherrer rings. The structures were determined to be dominantly cubic, but each undergoes different dynamics after the ultrafast substrate temperature jump. From changes in local bond distances (OH.O and O.O) with time, we elucidated the structural changes in the far-from-equilibrium regime at short times and near-equilibration at long times.

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The static structure of macromolecular assemblies can be mapped out with atomic-scale resolution by using electron diffraction and microscopy of crystals. For transient nonequilibrium structures, which are critical to the understanding of dynamics and mechanisms, both spatial and temporal resolutions are required; the shortest scales of length (0.1-1 nm) and time (10(-13) to 10(-12) s) represent the quantum limit, the nonstatistical regime of rates. Here, we report the development of ultrafast electron crystallography for direct determination of structures with submonolayer sensitivity. In these experiments, we use crystalline silicon as a template for different adsorbates: hydrogen, chlorine, and trifluoroiodomethane. We observe the coherent restructuring of the surface layers with subangstrom displacement of atoms after the ultrafast heat impulse. This nonequilibrium dynamics, which is monitored in steps of 2 ps (total change