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Based on our previous study [Chin. Phys. Lett. 24 (2007) 2238] in which the Fresnel operator corresponding to classical Fresnel transform was introduced, we derive the fractional Fourier transformation operator, and the optical operator method is then enriched. [ABSTRACT FROM AUTHOR]

This paper extends the definition of fractional Fourier transform (FRFT) proposed by Namias V by using other orthonormal bases for L2 (R) instead of Hermite-Gaussian functions. The new orthonormal basis is gained indirectly from multiresolution analysis and orthonormal wavelets. The so defined FRFT is called wavelets-fractional Fourier transform. [ABSTRACT FROM AUTHOR]

We generalize Bochner's theorem for functions of the positive type--theorem 1--to more general integral transforms using the Jost solution of the radial Schrödinger equation. The generalized theorem is theorem 2. We then use Bochner's theorem to obtain an integral representation for the phase shift, shown in theorem 4. In a forthcoming paper, this theorem will be used in inverse scattering theory. The proofs are simple, and make use of well-known theorems of real analysis and Fourier transforms of L1, L1[?]L2, ... functions. [ABSTRACT FROM AUTHOR]

Mehta has shown that eigenvectors of the N × N finite Fourier transform can be written in terms of the standard Hermite eigenfunctions of the quantum harmonic oscillator (1987 J. Math. Phys. 28 781). Here, we construct a one-parameter family of q-extensions of these eigenvectors, based on the continuous q-Hermite polynomials of Rogers. In the limit when q - 1 these q-extensions coincide with Mehta's eigenvectors, and in the continuum limit as N - [?] they give rise to q-extensions of eigenfunctions of the Fourier integral transform. [ABSTRACT FROM AUTHOR]

There exists a fundamental relation between the response of a moving detector, such as the Laser Interferometer Space Antenna (LISA), to the signals from a set of sources and the Radon transform of the unknown source density function. The tomographic approach (Mohanty and Nayak 2006 Phys. Rev. D 73 083006, Nayak et al 2006 Proc. 6th Int. LISA Symp.) is based on this relation and, using two successive Fourier transforms, can resolve unknown sources in both sky position and frequency. The amplitude/phase modulations due to the antenna pattern of LISA can be folded into this formalism (Nayak et al 2006 Proc. 6th Int. LISA Symp.) as can an arbitrary detector motion. We show how, by suitably combining TDI observables, both types of modulations lead to significant improvements in the raw resolving power of the method. Ongoing experiments with a variety of deconvolution methods will lead to a final pipeline. One candidate pipeline is applied to the Mock LISA Data Challenge (MLDC) data (challenge data 1.1.1-1.1.4) and the results regarding source position and frequency reconstruction as well as computational requirements are reported. [ABSTRACT FROM AUTHOR]

We develop fast discrete Fourier transforms (and their adjoints) from a square in space to a disk in the Fourier domain. Since our new transforms are not unitary, we develop a fast inversion algorithm and derive corresponding estimates that allow us to avoid iterative methods typically used for inversion. We consider the eigenfunctions of the corresponding band-limiting and space-limiting operator to describe spaces on which these new transforms can be inverted and made useful. In the process, we construct polar grids which provide quadratures and interpolation with controlled accuracy for functions band-limited within a disk. For rapid computation of the involved trigonometric sums we use the unequally spaced fast Fourier transform, thus yielding fast algorithms for all new transforms. We also introduce polar grids motivated by linearized scattering problems which are obtained by discretizing a family of circles. These circles are generated by using a single circle passing through the origin and rotating this circle with the origin as a pivot. For such grids, we provide a fast algorithm for interpolation to a near optimal grid in the disk, yielding an accurate adjoint transform and inversion algorithm. [ABSTRACT FROM AUTHOR]

The structure of porous Si samples prepared by conventional photoexcited electrochemical etching in hydrofluoric acid solution is presented. Strain enhanced cracking was evidenced at the surface of the sample, which was synthesized at higher incidence angle of light. Combined modes of carbon-fluorine and/or oxygen related impurities, and silicon-oxides are revealed from Fourier transform infrared investigation. A resonant feature at ?467?nm, originating from a strong coupling of localized excitons at the Si/SiO2interfacial states and Si-O vibrational modes, is examined during photoluminescence measurements for an excitation wavelength of 320?nm. Furthermore, the appearance of luminescence bands in the range 378-412?nm is discussed in the light of a quantum confinement assisted radiative recombination of electrons and holes at impurity related defects or at the vacancies of neutral oxygen. [ABSTRACT FROM AUTHOR]

In the present study, we introduce an electroencephalography (EEG)-based, real-time, cortical rhythmic activity monitoring system which can monitor spatiotemporal changes of cortical rhythmic activity on a subject's cortical surface, not on the subject's scalp surface, with a high temporal resolution. In the monitoring system, a frequency domain inverse operator is preliminarily constructed, considering the subject's anatomical information and sensor configurations, and then the spectral current power at each cortical vertex is calculated for the Fourier transforms of successive sections of continuous data, when a particular frequency band is given. A preliminary offline simulation study using four sets of artifact-free, eye-closed, resting EEG data acquired from two dementia patients and two normal subjects demonstrates that spatiotemporal changes of cortical rhythmic activity can be monitored at the cortical level with a maximal delay time of about 200 ms, when 18 channel EEG data are analyzed under a Pentium4 3.4 GHz environment. The first pilot system is applied to two human experiments--(1) cortical alpha rhythm changes induced by opening and closing eyes and (2) cortical mu rhythm changes originated from the arm movements--and demonstrated the feasibility of the developed system. [ABSTRACT FROM AUTHOR]

