A derivative based simplified phase tracker for a single fringe pattern demodulation

In this paper, a novel fringe demodulation method for the estimation of phase and its first-order derivative from a closed-fringe interferogram is proposed. The proposed method determines the phase derivatives in both x&y directions from fringe orientation and density. The phase derivatives are subsequently used to determine phase values using a novel simplified phase tracker. In the phase tracking model, the complexity of the cost function is reduced using predetermined derivatives so computation time required for phase tracking is reduced considerably. The proposed model is more robust while dealing with saddle points in fringes than the conventional phase tracker model. Hence it does not require any specialized scanning strategy. The proposed method is validated with simulated and experimental fringe patterns (obtained using electronic speckle pattern interferometry and optical holographic interferometry) and a comparison study is carried out with conventional regularized phase tracker. The simulation results show that the proposed method has good accuracy and requires less computation time than existing phase-tracking algorithms. The experimental results demonstrate the robustness of the proposed method against speckle noise and its practical applicability for static and dynamic applications.     

Linear and nonlinear liftings of states of quantum systems

In this paper, we study the representability of an arbitrary quantum state ?? ?? ??(H) as the reduction of a vector state r ?? ??(H) of the extended system. We extend the operation of lifting from the set of states ?? _n (H) to the set of generalized states ??(H). A method of constructing the Hilbert space H and the affine linear lifting ??(H) ?? ??(H) is studied. The construction of individual expansion H _?? of the space H for which the state ?? is a reduction of a vector state H _?? is of special interest.     

Self-avoiding Fractional Brownian Motion��The Edwards Model

In this work we extend Varadhan??s construction of the Edwards polymer model to the case of fractional Brownian motions in ? ^d , for any dimension d??2, with arbitrary Hurst parameters H??1/d.     

Non-normal tracer diffusion from stirring by swimming microorganisms

The experimentally observed non-Gaussian form of passive tracer distributions in media stirred by active swimmers (Leptos et al., Phys. Rev. Lett. 103, 198103 (2009)) are analyzed in terms of continuous time random walks. The walks are characterized by a trapping time distribution ??(??) with long time behaviour ??(??) ?? ?? ^?1??? and a step size distribution p(??x) ?? (??x)^?2??? . The experimentally observed behaviour that ??x ²?? ?? t is obtained for a one-parameter family of exponents with ?? = 2??. However, the distribution function for this case is non-Gaussian and shows exponential tails. The shape of the distributions agrees rather well with the experimental observations from Leptos et al. and allows for the determination of the exponents.      

Third-harmonic generation in relative-phase-controlled two-color laser field

We experimentally demonstrate third-harmonic generation (THG) by intense femtosecond laser pulse at a central wavelength of ??800?nm superposed by its second harmonic in air. The third-harmonic signal shows a periodic modulation with a period of ??0.67?fs when the delay between fundamental and second-harmonic wave is continuously changed. The periodic modulation of THG can be attributed to the interference of third-harmonic signals generated from a direct THG channel (3??=??+??+??) and a four-wave mixing (FWM) channel (3??=2??+2?????). With high pump intensity, the fitting of the measured TH spectrum as a function of delay implies that the pump pulse undergoes a strong pulse splitting and self-phase modulation at the focus.     

Density-matrix renormalization group study of the spin-Peierls instability in the antiferromagnetic Heisenberg ladder

The columnar dimerized antiferromagnetic S?=?1/2 spin ladder is numerically studied by the density-matrix renormalization-group (DMRG) method. The elastic lattice with spin-phonon coupling ?? and lattice elastic force k is introduced into the system. Thus the S?=?1?/?2 Heisenberg spin chain is unstable towards dimerization (the spin-Peierls transition). However, the dimerization should be suppressed if the rung coupling J _?? is sufficiently large, and a Columnar dimer to Rung singlet phase transition takes place. After a self-consistent calculation of the dimerization, we determine the quantum phase diagram by numerically computing the singlet-triplet gap, the dimerization amplitude, the order parameters, the rung spin correlation and quantum entropies. Our results show that the phase boundary between the Columnar dimer phase and Rung singlet phase is approximately of the form J _?? ~ \hbox{$(\frac{k}{\alpha^{2}})^{-\frac{5}{4}}$} ( k ?? 2 ) ? 5 4.     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

