Time-delay Maps Research Articles

Extended source of indistinguishable polarization-entangled photons over wide angles of emission

The generation of high-fidelity polarization-entangled photon pairs, to date, has been demonstrated on specific spatial modes or over relatively narrow apertures. We put forward and demonstrate an experimental scheme to extend the temporal and spatial indistinguishability of polarization-entangled photons over wide emission angles, which can be applied to cover the whole spontaneous parametric downconversion (SPDC) cone. Over such a wide angular extent, while the time-delay map is almost flat which renders the conventional compensation via a birefringent element an appropriate approach, the relative-phase map—verified as a quadratic function—necessitates a tunable compensation paradigm. Here, to do so, we employ a phase-only two-dimensional spatial light modulator (2D SLM) loaded by the complementary of the relative phase map to equalize the phase variations for one third of the noncollinear SPDC emission. After eliminating the temporal and spatial distinguishability over the 2D SLM area, a 97% polarization visibility is verified for the entangled photon pairs scattered widely across the SPDC cone.

Distance Estimation of High-Speed Underwater Targets Based on a Frequency-Coded Continuous Wave

Robust and continuous distance estimation of a rapidly approaching threat is a significant concern in underwater technology. Although frequency modulated continuous waves (FMCWs) have been widely used in near-range situations, FMCWs are challenging to use in a specific underwater situation. If a high-speed underwater target appears, the target echo can no longer be modeled as a simple Doppler-shifted version of the wave, which increases the distance estimation error of conventional FMCW methods. This situation also requires frequent updates of distance estimates. Thus, to obtain the distance of a high-speed underwater target, we propose a signal format of a frequency coded continuous wave (FCCW) and develop an FCCW-based distance estimation scheme. The proposed distance estimation algorithm has three steps: group correlators and accumulated sum (GCAS), time-delay map (TDM), and Doppler line fitting (DLF). The structure of the proposed FCCW enables the detection of each frequency hopping time (FHT) within a shorter period than the observation time. The GCAS algorithm detects FHTs in the FCCW and is designed to easily extend the matched filter length, resulting in an extension of the acquisition time. The TDM and DLF provide robust distance estimates and enable the classification of multiple targets. Simulation results show that the proposed method can detect FHTs and estimate the target distance more stably in low signal-to-noise-ratio environments by increasing the matched filter's acquisition time.

Application of terahertz time domain spectroscopy for NDT of oxide-oxide ceramic matrix composites

Fiber-reinforced oxide-oxide ceramic matrix composites (CMC) find increasing applications in aircraft turbines due to their higher strength, toughness and erosion resistance. Research and development of new technologies for non-destructive testing (NDT) of these kinds of components become important to ensure the safe and reliable use in harsh turbine combustion environments. The well-known NDT techniques such as air-coupled ultrasound, x-ray computed tomography and pulse- or lock-in thermography can be used for characterization of material properties and for detection of defects in materials. Due to higher porosity and lower heat diffusivity of CMC materials these conventional NDT methods are quite limited or not suitable for quality control of CMC materials in manufacturing or in maintenance. Terahertz technologies as subsurface quantitative detection techniques are applicable for various materials and structures such as foams or heat resistant spacecraft components. Terahertz time domain spectroscopy (THz-TDS) becomes an alternative NDT-technique for layered materials because of its sensitivity to refractive index changes and high penetration of Terahertz pulses in polymer, ceramics, ceramic coatings and semiconductor materials. Terahertz reflection and transmission measurement modes in combination with a scanning stage can achieve contactless imaging of samples in a short time, which is well suited for characterizing CMC materials. In order to improve quantitative analysis for NDT of CMC materials, the impulse response deconvolution algorithm was developed for two mapping modes: time delay map and maximum correlation amplitude map. The time delay map shows depth-dependent material changes in the samples e.g. depth of boundary changes or depth of hidden defects, whereas the amplitude of a back-wall reflection signal is much more sensitive to small defects because of enhanced reflections and scatterings of incident terahertz pulsed waves in small defects in materials. These two imaging modes are complementary and can be useful for NDT applications. The measurement results in this paper show the feasibility of the pulsed terahertz technique for NDT of oxide-oxide CMC materials. Hidden defects, delamination or moist areas can be detected quantitatively.

Variable speed of sound compensation in the linear-array photoacoustic tomography using a multi-stencils fast marching method

Abstract Despite the promising clinical application of linear-array photoacoustic tomography, it has been shown the variable speed of sound would severely affect the photoacoustic imaging quality, resulting in the target deterioration and inaccurate depth positioning in the conventional constant speed assumed delay and sum (DAS) reconstruction. By contrast, multi-stencils fast marching (MSFM) method is able to produce accurate time delay map for the tissue with inhomogeneous acoustic speed. This study explored the combination of DAS reconstruction algorithm with the MSFM approach to reduce the imaging distortions due to the speed spatial variation, where the target structure and target position in depth could be measured more precisely. To validate the performance of the proposed method, numerical, phantom, and in vivo photoacoustic studies were conducted with the qualitative and quantitative analysis, especially in the detection of mouse deep brain tumor with an intact skull.

