On the peak factor of stationary Gaussian processes

New simple approximate formulae are introduced for the average and the standard deviation of the peak factor of stationary Gaussian processes. The formulae take into account the bandwidth of the process and are based on the assumption that the extreme point process is Markovian. Also presented are simulation results for various spectral shapes (response of the linear oscillator to a white noise, bimodal spectrum, and ideal bandpass process). These suggest that none of the currently available bandwidth parameters can represent accurately the overall effect of the spectral shape on the peak factor. The approximate formulae, however, give reasonable estimates, if one excludes bimodal spectra with very light modal damping. The various definitions of the envelope process (essential in the Markov approximation) are reviewed and unified.     

Multiphoton intrapulse interference. IV. Ultrashort laser pulse spectral phase characterization and compensation

We introduce a noninterferometric single beam method to characterize and compensate the spectral phase of ultrashort femtosecond pulses accurately. The method uses a pulse shaper that scans calibrated phase functions to determine the unknown spectral phase of a pulse. The pulse shaper can then be used to synthesize arbitrary phase femtosecond pulses or it can introduce a compensating spectral phase to obtain transform-limited pulses. This method is ideally suited for the generation of tailored spectral phase functions required for coherent control experiments.     

多层膜体折射率弱不均匀度反演计算的近似模型及性能分析

实际应用中的薄膜或多或少存在体折射率不均匀缺陷,其准确表征对于镀膜工艺参数调校、低损耗薄膜设计与制备分析等具有影响。从Schr-der近似出发,推导了体折射率弱不均匀薄膜的膜系特征矩阵,通过特征矩阵法推广,建立了体折射率弱不均匀多层膜光谱特性计算的近似模型。利用基于有效介质理论的多层均匀膜近似方法,讨论了上述近似模型的有效性、计算精度和时间消耗特性。结果表明,上述模型矩阵计算中引入体折射不均匀度这一参数,为多层膜体折射率不均匀缺陷反演提供了一种有效的手段,为基于宽带光谱测量数据拟合的膜层缺陷数值反演应用奠定了基础。     

A parametric approach to spectral-spatial EPR imaging

Continuous wave electron paramagnetic resonance imaging for in vivo mapping of spin distribution and spectral shape requires rapid data acquisition. A spectral-spatial imaging technique is presented that provides an order of magnitude reduction in acquisition time, compared to iterative tomographic reprojection. The proposed approach assumes that spectral shapes in the sample are well-approximated by members from a parametric family of functions. A model is developed for the spectra measured with magnetic field modulation. Parameters defining the spin distribution and spectral shapes are then determined directly from the measurements using maximum a posteriori probability estimation. The approach does not suffer approximation error from limited sweep width of the main magnetic field and explicitly incorporates the variability in signal-to-noise ratio versus strength of magnetic field gradient. The processing technique is experimentally demonstrated on a one-dimensional phantom containing a nitroxide spin label with constant g-factor. Using an L-band EPR spectrometer, spectral shapes and spin distribution are accurately recovered from two projections and a spectral window which is comparable to the maximum linewidth of the sample.     

Evaluation of the absorbed dose of the discharge lamp radiation

The compliance of the spectral characteristics of a discharge lamp mounted in a light-tight metal housing with the Planck radiation law is noted. In a blackbody approximation for the radiation flux density of a discharge lamp, the absorbed radiation dose is expressed as an expansion in terms of spectral components. It is demonstrated that a photodiode can be used for evaluation of the absorbed radiation dose.     

Electron spectral density in a disordered system of hard sphere scatterers

The spectral density of an electron propagating in a disordered system of hard sphere scatterers is studied by use of a self-consistent approximation for the self-energy. The spectral density at fixed wavenumber is found to be a single-peaked function of energy. The approximation yields a sharp wavenumber-dependent band edge. For large wavenumbers the spectral density is well approximated by a Lorentzian, but for small wavenumbers it is dominated by a characteristic square root singularity at the band edge.     

Improvement of the parametric method of the theory of vibronic spectra of polyatomic molecules: Absorption spectra and the structure of butadiene, hexatriene, and octatetraene in the excited state

The structure of the excited states and absorption spectra of butadiene, hexatriene, and octatetraene are calculated by the parametric method of the theory of vibronic spectra using models of the first-and second-order approximations. It is shown that these molecular models adequately reflect the molecular structure and allow one to predict quantitatively the shape and fine vibrational structure of the absorption spectra. When passing to the second-order approximation, only two additional (angular) parameters are used. These parameters are transferable in the series of polyenes. Compared to the first-order approximation model, the second-order approximation model more accurately takes into account the angular deformations of polyenes upon their excitation and describes the intensity distribution in the vibrational spectrum, including weak lines. In addition, the calculations also quantitatively predict spectral variations in the molecular series. The parametric method is more efficient for modeling polyatomic molecules in the excited states and their vibrational spectra compared to other semiempirical and ab initio methods.     