单幅条纹图相位解调的小波分析方法

相位解调是条纹相位分析的关键问题.本文提出一种应用小波频率估计联合频率导数对变形条纹进行瞬时频率分析,从中提取参考基频,从而依靠单一变形条纹实现相位解调的方法.首先,理论上证明了当变形条纹瞬时频率空间导数等于零,该空间点的瞬时频率等于参考基频频率;其次,引入Gabor小波提取变形条纹的瞬时频率空间分布,利用变形条纹瞬时频率的空间导数分布识别提取参考基频,从而实现相位解调.利用该方法进行了三维形貌测量的实验,结果表明该方法在实现相位解调中效果良好.     

Mechanism of pion production in αp scattering at 1 GeV/nucleon

An analysis of the experimental data on one-pion and two-pion production in the p(??, ????)X reaction studied in a semi-exclusive experiment at an energy of E _?? = 4.2 GeV has been performed. The obtained results demonstrate that the inelastic ??-particle scattering on the proton at the energy of the experiment proceeds either through excitation and decay of the ?? resonance in the projectile ?? particle, or through excitation in the target proton of the Roper resonance, which decays into a nucleon and a pion, or a nucleon and a ?? meson??a system of two pions in the isospin I = 0, S-wave state.     

Glauber Dynamics for the Mean-Field Potts Model

We study Glauber dynamics for the mean-field (Curie-Weiss) Potts model with q??3 states and show that it undergoes a critical slowdown at an inverse-temperature ?? _s (q) strictly lower than the critical ?? _c (q) for uniqueness of the thermodynamic limit. The dynamical critical ?? _s (q) is the spinodal point marking the onset of metastability. We prove that when ??<?? _s (q) the mixing time is asymptotically C(??,q)nlogn and the dynamics exhibits the cutoff phenomena, a sharp transition in mixing, with a window of order n. At ??=?? _s (q) the dynamics no longer exhibits cutoff and its mixing obeys a power-law of order n ^4/3. For ??>?? _s (q) the mixing time is exponentially large in n. Furthermore, as ?????? _s with n, the mixing time interpolates smoothly from subcritical to critical behavior, with the latter reached at a scaling window of O(n ^?2/3) around ?? _s . These results form the first complete analysis of mixing around the critical dynamical temperature??including the critical power law??for a model with a first order phase transition.     

Determination of the energy measurement accuracy for charged particles by their range in nuclear photoemulsion

Ranges of monochromatic muons in nuclear photoemulsion, produced in the ?? ?? ??? _?? decay, are measured by the coordinate method to determine their energy by the range. The variance of the muon energymeasured by this method ?? _?? = (0.11±0.01) MeV, which corresponds to the accuracy of the determination of the charged particle energy by the range in nuclear emulsion ??3.1%. The developed technique will allow electron energy measurements in the 2??-decay (??3 MeV)with an accuracy of (5?C6)%.     

���Ѧ� Interaction Leading to N* and ��* Resonances

We have performed a calculation for the three-body ????? system by using the fixed center approximation to Faddeev equations, taking the interaction between ?? and ??, ?? and ??, and ?? and ?? from the chiral unitary approach. We find several peaks in the modulus squared of the three-body scattering amplitude, indicating the existence of resonances, which can be associated to known I?=?1/2, 3/2 and J ^P ?=?1/2⁺, 3/2⁺ and 5/2⁺ baryon states.     

Iterative two-step temporal phase-unwrapping applied to high sensitivity three-dimensional profilometry