Two coupled parametric four-wave-mixing processes in Rb atoms are studied using perturbation theory, which reveals clear evidence of the appearance of quantum beat at 608 cm[?]1, corresponding to the energy difference of the 7s[?]5d states of Rb atoms, in the parametric four-wave-mixing signals. A pump-probe technique is utilized to observe the quantum beat. Time-varying characteristics of the quantum beat are investigated using time-dependent Fourier transform. The results show that the time-varying characteristics of the quantum beat not only offers a sensitive detecting method for observing the decay of atomic wave packets, but also provides a potential tool for monitoring the dissociation of molecules. [ABSTRACT FROM AUTHOR]

The squared eigenfunctions of the spectral problem associated with the Camassa-Holm equation represent a complete basis of functions, which helps to describe the inverse scattering transform for the Camassa-Holm hierarchy as a generalized Fourier transform. The main result of this work is the derivation of the completeness relation for the squared solutions of the Camassa-Holm spectral problem. We show that all the fundamental properties of the Camassa-Holm equation such as the integrals of motion, the description of the equations of the whole hierarchy and their Hamiltonian structures can be naturally expressed making use of the completeness relation and the recursion operator, whose eigenfunctions are the squared solutions. [ABSTRACT FROM AUTHOR]

An original dc double anode plasma torch which provides a long-time and highly stable atmospheric plasma jet has been devised for the purpose of hazardous waste treatment. The arc fluctuations and dynamic behaviour of the argon and argon-nitrogen plasma jets under different operating conditions have been investigated by means of classical tools, such as the statistic method, fast Fourier transform (FFT) and correlation analysis. In our experiments, the takeover mode is identified as the fluctuation characteristic of the argon plasma jet while the restrike mode is typical in the argon-nitrogen plasma dynamic behaviour. In the case of pure argon, the FFT and correlation calculation results of electrical signals exhibit the only characteristic frequency of 150 Hz, which originates from the torch power and is independent of any change in the operating conditions. It indicates that the nature of fluctuations in an argon plasma jet is mainly induced by the undulation of the tri-phase rectified power supply. In contrast, besides the same low frequency bulk fluctuation, the dynamic behaviour of the argon-nitrogen plasma jet at high frequency (4.1 kHz) is ascribed to the rapid motion of both arc roots on the anode surface. In addition, it is found that each arc root attachment is rather diffused than located at a fixed position on the anode wall in the argon plasma jet, while constricted arc roots occur when nitrogen is added into argon as the plasma working gas. [ABSTRACT FROM AUTHOR]

The photodetachment cross section of H[?] in parallel electric and magnetic fields near an elastic surface is derived and calculated by using the closed orbit theory. It is found that the elastic surface can produce some interesting effects. Besides the closed orbits previously found by Peters et al. for the H[?] in parallel electric and magnetic fields, some additional closed orbits are produced due to the effect of the elastic surface. The results show that the cross section oscillation is much more complicated in comparison with the cross section of H[?] in parallel external fields without surface. Each peak in the Fourier transformed cross section corresponds to the period of one detached electron closed orbit. This study provides a new understanding of the photodetachment of negative ions in the presence of external fields and surface. [ABSTRACT FROM AUTHOR]

An exact calculation of the Voigt spectral line profile in spectroscopy has been derived using the Fourier transform method. The analytical formula we calculated is a real function, rather than a complex function as has been previously discussed, because the imaginary part will be zero in our calculation. The analytical formula is very convenient in practical applications. The relationship of the half width of the Voigt profile, the Gaussian profile and the Lorentzian profile is also discussed. Through analysis using a computer simulation, we find that the formula we calculated is in good agreement with the experimental result. [ABSTRACT FROM AUTHOR]

A number of elegant approaches have been developed for the identification of quantum circuits which can be efficiently simulated on a classical computer. Recently, these methods have been employed to demonstrate the classical simulability of the quantum Fourier transform (QFT). Here we show that one can demonstrate a number of simulability results for QFT circuits in a straightforward manner using Griffiths and Niu's semi-classical QFT construction (Griffiths and Niu 1996 Phys. Rev. Lett. 76 3228). We use this to analyse the simulability properties of the QFT with a variety of classes of entangled input states. We then discuss the consequences of these results in the context of Shor's factorization algorithm. [ABSTRACT FROM AUTHOR]