The static approximation in the interpretation of collision broadening

The validity of the static approximation for analyses of spectral line profiles is considered. The Fourier transform of the profile of an isolated line is compared for representative cases with the unified theory, and it is shown that the simple static approximation can be used effectively to interpret low spectral resolution experiments. This result applies to the entire profile in the limit of high density, but it also applies at low density if the instrumental line width is sufficiently large. Furthermore, in the absence of turning points in the interatomic potential, the unified and static theories produce almost identical line-wing profiles. Easily evaluated criteria are provided to guide application of the straightforward static theory to the interpretation of interatomic potentials.     

基于多光谱成像的光谱反射率重建

一些对颜色重现要求较高的应用领域需要获取目标表面上各点的光谱反射率。大多数天然物质表面的光谱反射率曲线比较平滑,可视为几个基向量的线性组合。基于这一原理的多光谱成像技术可以准确快速地重建目标表面的光谱反射率。通过对NCS色卡进行主成分分析,得出了彩色印刷品光谱反射率的基向量。建立了一个多光谱成像系统,用以比较基向量个数不同对反射率重建效果的影响。     

On the modulation equations and stability of periodic generalized Korteweg–de Vries waves via Bloch decompositions

In this paper, we consider the relation between Evans-function-based approaches to the stability of periodic travelling waves and other theories based on long-wavelength asymptotics together with Bloch wave expansions. In previous work it was shown by rigorous Evans function calculations that the formal slow modulation approximation resulting in the linearized Whitham averaged system accurately describes the spectral stability to long-wavelength perturbations. To clarify the connection between Bloch-wave-based expansions and Evans-function-based approaches, we reproduce this result without reference to the Evans function by using direct Bloch expansion methods and spectral perturbation analysis. One of the novelties of this approach is that we are able to calculate the relevant Bloch waves explicitly for arbitrary finite-amplitude solutions. Furthermore, this approach has the advantage of being applicable in the more general multi-periodic setting where no conveniently computable Evans function has yet been devised.     

A spectral fictitious domain method with internal forcing for solving elliptic PDEs

A fictitious domain method is presented for solving elliptic partial differential equations using Galerkin spectral approximation. The fictitious domain approach consists in immersing the original domain into a larger and geometrically simpler one in order to avoid the use of boundary fitted or unstructured meshes. In the present study, boundary constraints are enforced using Lagrange multipliers and the novel aspect is that the Lagrange multipliers are associated with smooth forcing functions, compactly supported inside the fictitious domain. This allows the accuracy of the spectral method to be preserved, unlike the classical discrete Lagrange multipliers method, in which the forcing is defined on the boundaries. In order to have a robust and efficient method, equations for the Lagrange multipliers are solved directly with an influence matrix technique. Using a Fourier–Chebyshev approximation, the high-order accuracy of the method is demonstrated on one- and two-dimensional elliptic problems of second- and fourth-order. The principle of the method is general and can be applied to solve elliptic problems using any high order variational approximation.     

Luttinger liquids with boundaries: Power-laws and energy scales

We present a study of the one-particle spectral properties for a variety of models of Luttinger liquids with open boundaries. We first consider the Tomonaga-Luttinger model using bosonization. For weak interactions the boundary exponent of the power-law suppression of the spectral weight close to the chemical potential is dominated by a term linear in the interaction. This motivates us to study the spectral properties also within the Hartree-Fock approximation. It already gives power-law behavior and qualitative agreement with the exact spectral function. For the lattice model of spinless fermions and the Hubbard model we present numerically exact results obtained using the density-matrix renormalization-group algorithm. We show that many aspects of the behavior of the spectral function close to the boundary can again be understood within the Hartree-Fock approximation. For the repulsive Hubbard model with interaction U the spectral weight is enhanced in a large energy range around the chemical potential. At smaller energies a power-law suppression, as predicted by bosonization, sets in. We present an analytical discussion of the crossover and show that for small U it occurs at energies exponentially (in -1/U) close to the chemical potential, i.e. that bosonization only holds on exponentially small energy scales. We show that such a crossover can also be found in other models. Received 8 February 2000 and Received in final form 25 April 2000     