Although temporal phase unwrapping method can be applied to solve some problems to measure an object with steep shapes, isolated parts or fringe undersampling in three-dimensional (3D) shape measurement, it needs to acquire and process a sequence of fringe pattern images which would take much time. Servin et al. proposed a 2-step temporal phase unwrapping algorithm, which only needs the 2 extreme phase-maps to achieve exactly the same results as standard temporal unwrapping method. But this method is only validated by computer simulation, shortage of experimental demonstration, its sensitivity coefficient G is limited, and it cannot be used when the G value is larger. We proposed an iterative two-step temporal phase-unwrapping algorithm which is an extension of Servin׳s method. First, add a fringe pattern with an intermediate sensitivity, project the fringe patterns of different sensitivity onto the tested object’s surface, and collect deformed fringe patterns with a CCD camera. Then we obtain the unwrapped phase with larger sensitivity coefficient G by cascading the sensitivity coefficients. And we derive the initial phase conditions of the 2-step temporal phase unwrapping algorithm. Finally, the experimental evaluation is conducted to prove the validity of the proposed method. The results are analyzed and compared with Servin׳s method. The experimental results show that the proposed method can achieve higher sensitivity and more accurate measurement, and it can overcome the main disadvantages encountered by Servin׳s method.     

Measurement of a transparent object by using an automated Talbot interferometer

It is reported that the first partial derivative of the phase distribution for a transparent object can be measured automatically by a personal computer with an image processor. The moire pattern is formed by superimposing the Fourier image distorted by the transparent object on the master grating. But if only the moire patterns are observed, it is not shown if the fringe order numbers increase or decrease. The fringe scanning method is presented to overcome the fringe order numbers. The four-step method is used to calculate the first partial derivative. By a simple experiment, the first partial derivative can be shown in the three dimensional graphics.     

Synthesis and Photophysics of Some Novel Imidazole Derivatives Used as Sensitive Fluorescent Chemisensors

Some novel imidazole derivatives were developed for highly sensitive chemisensors for transition metal ions. Since these compounds are sensitive to different external stimulations such as UV irradiation, heat, increasing pressure and changing the environmental pH causing colour change and so they can be used as a ??multi-way?? optically switchable material. A prominent fluorescence enhancement was found in the presence of transition metal ions such as Hg²⁺, Pb²⁺ and Cu²⁺ and this was suggested to result from the suppression of radiationless transitions from the n-??* state in the chemisensors. The existence of C-H??.O intramolecular hydrogen bonding in dmphnpi is confirmed by the Natural Bond Orbital analysis (NBO). The Mulliken, NBO charge analysis and the HOMO-LUMO energies were also calculated. The electric dipole moment (??) and the first-hyperpolarisability (??) value of the investigated molecules have been studied both experimentally and theoretically which reveal that the synthesized molecules have microscopic non-linear optical (NLO) behaviour with non-zero values. Ground and excited state DFT calculation were carried out in order to find out dipole moment and energy.     

New approach to analyzing and evaluating cross sections for partial photoneutron reactions

The presence of substantial systematic discrepancies between the results of different experiments devoted to determining cross sections for partial photoneutron reactions??first of all, (??, n), (??, 2n), and (??, 3n) reactions??is a strong motivation for studying the reliability and authenticity of these data and for developing methods for taking into account and removing the discrepancies in question. In order to solve the first problem, we introduce objective absolute criteria involving transitional photoneutron-multiplicity functions F ₁, F ₂, F ₃, ??; by definition, their values cannot exceed 1.0, 0.5, 0.33, ??, respectively. With the aim of solving the second problem, we propose a new experimental-theoretical approach. In this approach, reaction cross sections are evaluated by simultaneously employing experimental data on the cross section for the total photoneutron yield, ?? ^expt(??, xn) = ?? ^expt(??, n) + 2?? ^expt(??, 2n) + 3?? ^expt(??, 3n) + ??, which are free from drawbacks plaguing experimental methods for sorting neutrons in multiplicity, and the results obtained by calculating the functions F _theor ¹ , F _theor ² , F _theor ³ , ?? on the basis of the modern model of photonuclear reactions. The reliability and authenticity of data on the cross sections for (??, n), (??, 2n), and (??, 3n) partial reactions???? ^eval(??, in) = F _i ^theor ?? ^expt(??, xn)??were evaluated for the ⁹⁰Zr, ¹¹⁵In, ^{112,114,116,117,118,119,120,122,124}Sn, ¹⁵⁹Tb, and ¹⁹⁷Au nuclei.     