We study the symbolic sequences associated with a two-dimensional nonlinear map describing a digital filter with 2's complement arithmetic, and the role of the filter parameter a= 2cos in determining admissibility of these sequences. We solve an appropriately specialized form of Chua and Lin's inequalities governing admissibility, and obtain a complete identification of the infinite class of periodic symbolic sequences admissible in an open interval having parameter value = 0 as left end-point. A key step in the argument, easily established by parity for sequences having odd period, requires a more penetrating analysis in the even case. Computer searches for sequences with periods up to 200 have revealed that this class accounts for the greater number of admissible periodic sequences associated with the map. Our solution provides an efficient construction for the periodic symbolic sequences admissible adjacent to zero, parametrized by the period and the number of +? digit pairs present. We also show that the precise interval of admissibility is (0, ?/N), where Nis the least period, which permits us to relate the sequences to the points of state space that give rise to them. We thereby obtain a bound on the measure of the subset of state space consisting of the points associated with periodic symbolic sequences, improving previously published bounds. A similar identification of the periodic sequences admissible at the far end of the parameter range, adjacent to = ?, is deduced. [ABSTRACT FROM AUTHOR]

Experiments were conducted to confirm the isotropic spatial resolution of multislice CT with a 0.5 mm slice thickness. Isotropic spatial resolution means that the spatial resolution in the transaxial plane (X-Yplane) and that in the longitudinal direction (Zdirection) are equivalent. To obtain point spread function (PSF) values in the X-Y-Zdirections, three-dimensional voxel data were obtained by helical scanning of a bead phantom. The modulation transfer function (MTF) values were then obtained by three-dimensional Fourier transform of the PSF. Evaluation of the spatial resolution in the X-Y-Zdirections by the MTF values showed that the spatial resolution in the Zdirection does not depend on the reconstruction kernel used. It was also found that the spatial resolution in the Zdirection, as compared with that in the X-Yplane, is superior with the standard kernel for the abdomen and is inferior with the high-definition kernel for the ears/bones. By performing sharpening filter processing in the Zdirection with a high-definition kernel, comparable spatial resolution could be obtained in the X-Y-Zdirections. It was confirmed that adjusting the spatial resolution in the Zdirection with the reconstruction kernel used is an effective method for isotropic imaging. [ABSTRACT FROM AUTHOR]

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are ?2= 4.69and ?4= 4.6, which are comparable with the theoretical asymptotic value ? = 4.669. [ABSTRACT FROM AUTHOR]

A nonchaotic attractor is observed in an infinite-dimensional system which is related to optical bistability and described by a nonlinear time-delay differential equation. The observed nonchaotic attractor is characterized by the strange trajectory of attractor but with negative value for the largest Lyapunov exponent, as well as the Fourier power spectra. [ABSTRACT FROM AUTHOR]

Starting out from the recently established quantum correlation function expression of the characteristic function for the work performed by a force protocol on the system in Talkner et al(2007 Phys. Rev.E 75050102 (Preprintcond-mat/0703213)) the quantum version of the Crooks fluctuation theorem is shown to emerge almost immediately by the mere application of an inverse Fourier transformation. [ABSTRACT FROM AUTHOR]

Chirped and non-chirped Super Gaussians (SG) are very common in pulse modeling for optical communications. However, unlike Gaussian pulses, the propagation (and distortions) of SG pulses in dispersive media cannot be expressed in closed-form analytical expression, nor can its Fourier transform, i.e. its spectrum. In this paper, it is shown that analytical smooth rectangular can be utilized to formulate analytically (in both time and frequency domains) with high accuracy the propagation of chirped SG pulses in dispersive medium. The paper also elaborates on chirped pulses cascading and on the propagation of asymmetric SG pulses. [ABSTRACT FROM AUTHOR]

The tunable electronic structure of graphene nanoribbons (GNRs) has attracted much attention due to the great potential in nanoscale electronic applications. Most methods to produce GNRs rely on the lithographic process, which suffers from the process-induced disorder in the graphene and scalability issues. Here, we demonstrate a novel approach to directly grow free-standing GNRs on step-bunched facets of off-oriented 4H-SiC epilayers without any patterning or lithography. First, the 4H-SiC epilayers with well-defined bunched steps were intentionally grown on 4 degree off-axis 4H-SiC substrates by the sublimation epitaxy technique. As a result, periodic step facets in-between SiC terraces were obtained. Then, graphene layers were grown on such step-structured 4H-SiC epilayers by thermal decomposition of SiC. Scanning tunneling microscopy (STM) studies reveal that the inclined step facets are about 13–15 nm high and 30–35 nm wide, which gives an incline angle of 23–25 degrees. LEEM and LEED results showed that the terraces are mainly covered by monolayer graphene and the buffer layer underneath it. STM images and the analysis of their Fourier transform patterns suggest that on the facets, in-between terraces, graphene is strongly buckled and appears to be largely decoupled from the surface. [ABSTRACT FROM AUTHOR]

Although Fourier transformation (FT) is the most commonly used method to retrieve the phase and amplitude information of a spectral interferogram, its accuracy is usually degraded due to effects such as fringe truncation, uneven distribution of fringes, noise and fringe density, etc. In this work, we propose an improved FT based method to process the spectral interferogram. By using a Gaussian envelope and a self-designed flat-top cap window function, significant improvements in accuracy and robustness can be achieved compared to the conventional FT method. Besides, by analyzing the correlation between the fringe density and the data processing error, the optimal configuration in an actual spectral interferometry experiment can be screened out. At last, we have applied the proposed method on the actual spectral interferograms obtained in our laser-induced shock wave loading experiment for effectiveness demonstration, and the results show a dramatical reduction of the measurement error compared to the traditional FT method. [ABSTRACT FROM AUTHOR]