Relative-phase and time-delay maps all over the emission cone of hyperentangled photon source

High flux of hyperentangled photons entails collecting the two-photon emission over relatively wide extent in frequency and transverse space within which the photon pairs are simultaneously entangled in multiple degrees of freedom. In this paper, we present a numerical approach to determining the spatial-spectral relative-phase and time-delay maps of hyperentangled photons all over the spontaneous parametric down conversion (SPDC) emission cone. We consider the hyperentangled-photons produced by superimposing noncollinear SPDC emissions of two crossed and coherently-pumped nonlinear crystals. We adopt a vectorial representation for all parameters of concern. This enables us to study special settings such as the self-compensation via oblique pump incidence. While rigorous quantum treatment of SPDC emission requires Gaussian state representation, in low-gain regime (like the case of the study), it is well approximated to the first order to superposition of vacuum and two-photon states. The relative phase and time-delay maps are then calculated between the two-photon wavepackets created along symmetrical locations of the crystals. Assuming monochromatic plane-wave pump field, the mutual signal-idler relations like energy conservation and transverse-momentum conservation define well one of the two-photon with reference to its conjugate. The weaker conservation of longitudinal momentum (due to relatively thin crystals) allows two-photon emission directions coplanar with the pump beam while spreading around the perfect phase-matching direction. While prior works often adopt first-order approximation, it is shown that the relative-phase map is a very well approximated to a quadratic function in the polar angle of the two-photon emission while negligibly varying with the azimuthal angle.

Study on cascading invulnerability of multi-coupling-links coupled networks based on time-delay coupled map lattices model

The couplings among different networks facilitate their communications, while at the same time they also bring the risk of enhancing the wide spread of cascading failures to the coupled networks. Given that there is usually the time-delay during the spread of failures and more than one coupling link a node might possess, a cascading failure model for scale-free multi-coupling-link coupled networks is built in this paper, based on time-delay coupled map lattices (CML) model, which may be wider representative than previous models. Our research shows that in BA (Barabási-Albert) scale-free coupled networks, there is a threshold hT ≈ 3: when the coupling strength is bellow this threshold, the stronger coupling strength corresponds to a lower invulnerability; and vice versa, the stronger coupling strength would bring a higher invulnerability. In addition, our studies show that the presence of time-delay not only prolongs the failure spreading time during which measures can be taken to suppress cascading failures, but also has a significant influence on the eventual cascading size, for detail, if intra-layer time-delay τ1 and inter-layer time-delay τ2 can have any values, then the multiples of the two numbers will cause larger cascading size. We hope our research can provide a reference for building high-invulnerable coupled networks or the increase of the invulnerability of the coupled networks.

Vascular Steal Explains Early Paradoxical Blood Oxygen Level-Dependent Cerebrovascular Response in Brain Regions with Delayed Arterial Transit Times

Introduction: Blood oxygen level-dependent (BOLD) magnetic resonance imaging (MRI) during manipulation of inhaled carbon dioxide (CO₂) can be used to measure cerebrovascular reactivity (CVR) and map regions of exhausted cerebrovascular reserve. These regions exhibit a reduced or negative BOLD response to inhaled CO₂. In this study, we sought to clarify the mechanism behind the negative BOLD response by investigating its time delay (TD). Dynamic susceptibility contrast (DSC) MRI with the injection of a contrast agent was used as the gold standard in order to provide measurement of the blood arrival time to which CVR TD could be compared. We hypothesize that if negative BOLD responses are the result of a steal phenomenon, they should be synchronized with positive BOLD responses from healthy brain tissue, even though the blood arrival time would be delayed. Methods: On a 3-tesla MRI system, BOLD CVR and DSC images were collected in a group of 19 patients with steno-occlusive cerebrovascular disease. For each patient, we generated a CVR magnitude map by regressing the BOLD signal with the end-tidal partial pressure of CO₂ (P_ETCO₂), and a CVR TD map by extracting the time of maximum cross-correlation between the BOLD signal and P_ETCO₂. In addition, a blood arrival time map was generated by fitting the DSC signal with a gamma variate function. ROI masks corresponding to varying degrees of reactivity were constructed. Within these masks, the mean CVR magnitude, CVR TD and DSC blood arrival time were extracted and averaged over the 19 patients. CVR magnitude and CVR TD were then plotted against DSC blood arrival time. Results: The results show that CVR magnitude is highly correlated to DSC blood arrival time. As expected, the most compromised tissues with the longest blood arrival time have the lowest (most negative) CVR magnitude. However, CVR TD shows a noncontinuous relationship with DSC blood arrival time. CVR TD is well correlated to DSC blood arrival time (p < 0.0001) for tissue of positive reactivity, but fails to maintain this trend for tissue of negative reactivity. Regions with negative reactivity have similar CVR TD than healthy regions. Conclusion: These results support the hypothesis that negative reactivity is the result of a steal phenomenon, lowering the BOLD signal as soon as healthier parts of the brain start to react and augment their blood flow. BOLD CVR MRI is capable of identifying this steal distribution, which has particular diagnostic significance as it represents an actual reduction in flow to already compromised tissue.