Isotope-selective ionization utilizing molecular alignment and non-resonant multiphoton ionization

We demonstrate laser nitrogen isotope separation, which is based on field-free alignment and angular-dependent ionization of ¹⁴N₂ and ¹⁵N₂ isotopologues. A linearly polarized short laser pulse (???~?795?nm, ?????~?60?fs) creates rotational wave packets in the isotopologues, which periodically revive with different revival times as a result of different moments of inertia. Another linearly polarized short laser pulse (???~?795?nm, ?????~?60?fs) ionizes one of the isotopologues selectively as a result of their different angular distributions. In the present experiments, the ion yield ratio R [=I(¹⁵N₂ ⁺)/I(¹⁴N₂ ⁺)] can be changed in the range from 0.85 to 1.22, depending on the time delay between the two laser pulses.     

Structural, thermal, and electrical properties of (100?x) ZrO2 (x) Bi2O3 compound

Composition (100?x) ZrO₂ (x) Bi₂O₃ (x?=?15, 20, 25) is synthesized by solid-state reaction method to study the effect of Bi₂O₃ doping on ZrO₂. The as-prepared samples are characterized by various methods. The X-ray diffraction pattern of all these samples exhibits three phases, namely, m-ZrO₂, ??_III-Bi₂O₃, and ??-Bi₂O₃. The differential thermal analysis curves do not show any phase transition/decomposition, which clearly indicated the stabilization of ??-Bi₂O₃ phase. The conductivity changes in all the samples are discussed in terms of different phase formations and their volume fractions. The microstructural and energy dispersive analyses indicate the presence of different phases. A maximum conductivity at high temperature (800?°C) was observed for the x?=?25 composition, i.e., ???=?4.21?×?10^?2 S/cm.     

The formation of correlated states and the increase in barrier transparency at a low particle energy in nonstationary systems with damping and fluctuations

We consider peculiarities in the formation of a coherent correlated state (CCS) of a particle in a periodically modulated harmonic oscillator with damping for various types of stochastic perturbation. It is shown that in the absence of stochastic perturbation, an optimal relation exists between the damping parameter (damping coefficient) and the modulation depth, for which the ??extrinsic?? characteristics of the oscillator (amplitudes of ??classical?? oscillation and the momentum of a particle) remain unchanged, while the correlation coefficient rapidly increases from |r| = 0 to |r|_max ?? 1; this corresponds to a completely correlated coherent state. Under nonoptimal conditions, the formation of the CCS with a simultaneous increase in is accompanied by damping or excitation of the oscillator. It is shown that for a certain relation between the damping coefficient and the modulation depth, the presence of a stochastic external force acting on the nonstationary oscillator does not prevent the formation of a CCS with |r|_max ?? 1. A fundamentally different effect is observed under a stochastic influence on the nonstationary frequency of the oscillator; this effect always limits the value of |r| at a level |r|_max < 1; a CCR cannot be formed with an unlimited increase in its intensity, and |r|_max ?? 0. The influence of the CCS formation on the averaged probability ??D?? of the tunnel effect (transparency of the potential barrier) is considered for a particle in an oscillator with damping both in the absence and in the presence of a stochastic force. It is shown using a specific example that complete clearing of the potential barrier and the increase in the barrier transparency from the initial value ??D _r=0?? = 10^?80 to ??D?? ?? 1 can occur over a comparatively short time interval in both these cases. These effects can be used to obtain highly efficient nuclear fusion at a low energy of interacting particles.     

Two-dimensional multiscale windowed Fourier transform based on two-dimensional wavelet transform for fringe pattern demodulation

A two-dimensional multiscale windowed Fourier transform (2D-MWFT), based on two-dimensional Gabor wavelet transform (2D-GWT), for the phase extraction from a spatial fringe pattern in fringe projection profilometry is presented. First, the instantaneous frequencies on x and y direction of the modulated fringe pattern are determined by 2D-GWT, and then the local stationary lengths are obtained. The 2D-MWFT with different two-dimensional Gaussian windows whose width is set according to the local stationary length is preformed for each section of the modulated fringe pattern to achieve multiresolution analysis and phase demodulation. Comparing the result of the phase demodulated by 2D-GWT and two-dimensional windowed Fourier transform (2D-WFT) with that by 2D-MWFT in a numerical simulation, we show that the 2D-MWFT method is superior to these methods, especially for the local non-stationary signal with low frequency. The theory and the results of a simulation and experiment are shown.