Elliptic fundamental, dipole and vortex solitons in nonlocal nonlinear media with linear anisotropic diffraction are investigated analytically and numerically. In particular we do this for the whole range of degrees of nonlocality. Analytical solutions for the solitons are obtained with the variational approach. The dynamics of elliptic solitons are also numerically demonstrated with the split-step Fourier transform method. With the help of linear anisotropic diffraction, stable elliptic fundamental and dipole solitons can be obtained. However, elliptic vortex solitons are always unstable and transfer into spiraling elliptic vortex solitons. [ABSTRACT FROM AUTHOR]

We give a general definition of spin foam models, and then of models of 4d quantum gravity based on constraining BF theory. We highlight the construction and quantization ambiguities entering model building, among which the choice of quantization map applied to the B variables carrying metric information after imposing simplicity constraints, and the different strategies for imposing the latter constraints. We then construct a new spin foam model for 4d quantum gravity, using the flux representation of states and amplitudes, based on the Duflo quantization map and the associated non-commutative Fourier transform for Lie groups. The advantages of the new model are the geometrically transparent way in which constraints are imposed, and the underlying mathematical properties of the Duflo map itself. Finally, the presence of a closed analytical formula for the model's amplitudes is another valuable asset for future applications. [ABSTRACT FROM AUTHOR]

This article describes the occurrence of a phenomenon that is observed while recording mid-infrared (4000–700 cm−1) absorption spectra of dielectric barrier discharges sustained at frequencies ranging from 300 Hz to 15 kHz. This phenomenon is observed as the presence of very sharp spikes in the spectrum, for which the wavenumber depends on both the high voltage frequency used to generate the discharge and the velocity of the moving mirror of the interferometer (which in turn determines the interferogram sampling frequency). While it is well known that the consumption of gas precursor within plasmas can be followed, we demonstrate that Fourier transform infrared spectroscopy also makes it possible to monitor frequencies and coupling of excitation mechanisms occurring in the plasma. [ABSTRACT FROM AUTHOR]

One of the challenges in single particle reconstruction in cryo-electron microscopy is to find a three-dimensional model of a molecule using its two-dimensional noisy projection-images. In this paper, we propose a robust ‘angular reconstitution’ algorithm for molecules with n-fold cyclic symmetry, that estimates the orientation parameters of the projections-images. Our suggested method utilizes self common lines which induce identical lines within the Fourier transform of each projection-image. We show that the location of self common lines admits quite a few favorable geometrical constraints, thus allowing to detect them even in a noisy setting. In addition, for molecules with higher order rotational symmetry, our proposed method exploits the fact that there exist numerous common lines between any two Fourier transformed projection-images of such molecules, thus allowing to determine their relative orientation even under high levels of noise. The efficacy of our proposed method is demonstrated using numerical experiments conducted on simulated and experimental data. [ABSTRACT FROM AUTHOR]

Estimation of the discrete-time Fourier transform (DTFT) at points of a finite domain arises in many imaging applications. A new approach to this task, the golden angle linogram Fourier domain (GALFD), is presented, together with a computationally fast and accurate tool, named golden angle linogram evaluation (GALE), for approximating the DTFT at points of a GALFD. A GALFD resembles a linogram Fourier domain (LFD), which is efficient and accurate. A limitation of linograms is that embedding an LFD into a larger one requires many extra points, at least doubling the domain’s cardinality. The GALFD, on the other hand, allows for incremental inclusion of relatively few data points. Approximation error bounds and floating point operations counts are presented to show that GALE computes accurately and efficiently the DTFT at the points of a GALFD. The ability to extend the data collection in small increments is beneficial in applications such as magnetic resonance imaging. Experiments for simulated and for real-world data are presented to substantiate the theoretical claims. The mathematical analysis, algorithms, and software developed in the paper are equally suitable to other angular distributions of rays and therefore we bring the benefits of linograms to arbitrary radial patterns. [ABSTRACT FROM AUTHOR]

In many practical situations, the recovery of information about some phenomenon of interest f  reduces to performing deconvolution on indirect measurements , corresponding to the convolution of f  with a known kernel (point spread function) p . However, in practice, only discrete measurements of g will be available. Consequently, the construction of discrete approximations to f  reduces to deriving discrete versions of . How this is done depends crucially on what is assumed about the properties of the kernel p . Here, it is assumed that p  is symmetric and integrable, and that the Fourier transform of p  is strictly positive. Different discrete versions are obtained depending on how the discretisation of is performed. After establishing convergence of the truncated schemes, we discuss the underlying difficulties reflecting their ill-posedness and detail how approximations have to be treated with due care. Some of the technical issues underlying the arguments are treated in the appendix. [ABSTRACT FROM AUTHOR]