Ambiguities in the implementation of the impulse approximation for the response of many-fermion systems

Within the impulse approximation, the response of a many-body system at large momentum transfer can be directly related to ground state properties. Although the physics assumptions underlying impulse approximation are well defined, their implementation involves ambiguities that may cause significant differences in the calculated responses. We show that, while minimal use of the impulse approximation assumptions naturally leads to write the response in terms of the spectral function, the alternative definition in terms of the momentum distribution involves a more extended use of the same assumptions.     

农产品品质光谱成像的空间预测规律

由于受到化学检测手段限制,无法获取光谱图像中的农产品品质在各像素位置处的参考值,因此无法直接验证基于光谱图像得到的农产品品质空间预测结果。为探索基于光谱图像的农产品空间品质检测规律,本文采用计算机生成已知空间品质样本,并分别以固定曝光和变曝光方式采集不同灰度等级标准板的光谱图像。定量分析采集系统误差,借助样本区域光谱与区域指标之间的全波段偏最小二乘（ALL-PLS）和遗传特征波长偏最小二乘（GA-PLS）预测函数,研究出区域指标预测准确时样本空间品质指标的预测精度规律,建立光谱成像空间预测准确度模型。实验结果表明：变曝光方式下的数据采集可以提高光谱图像信噪比,在波段两侧极限处尤为明显;应用区域品质数据预测空间品质分布,空间预测误差主要受光谱图像采集噪声影响：即使区域预测准确,空间预测可能已完全失真。通过衡量数据采集系统误差,可以间接评价农产品品质空间预测的准确度。只有在数据采集系统误差在允许范围内时,光谱成像技术才可准确预测农产品品质的空间分布。     

Microscopic mechanism of stability in yttria-doped zirconia

The relaxed configurations of yttria-stabilised zirconia (YSZ) between 3 and 10 mol % of Y₂O₃ were modeled using the pseudopotential technique. In the displacive limit of a double-well potential model, the vibrational mode corresponding to the soft phonon in pure c-ZrO₂ was calculated for each Y₂O₃ composition. These anharmonic vibrations, associated with the stabilization of YSZ, were investigated within the self-consistent phonon approximation making obtainable the fine structure in spectral density. In studying the phonon dynamics, we use the displacement probability density, which can quantify very accurately the transition temperature necessary for stabilizing the YSZ cubic phase.     

Propagation of a few-cycle laser pulse in a V-type three-level system

Propagation of a few-cycle laser pulse in a V-type three-level system (fine structure levels of rubidium) is investigated numerically. The full three-level Maxwell-Bloch equations without the rotating wave approximation and the standing slowly varying envelope approximation are solved by using a finite-difference time-domain method. It is shown that, when the usual unequal oscillator strengths are considered, self-induced transparency cannot be recovered and higher spectral components can be produced even for small-area pulses.     

应用"Maple"数学软件来推求同科电子光谱项

推求光谱项对于研究原子的结构和光谱十分重要.怎样确定复杂的多电子原子体系的光谱项是原子物理学研究的重要内容之一.受泡利原理的限制,含有多个同科电子的原子电子组态的光谱项的推求一直是原子物理学,结构化学等学科研究的难点,人工方法推求其谱项困难很大.本文根据同科电子在L-S耦合下量子数取值的组合特点,推出了总轨道磁量子数为ML时出现次数的计算公式,结合Maple数学软件,给出了一种推求同科电子光谱项的新方法.根据该公式,使用Maple数学软件,能快速、准确的求得同科电子在L-S耦合下的光谱项.文中我们举例应用该方法,具体推求了同科电子体系d3,f7电子组态在L-S耦合下的光谱项,所得结果与文献给出的一致.     

Spectral calibration in spectral domain optical coherence tomography

A novel spectral calibration method is developed for spectral domain optical coherence tomography system. The method is based on two measurements of interference spectra from two reference mirror positions. It removes the influence of dispersion mismatch, and hence accurately determines the spectral distribution on the line-scan charge-coupled device (CCD) for sequent precise interpolation. High quality imaging can be realized with this method. Elimination of the degradation effect caused by dispersion mismatch is verified experimentally, and improved two-dimensional (2D) imaging of fresh orange pulp based on the proposed spectral calibration method is demonstrated.