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Linowski, T., Schlichtholz, K., Sorelli, G., Gessner, M., Walschaers, M., Treps, N., et al. (2023). Application range of crosstalk-affected spatial demultiplexing for resolving separations between unbalanced sources. New J. Phys., 25(10), 103050–13pp.
Abstract: Super resolution is one of the key issues at the crossroads of contemporary quantum optics and metrology. Recently, it was shown that for an idealized case of two balanced sources, spatial mode demultiplexing (SPADE) achieves resolution better than direct imaging even in the presence of measurement crosstalk (Gessner et al 2020 Phys. Rev. Lett. 125 100501). In this work, we consider arbitrarily unbalanced sources and provide a systematic analysis of the impact of crosstalk on the resolution obtained from SPADE. As we dissect, in this generalized scenario, SPADE's effectiveness depends non-trivially on the strength of crosstalk, relative brightness and the separation between the sources. In particular, for any source imbalance, SPADE performs worse than ideal direct imaging in the asymptotic limit of vanishing source separations. Nonetheless, for realistic values of crosstalk strength, SPADE is still the superior method for several orders of magnitude of source separations.
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Brzezinski, K., Oliver, J. F., Gillam, J., & Rafecas, M. (2014). Study of a high-resolution PET system using a Silicon detector probe. Phys. Med. Biol., 59(20), 6117–6140.
Abstract: A high-resolution silicon detector probe, in coincidence with a conventional PET scanner, is expected to provide images of higher quality than those achievable using the scanner alone. Spatial resolution should improve due to the finer pixelization of the probe detector, while increased sensitivity in the probe vicinity is expected to decrease noise. A PET-probe prototype is being developed utilizing this principle. The system includes a probe consisting of ten layers of silicon detectors, each a 80 x 52 array of 1 x 1 x 1 mm(3) pixels, to be operated in coincidence with a modern clinical PET scanner. Detailed simulation studies of this system have been performed to assess the effect of the additional probe information on the quality of the reconstructed images. A grid of point sources was simulated to study the contribution of the probe to the system resolution at different locations over the field of view (FOV). A resolution phantom was used to demonstrate the effect on image resolution for two probe positions. A homogeneous source distribution with hot and cold regions was used to demonstrate that the localized improvement in resolution does not come at the expense of the overall quality of the image. Since the improvement is constrained to an area close to the probe, breast imaging is proposed as a potential application for the novel geometry. In this sense, a simplified breast phantom, adjacent to heart and torso compartments, was simulated and the effect of the probe on lesion detectability, through measurements of the local contrast recovery coefficient-to-noise ratio (CNR), was observed. The list-mode ML-EM algorithm was used for image reconstruction in all cases. As expected, the point spread function of the PET-probe system was found to be non-isotropic and vary with position, offering improvement in specific regions. Increase in resolution, of factors of up to 2, was observed in the region close to the probe. Images of the resolution phantom showed visible improvement in resolution when including the probe in the simulations. The image quality study demonstrated that contrast and spill-over ratio in other areas of the FOV were not sacrificed for this enhancement. The CNR study performed on the breast phantom indicates increased lesion detectability provided by the probe.
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Fujita, Y., Rubio, B., & Gelletly, W. (2011). Spin-isospin excitations probed by strong, weak and electro-magnetic interactions. Prog. Part. Nucl. Phys., 66(3), 549–606.