We present an efficient method for estimating the eigenvalues of a Hamiltonian H from the expectation values of the evolution operator for various times. For a given quantum state ρ, our method outputs a list of eigenvalue estimates and approximate probabilities. Each probability depends on the support of ρ in those eigenstates of H associated with eigenvalues within an arbitrarily small range. The complexity of our method is polynomial in the inverse of a given precision parameter ϵ, which is the gap between eigenvalue estimates. Unlike the well-known quantum phase estimation algorithm that uses the quantum Fourier transform, our method does not require large ancillary systems, large sequences of controlled operations, or preserving coherence between experiments, and is therefore more attractive for near-term applications. The output of our method can be used to estimate spectral properties of H and other expectation values efficiently, within additive error proportional to ϵ. [ABSTRACT FROM AUTHOR]

We present in this work a study of the effect of Raman enhancement on axially heterostructured semiconductor nanowires (NWs). The investigation is motivated by the recent detection of a Raman signal enhancement effect at the heterojunction (HJ) of axially heterostructured NWs. Semiconductor NWs offer very interesting properties as compared to their bulk counterparts, making them the building blocks of future optoelectronic nanodevices. The use of HJs turns out to be essential for a great variety of devices. As a result, understanding the optical properties of heterostructured NWs is a fundamental step for their possible application on future technologies. In order to unveil the underlying physics of the light/NW interaction, the complex-valued electromagnetic (EM) field distribution induced inside heterostructured NWs under light exposure is studied. The use of the Fourier transform is presented as a key tool in order to ascertain the different components of the EM field generated inside the NW. The results show the presence of two components: one associated with the incident light beam and a second one which appears as a consequence of the presence of the axial HJ. This second component explains the emergence of the Raman enhancement effect as a result of the interaction of the incident beam with the dielectric discontinuity associated with the HJ. [ABSTRACT FROM AUTHOR]

Advanced semiconductor devices have 3D morphologies with nanometer sized features. Therefore, their structural and chemical characterization requires analysis techniques with high spatial 3D resolution. Through focal integrated differential phase contrast and high angle annular dark field scanning transmission electron microscopy (STEM) depth sectioning are among the techniques that can potentially fulfill these needs. In this work they are applied to Si and Ge nanowire structures with gate all around replacement metal gates. It is shown that with both imaging modes slicing with 2D lattice resolution through the polycrystalline gate stack and the monocrystalline wires is possible, while a resolution in the viewing direction on the order of 5 nm is obtained. Based on fast Fourier transformation analysis the crystal distribution in the gate stack and morphology of the nanowires are analyzed. Similar structures are investigated with combined STEM-energy dispersive spectroscopy 180° tomography on pillar shaped TEM specimens. Comparison of the 3D imaging modes and standard TEM/STEM imaging is discussed. [ABSTRACT FROM AUTHOR]

We continue to study the matrix model of the Nf   =  2 case that represents the irregular conformal block. What provides us with the Painlevé system is not the instanton partition function per se but rather a finite analog of its Fourier transform that can serve as a generating function. The system reduces to the extension of the Gross–Witten–Wadia unitary one-matrix model by the logarithmic potential while keeping the planar critical behavior intact. The double scaling limit to this critical point is a constructive way to study Argyres–Douglas type theory from IR. We elaborate upon the method of orthogonal polynomials and its relevance to these problems, developing it further for the case of a generic unitary matrix model and that of a special case with the logarithmic potential. [ABSTRACT FROM AUTHOR]

We present limits on the 21 cm power spectrum from the Epoch of Reionization using data from the 64 antenna configuration of the Donald C. Backer Precision Array for Probing the Epoch of Reionization (PAPER) analyzed through a power spectrum pipeline independent from previous PAPER analyses. Previously reported results from PAPER have been found to contain significant signal loss. Several lossy steps from previous PAPER pipelines have not been included in this analysis, namely delay-based foreground filtering, optimal fringe-rate filtering, and empirical covariance-based estimators. Steps that remain in common with previous analyses include redundant calibration and local sidereal time (LST) binning. The power spectra reported here are effectively the result of applying a linear Fourier transform analysis to the calibrated, LST-binned data. This analysis also uses more data than previous publications, including the complete available redshift range of z ∼ 7.5 to 11. In previous PAPER analyses, many power spectrum measurements were found to be detections of noncosmological power at levels of significance ranging from two to hundreds of times the theoretical noise. Here, excess power is examined using redundancy between baselines and power spectrum jackknives. The upper limits we find on the 21 cm power spectrum from reionization are , , , , , and at redshifts z = 10.87, 9.93, 8.68, 8.37, 8.13, and 7.48, respectively. For reasons described in Cheng et al., these limits supersede all previous PAPER results. [ABSTRACT FROM AUTHOR]