Power spectrum scale invariance identifies prefrontal dysregulation in paranoid schizophrenia

Theory and experimental evidence suggest that complex living systems function close to the boundary of chaos, with erroneous organization to an improper dynamical range (too stiff or chaotic) underlying system-wide dysregulation and disease. We hypothesized that erroneous organization might therefore also characterize paranoid schizophrenia, via optimization abnormalities in the prefrontal-limbic circuit regulating emotion. To test this, we acquired fMRI scans from 35 subjects (N = 9 patients with paranoid schizophrenia and N = 26 healthy controls), while they viewed affect-valent stimuli. To quantify dynamic regulation, we analyzed the power spectrum scale invariance (PSSI) of fMRI time-courses and computed the geometry of time-delay (Poincaré) maps, a measure of variability. Patients and controls showed distinct PSSI in two clusters (k(1) : Z = 4.3215, P = 0.00002 and k(2) : Z = 3.9441, P = 0.00008), localized to the orbitofrontal/medial prefrontal cortex (Brodmann Area 10), represented by β close to white noise in patients (β ≈ 0) and in the pink noise range in controls (β ≈ -1). Interpreting the meaning of PSSI differences, the Poincaré maps indicated less variability in patients than controls (Z = -1.9437, P = 0.05 for k(1) ; Z = -2.5099, P = 0.01 for k(2) ). That the dynamics identified Brodmann Area 10 is consistent with previous schizophrenia research, which implicates this area in deficits of working memory, executive functioning, emotional regulation and underlying biological abnormalities in synaptic (glutamatergic) transmission. Our results additionally cohere with a large body of work finding pink noise to be the normal range of central function at the synaptic, cellular, and small network levels, and suggest that patients show less supple responsivity of this region.

Worldwide distribution of ages of the continental lithosphere derived from a global seismic tomographic model

It has long been known that continental regions of different age have different seismic properties: the older the lithosphere, the greater the velocity. Here we ask whether we can obtain a more formal relationship between seismological observations and the age of continents. The deep structure of continents has been seismically mapped for the entire Earth. S-vertical travel time delay maps were computed from velocity maps. S-delay maps (using [Shapiro, N.M., Ritzwoller, M.H., 2002. Monte-Carlo inversion of broad-band surface wave dispersion for a global shear wave velocity model of the crust and upper mantle. Geophys. J. Int. 151, 88-105]) correlate with maps show a broad correlation with the ages of surface rocks but when studied in detail, the correlation is not good. The histogram of the S delays for continents is not Gaussian but contains two maxima. From a study in North American stations, Romanowicz and Cara [Romanowicz, B.A., Cara, M., 1980. Reconsideration of the relationship between S and P station anomalies in North America. Geophys. Res. Lett. 7, 417-420] found that the ratio of S- to P-delay does not fit a linear relationship: different intercept times have to be used for positive and for negative S to P ratios. They explained this by the presence of low-velocity mantle beneath tectonically active regions but not beneath stable cratons. By imposing that the negative peak of the S-delay histogram corresponds to a major period of continent growth, a relationship between S delay and age is obtained. Using this relationship, a “seismic continental growth curve” is derived. This growth curve is similar to curves published by geochronologists in that it shows strong growth between 3 and 1 Ga. Many uncertainties remain, particularly on the exact meaning of the age of a continental region.

A data-fitting procedure for chaotic time series

In this paper we introduce data characterizations for fitting chaotic data to linear combinations of one-dimensional maps (say, of the unit interval) for use in subgrid-scale turbulence models. We test the efficacy of these characterizations on data generated by a chaotically-forced Burgers' equation and demonstrate very satisfactory results in terms of modeled time series, power spectra and delay maps.

Multiplane gravitational lensing. I. Morse theory and image counting

The image counting problem for gravitational lensing by general matter deflectors distributed over finitely many lens planes is considered. Counting formulas and lower bounds are found via Morse theory for the number of images of a point source not on a caustic. Images are counted within a compact region D not necessarily assumed to properly contain the deflector space. In addition, it is shown that Morse theory is applicable because multiplane time-delay maps Ty generically satisfy the Morse boundary conditions relative to D. All results obtained depend only on the topological properties induced in the lens planes by the deflector potentials and the behavior of grad Ty at boundary points of D.

Morse theory and gravitational microlensing

Morse theory is used to rigorously obtain counting formulas and lower bounds for the total number of images of a background point source, not on a caustic, undergoing lensing by a single-plane microlens system having compact bodies plus either subcritical or supercritical continuously distributed matter. An image-counting formula is also found for the case when external shear is added. In addition, it is proven that a microlens system consisting of k lens planes will generate N = 2M− + Πki=1(1 − gi) images of a background point source not on a caustic, where M− is the total number of critical points of odd index of the time-delay map and gi is the number of stars on the ith lens plane. Morse theoretic tools also yield that the smallest value N can have is Πi=1k(1+gi).