Abstract: Gamow-Teller (GT) transitions are the most common weak interaction processes of spin-isospin (sigma tau) type in atomic nuclei. They are of interest not only in nuclear physics but also in astrophysics; they play an important role in supernovae explosions and nucleosynthesis. The direct study of weak decay processes, however, gives relatively limited information about GT transitions and the states excited via GT transitions (GT states); beta decay can only access states at excitation energies lower than the decay Q-value, and neutrino-induced reactions have very small cross-sections. However, one should note that beta decay has a direct access to the absolute GT transition strengths B(GT) from a study of half-lives, Q(beta)-values and branching ratios. They also provide information on GT transitions in nuclei far-from-stability. Studies of M1 gamma transitions provide similar information. In contrast, the complementary charge-exchange (CE) reactions, such as the (p, n) or ((3)He, t) reactions at intermediate beam energies and 0 degrees, can selectively excite GT states up to high excitation energies in the final nucleus. It has been found empirically that there is a close proportionality between the cross-sections at 0 degrees and the transition strengths B(GT) in these CE reactions. Therefore, CE reactions are useful tools to study the relative values of B(GT) strengths up to high excitation energies. In recent ((3)He, t) measurements, one order-of-magnitude improvement in the energy resolution has been achieved. This has made it possible to make one-to-one comparisons of GT transitions studied in CE reactions and beta decays. Thus GT strengths in ((3)He, t) reactions can be normalised by the beta-decay values. In addition, comparisons with closely related M1 transitions studied in gamma decay or electron inelastic scattering [(e, e')1, and furthermore with “spin” M I transitions that can be studied by proton inelastic scattering [(p, p')[ have now been made possible. In these comparisons, the isospin quantum number T and associated symmetry structure in the same mass A nuclei (isobars) play a key role. Isospin symmetry can extend our scope even to the structures of unstable nuclei that are far from reach at present unstable beam factories.
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Aliaga, R. J. (2017). Real-Time Estimation of Zero Crossings of Sampled Signals for Timing Using Cubic Spline Interpolation. IEEE Trans. Nucl. Sci., 64(8), 2414–2422.
Abstract: A scheme is proposed for hardware estimation of the location of zero crossings of sampled signals with subsample resolution for timing applications, which consists of interpolating the signal with a cubic spline near the zero crossing and then finding the root of the resulting polynomial. An iterative algorithm based on the bisection method is presented that obtains one bit of the result per step and admits an efficient digital implementation using fixed-point representation. In particular, the root estimation iteration involves only two additions, and the initial values can be obtained from finite impulse response (FIR) filters with certain symmetry properties. It is shown that this allows online real-time estimation of timestamps in free-running sampling detector systems with improved accuracy with respect to the more common linear interpolation. The method is evaluated with simulations using ideal and real timing signals, and estimates are given for the resource usage and speed of its implementation.
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Cabello, J., Etxebeste, A., Llosa, G., & Ziegler, S. I. (2015). Simulation study of PET detector limitations using continuous crystals. Phys. Med. Biol., 60(9), 3673–3694.
Abstract: Continuous crystals can potentially obtain better intrinsic detector spatial resolution compared to pixelated crystals, additionally providing depth of interaction (DoI) information from the light distribution. To achieve high performance sophisticated interaction position estimation algorithms are required. There are a number of algorithms in the literature applied to different crystal dimensions and different photodetectors. However, the different crystal properties and photodetector array geometries have an impact on the algorithm performance. In this work we analysed, through Monte Carlo simulations, different combinations of realistic crystals and photodetector parameters to better understand their influence on the interaction position estimation accuracy, with special emphasis on the DoI. We used an interaction position estimation based on an analytical model for the present work. Different photodetector granulation schemes were investigated. The impact of the number of crystal faces readout by photodetectors was studied by simulating scenarios with one and two photodetectors. In addition, crystals with different levels of reflection and aspect ratios (AR) were analysed. Results showed that the impact of photodetector granularity is mainly shown near the edges and specially in the corners of the crystal. The resulting intrinsic spatial resolution near the centre with a 12 x 12 x 10 mm(3) LYSO crystal was 0.7-0.9 mm, while the average spatial resolution calculated on the entire crystal was 0.77 +/- 0.18 mm for all the simulated geometries with one and two photodetectors. Having front and back photodetectors reduced the DoI bias (Euclidean distance between estimated DoI and real DoI) and improved the transversal resolution near the corners. In scenarios with one photodetector, small AR resulted in DoI inaccuracies for absorbed events at the entrance of the crystal. These inaccuracies were slightly reduced either by increasing the AR or reducing the amount of reflected light, and highly mitigated using two photodetectors. Using one photodetector, we obtained a piecewise DoI error model with a DoI resolution of 0.4-0.9 mm for a 1.2 AR crystal, and we observed that including a second photodetector or reducing the amount of reflections reduced the DoI bias but did not significantly improve the DoI resolution. Translating the piecewise DoI error model obtained in this study to image reconstruction we obtained a spatial resolution variability of 0.39 mm using 85% of the FoV, compared to 2.59 mm and 1.87 mm without DoI correction or with a dual layer system, respectively.
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