Foreground power dominates the measurements of interferometers that seek a statistical detection of highly-redshifted H i emission from the Epoch of Reionization (EoR). The chromaticity of the instrument creates a boundary in the Fourier transform of frequency (proportional to k∥) between spectrally smooth emission, characteristic of the strong synchrotron foreground (the “wedge”), and the spectrally structured emission from H i in the EoR (the “EoR window”). Faraday rotation can inject spectral structure into otherwise smooth polarized foreground emission, which through instrument effects or miscalibration could possibly pollute the EoR window. For instruments pursuing a “foreground avoidance” strategy of simply measuring in the EoR window, and not attempting to model and remove foregrounds, as is the plan for the first stage of the Hydrogen Epoch of Reionization Array (HERA), characterizing the intrinsic instrument polarization response is particularly important. Using data from the HERA 19-element commissioning array, we investigate the polarization response of this new instrument in the power-spectrum domain. We perform a simple image-based calibration based on the unpolarized diffuse emission of the Global Sky Model, and show that it achieves qualitative redundancy between the nominally redundant baselines of the array and reasonable amplitude accuracy. We construct power spectra of all fully polarized coherencies in all pseudo-Stokes parameters, and discuss the achieved isolation of foreground power due to the intrinsic spectral smoothness of the foregrounds, the instrument chromaticity, and the calibration. We compare to simulations based on an unpolarized diffuse sky model and detailed electromagnetic simulations of the dish and feed, confirming that in Stokes I, the calibration does not add significant spectral structure beyond that expected from the interferometer array configuration and the modeled primary beam response. Furthermore, this calibration is stable over the 8 days of observations considered. Excess power is seen in the power spectra of the linear polarization Stokes parameters, which is not easily attributable to leakage via the primary beam, and results from some combination of residual calibration errors and actual polarized emission. Stokes V is found to be highly discrepant from the expectation of zero power, strongly pointing to the need for more accurate polarized calibration. [ABSTRACT FROM AUTHOR]

Fourier analysis plays a major role in the analysis and understanding of many phenomena in physics and contemporary engineering. However, students, who have often discovered this notion through numerical tools do not necessarily understand all the richness that can be derived from joint analysis in the temporal and spectral domains, particularly in the field of optics. As part of the second year of the master’s degree in Physics Lasers and Materials at the University of Burgundy, we have set up a series of experiments to highlight these concepts and to show, on a non-trivial example of periodic phase modulation, the precautions to be taken in the interpretation of the various experimentally accessible spectra. This hands-on session, made possible through the use of research infrastructure, is also an introduction to the use of standard optical telecommunications equipment. [ABSTRACT FROM AUTHOR]

Laser pulses facilitate multiphoton contributions to the trident pair production , where the label L indicates a laser field dressed electron (e−) or positron (e+ ). We isolate the impact of the pulse envelope in the trident S matrix element, formulated within the Furry picture, in leading order of a series expansion in the classical nonlinearity parameter a0. Generally, the Fourier transform of the envelope carries the information on the pulse length, which becomes an easily tractable function in the case of a pulse envelope. The transition to a monochromatic laser wave can be handled in a transparent manner, as also the onset of bandwidth effects for short pulses can be factorized out and studied separately. [ABSTRACT FROM AUTHOR]

In this paper, we present an analysis of the pulsating behavior of Kepler target KIC 10284901. The Fourier transform of the high-precision light curve reveals seven independent frequencies for its light variations. Among them, the first two frequencies are main pulsation modes: F0 = 18.994054(1) day−1 and F1 = 24.335804(4) day−1; the ratio F0/F1 = 0.7805 classifies this star as a double-mode high-amplitude δ Scuti (HADS) star; another two frequencies, fm1 = 0.4407 day−1 and fm2 = 0.8125 day−1, are detected directly, and the modulations of fm1 and fm2 to F0 and F1 modes (seen as quintuplet structures centered on these two modes in the frequency spectrum) are also found. This is the first detection of a double-modulation effect in the HADS stars. The features of the frequency pattern and the ratio (fm1/fm2 ≈ 1:2), as well as the cyclic variation of amplitude of the two dominant pulsation modes, which seem to be similar to that in Blazhko RR Lyrae stars, indicate this modulation might be related to the Blazhko effect. A preliminary analysis suggests that KIC 10284901 is in the bottom of the HADS instability strip and situated in the main sequence. [ABSTRACT FROM AUTHOR]

Radio interferometers consisting of identical antennas arranged on a regular lattice permit fast Fourier transform beamforming, which reduces the correlation cost from in the number of antennas to . We develop a formalism for describing this process and apply this formalism to derive a number of algorithms with a range of observational applications. These include algorithms for forming arbitrarily pointed tied-array beams from the regularly spaced Fourier transform–formed beams, sculpting the beams to suppress sidelobes while only losing percent-level sensitivity, and optimally estimating the position of a detected source from its observed brightness in the set of beams. We also discuss the effect that correlations in the visibility-space noise, due to cross talk and sky contributions, have on the optimality of Fourier transform beamforming, showing that it does not strictly preserve the sky information of the n2 correlation, even for an idealized array. Our results have applications to a number of upcoming interferometers, in particular the Canadian Hydrogen Intensity Mapping Experiment–Fast Radio Burst (CHIME/FRB) project. [ABSTRACT FROM AUTHOR]

The cosine-model analysis (CMA) method and the small angle x-ray scattering (SAXS) method are two major types of information retrieval algorithms, commonly utilized in x-ray phase-contrast imaging with a grating interferometer. However, there are significant differences between the two methods in algorithm implementation, and the existing literature has not completely revealed their intrinsic relationship. In this paper, we theoretically derive and experimentally verify the intrinsic connections between CMA and SAXS, and it is seen that SAXS can be interpreted well by the cosine-model assumption of CMA. To validate our analysis of the scattering distribution when applying the cosine model to the convolution used in SAXS, we applied a deconvolution process into CMA before using the Fourier transform to get the three contrasts. Furthermore, the principal component analysis (PCA) is introduced in this work, and two PCA-based retrieval algorithms are presented in order to simplify the iteration process of deconvolution in SAXS or to obtain absorption and dark-field signals instead of the Fourier transform in CMA. Applying a quantitative structural similarity (SSIM) index and a profile analysis to the results of an ex vivo mammography, it is proved that retrieved images via CMA and SAXS are consistent with each other (SSIM values are 1.0000, 0.9845 and 0.9767 respectively), and that the extra deconvolution process applied into CMA shows a good performance and our analytical analysis of the scattering distribution is valid when applying the cosine model to the convolution used in SAXS. Besides, it is concluded that PCA shows almost the same performance with the Fourier transform (SSIM values are 1.0000 for both absorption and dark-field images), and the simplified SAXS-analogous method works well with higher efficiency in computation and better stability relative to the original SAXS, while maintaining the similar level of image quality (SSIM values are 1.0000, 0.9839 and 0.9781 respectively). [ABSTRACT FROM AUTHOR]

We use two-dimensional Fourier transformation to measure the pitch angle (φ) of the dominant spiral Fourier mode of well-defined spiral arms in 13 protoplanetary disks, making use of near-infrared scattered-light images of AB Aur, SAO 206462, MWC 758, V1247 Ori, HD 142527, DZ Cha, LkHα 330, and HD 100453, and ALMA millimeter continuum images of Elias 2-27, IM Lup, AS 205, and HT Lup. We find that the measured pitch angle correlates strongly with disk mass (MD), such that more massive protoplanetary disks have smaller pitch angles, following . Interestingly, four disks with a known companion (HD 142527, HD 100453, AS 205, and HT Lup) share the same trend. Such a strong dependence of spiral arm pitch angle on disk mass suggests that the disk mass, independent of the formation mechanism, plays a fundamental role in determining the arm tightness of the observed spiral structure. The physical origin of the relation is still not clear. The pitch angle of spiral arms in protoplanetary disks provides an independent constraint on the disk mass. [ABSTRACT FROM AUTHOR]

We developed a near-infrared (NIR) superluminescent diode (SLD) based on self-assembled InAs quantum dots (QDs) and demonstrated high-axial-resolution optical coherence tomography (OCT) imaging using this QD-based SLD (QD-SLD). The QD-SLD utilized InAs QDs with controlled emission wavelengths as a NIR broadband light emitter, and a tilted waveguide with segmented electrodes was prepared for edge-emitting broadband electroluminescence (EL) spanning approximately 1–1.3 μm. The bandwidth of the EL spectrum was increased up to 144 nm at a temperature of 25 °C controlled using a thermoelectric cooler. The inverse Fourier transform of the EL spectrum predicted a minimum resolution of 3.6 μm in air. The QD-SLD was subsequently introduced into a spectral-domain (SD)-OCT setup, and SD-OCT imaging was performed for industrial and biological test samples. The OCT images obtained using the QD-SLD showed an axial resolution of ~4 μm, which was almost the same as that predicted from the spectrum. This axial resolution is less than the typical size of a single biological cell (~5 μm), and the practical demonstration of high-axial-resolution OCT imaging shows the application of QD-SLDs as a compact OCT light source, which enables the development of a portable OCT system. [ABSTRACT FROM AUTHOR]

We have studied a femtosecond (fs) ultrafast all-optical photonic crystal (PhC) switch, and a new dynamic mechanism of the interplay between nonlinearity and Bragg scattering is revealed. Almost all phenomena observed in the experiments are reproduced in our numerical simulations. Completely different from the traditional band-gap shift mechanism, we propose a new dynamic mechanism that can explain the considerable increase of transmission and almost all other complex transmission behaviors of the switch. First, the fs-level ultrashort-lifetime nonlinearity generated by the fs pumping pulse, which cannot generate a band-gap shift, only causes a sudden phase change on the signal field that is still inside the PhC. Second, such a phase change can partially destroy the destructive interference of Bragg scattering, which is the physical reason for the low transmission in the photonic gap of the PhC. The study by Fourier transform of the temporally transmitted field can clearly support our new explanation. New phenomena, such as the larger than unity sum of transmission and reflection, are predicted. The new dynamic mechanism could be widely used in other systems as a new method to amplify nonlinear effects, or as a detector for ultrafast (femto- or attosecond) electronic processes. [ABSTRACT FROM AUTHOR]

A general analytical theory of temporal relaxation processes in isolated quantum systems with many degrees of freedom is elaborated, which unifies and substantially amends several previous approximations. Specifically, the Fourier transform of the initial energy distribution is found to play a key role, which is furthermore equivalent to the so-called survival probability in case of a pure initial state. The main prerequisite is the absence of any notable transport currents, caused for instance by some initially unbalanced local densities of particles, energy, and so on. In particular, such a transportless relaxation scenario naturally arises when both the system Hamiltonian and the initial non-equilibrium state do not exhibit any spatial inhomogeneities on macroscopic scales. A further requirement is that the relaxation must not be notably influenced by any approximate (but not exact) constant of motion or metastable state. The theoretical predictions are compared with various experimental and numerical results from the literature. [ABSTRACT FROM AUTHOR]

It is well known that topics in physics which rely heavily on mathematics can present difficulties for graduate students; for example, problems involving the application of the Fourier transform. To overcome some related difficulties, an integrated approach where physics, mathematics and laboratory activities are strongly interconnected can be helpful. In this view, the present paper describes a device and a data analysis approach whose physics and mathematics facets are jointly taken into account. More specifically, we shall deal with a revised Rüchardt’s device, a topic that plays an important role in the physics curriculum, and we shall introduce the Fourier transform operator in order to extract the average oscillation frequency, thus avoiding computation of the average period of oscillations in the time space. Within this framework, it is shown how the use of the Fourier transform furnishes a straightforward measure of the experiment’s relevant physical quantities. [ABSTRACT FROM AUTHOR]

To overcome the difficulty of realizing large-scale quantum Fourier transform (QFT) within existing technology, this paper implements a resource-saving method (named t-bit semiclassical QFT over ), which could realize large-scale QFT using an arbitrary-scale quantum register. By developing a feasible method to realize the control quantum gate Rk, we experimentally realize the 2-bit semiclassical QFT over on IBM’s quantum cloud computer, which shows the feasibility of the method. Then, we compare the actual performance of 2-bit semiclassical QFT with standard QFT in the experiments. The squared statistical overlap experimental data shows that the fidelity of 2-bit semiclassical QFT is higher than that of standard QFT, which is mainly due to fewer two-qubit gates in the semiclassical QFT. Furthermore, based on the proposed method, N = 15 is successfully factorized by implementing Shor’s algorithm. [ABSTRACT FROM AUTHOR]

We present a generalized theory for describing encryption and decryption by using the double random phase encoding (DRPE) technique under the framework of the Collins diffraction transform formalism. The theory covers to a variety of diffraction domain which includes the Fourier domain (conventional 4f-optical processor), the Fresnel domain and the fractional Fourier transform (FRFT) domain. From the theoretical basis developed in this work, we present novel optical DRPE systems such as Gaussian imaging DRPE, inverse operation DRPE and Fresnel diffraction DRPE systems, which are plausible to implement. It is shown that the maximum number of degrees of freedom (or independent design parameters) of proposed DRPE system increases four times, when compared with the conventional 4f-optical system, which guarantee much more secure encryption and decryption. [ABSTRACT FROM AUTHOR]

We provide a detailed analysis of the three-dimensional cross correlation properties of speckle patterns in the deep Fresnel region scattered by random surface. Basing on Kirchhoff approximation, we first derive the quantitative relationship between the longitudinal correlation function and the fractal characteristics of random surface. A novel measuring method is proposed for extracting the roughness exponent of random surface from the longitudinal correlation function of speckles. In experiment, the speckle patterns deviating different distance from the object plane are acquired by a microscopic imaging system. The longitudinal correlation function of the speckles descends with the increase of deviating distance in the form of negative power law. By calculating the Fourier transform of the longitudinal correlation function, we obtain the roughness exponent of random surface by making linear fitting in the large spectrum region. The extracted results are in good agreement with those measured by an atomic force microscopic, which indicate our method has a satisfying accuracy. [ABSTRACT FROM AUTHOR]

The Fourier transform method can be applied to obtain electromagnetic knots, which are solutions of Maxwell equations in a vacuum with non-trivial topology of the field lines and special properties. The program followed in this work allows us to present the main ideas and the explicit calculations at undergraduate level, so they are not obscured by a more involved formulation. We make use of the helicity basis for calculating the electromagnetic helicity and the photon content of the fields. [ABSTRACT FROM AUTHOR]

In this paper we present a pedagogical strategy to introduce the Heisenberg uncertainty principle to high school students. The basis on which this proposal relies is the Fourier transform, connecting the quantum function in the x domain, , with the function in the wave number domain, . This mathematical relationship directly leads to the uncertainty principle: a state localized in the former domain will present an inversely proportional dispersion in the latter domain. Since in acoustic we have an analog situation we can carry out experiments with sounds leading students to the understanding of the uncertainty relation. In our approach a slightly modified musical theme from the Steven Spielberg movie ‘Close Encounters of the Third Kind’ is the starting point to reach the uncertainty relation. [ABSTRACT FROM AUTHOR]

The present paper is dedicated to an application of the discrete element method (DEM) to study heat transfer by conduction in continuous and heterogeneous media. Our objectives are threefold. First, we aim to set up an original process to generate a Voronoi tessellation based on a granular assembly. This efficiently provides suitable areas of transmission and a representative volume to each particle which are considered to model heat transfer in the continuous medium. Second, a proper expression of the heat flux density is derived from Fourier’s law at a mesoscopic scale represented by polygonal elements called specimens. In this context, investigations led on the sensitivity of the heat flux density distribution with respect to the number of particles within polygonal specimens are performed. Finally, we investigate the suitability of the DEM-based approach to yield thermal properties and heat flux density fields in continuous and heterogeneous media. Two heterogeneous configurations are tested, namely a classic single inclusion problem and a random particulate composite material for which the issue of representative volume element is also discussed. Results exhibit a good agreement with other numerical approaches such as the finite element method and the fast Fourier transform based technique. [ABSTRACT FROM AUTHOR]