Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions' Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

Angular spectrum approach to electromagnetic wave propagation in inhomogeneous media

The angular spectrum representation of the electromagnetic wave field is employed to solve the wave propagation in a weakly inhomogeneous medium. Taking the two-dimensional spatial Fourier transform of the radiation field as well as of the dielectric constant, the angular amplitude is shown to satisfy an integro-differential equation. A similar equation is also applicable for the propagation of radiation in a non-linear medium. This integro-differential equation is solved for two specific cases of interest, namely that of a stratified medium and of a square-law medium.     

Complex order fractional Fourier transforms and their use in diffraction theory. Application to optical resonators

The electromagnetic field transfer by diffraction from a spherical emitter to a spherical receiver is expressed by a fractional Fourier transform whose order depends on the distance between the emitter and the receiver and their curvature radii. Special attention is paid to complex order transforms: scaled variables and scaled field amplitudes are defined by complying with mathematical consistency. For a given distance of observation, a simple geometrical condition is set up to determine whether the corresponding transform order is a real or a complex number. The result is applied to check the stability of optical resonators.     

Extension of the angular spectrum method to calculate pressure from a spherically curved acoustic source

The angular spectrum method is an accurate and computationally efficient method for modeling acoustic wave propagation. The use of the typical 2D fast Fourier transform algorithm makes this a fast technique but it requires that the source pressure (or velocity) be specified on a plane. Here the angular spectrum method is extended to calculate pressure from a spherical transducer-as used extensively in applications such as magnetic resonance-guided focused ultrasound surgery-to a plane. The approach, called the Ring-Bessel technique, decomposes the curved source into circular rings of increasing radii, each ring a different distance from the intermediate plane, and calculates the angular spectrum of each ring using a Fourier series. Each angular spectrum is then propagated to the intermediate plane where all the propagated angular spectra are summed to obtain the pressure on the plane; subsequent plane-to-plane propagation can be achieved using the traditional angular spectrum method. Since the Ring-Bessel calculations are carried out in the frequency domain, it reduces calculation times by a factor of approximately 24 compared to the Rayleigh-Sommerfeld method and about 82 compared to the Field II technique, while maintaining accuracies of better than 96% as judged by those methods for cases of both solid and phased-array transducers.     

Contribution from cosmological scalar perturbations to the angular velocity spectrum of extragalactic sources

The possibility of the influence of adiabatic scalar perturbations on the angular velocity spectrum of extragalactic sources is considered. The multipole expansion coefficients of the angular velocity field in terms of vector spherical harmonics are calculated. We show that there is no contribution from adiabatic perturbations to the angular spectrum for a spatially flat Universe at the dusty stage, while there is a contribution only to the electric multiple coefficients at the stage of ??-term domination. The cases of long-wavelength and short-wavelength perturbations are considered separately. The relationship between the multipole angular velocity spectrum and the primordial scalar perturbation spectrum is discussed.     

Frequency converter based on a field electron emitter

An electron field emitter based on a carbon nanotube is considered as a frequency converter of the voltage applied to its electrodes. This property of the emitter relates to the nonlinear form of the current-voltage characteristic described by the classical Fowler-Nordheim expression. Calculations show that the number of higher harmonics in the spectrum of the emission current increases upon a decrease in the applied voltage and with increasing relative amplitude of the ac signal.     

Field-based angle-resolved light-scattering study of single live cells

We perform field-based angle-resolved light-scattering measurements from single live cells. We use a laser interferometer to acquire phase and amplitude images of cells at the image plane. The angular scattering spectrum is calculated from the Fourier transform of the field transmitted through the cells. A concurrent 3D refractive index distribution of the same cells is measured using tomographic phase microscopy. By measuring transient increases in light scattering by single cells during exposure to acetic acid, we correlate the scattering properties of single cells with their refractive index distributions and show that results are in good agreement with a model based on the Born approximation.     

Holographic registration of the amplitude of oscillation of a surface diffusely scattering light

By the example of a time-averaged recording of the hologram of a focused image of a surface executing simple harmonic oscillation in its own plane, and diffusely scattering light, an analysis in the Fresnel approximation is made of the formation of an interference pattern for determining the amplitude of the oscillation. Theoretically and experimentally, it is shown that in the case of illuminating the scattering surface with coherent diffusely scattered radiation, the interference pattern is localized in the plane of formation of the Fourier image of the surface scattering the light. In the process, the size of the field in the Fourier plane is magnified, due to the amplification of the angular spectrum of the scattered waves. In monitoring the amplitude of the oscillation, this permits the sensitivity threshold to be lowered.V. V. Kuibyshev State University, Tomsk. Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 11, pp. 30–34, November, 1992.     

Angular spectrum representation of the electromagnetic multipole fields, and their reflection at a perfect conductor

Angular spectrum representations are derived for electric and magnetic multipole fields of arbitrary order. The result involves generalized spherical harmonics and generalized vector spherical harmonics, and the representations are in the form of integrals over the k_∥-plane. The representations are especially useful for the study of reflection and transmission of multipole radiation by a plane interface. As an example, we have considered the reflection at a perfect conductor. The reflected field of a multipole field could be expressed in the form of an angular spectrum with a very simple relation to the angular spectrum of the source field. The radiation pattern of a multipole near the perfect conductor is obtained with the method of stationary phase. We also introduce a method for determining the mirror image of the source of an arbitrary multipole.     

Raster method for recording optical wave fields

We propose a new method for recording the wave field. The method is based on that the angular spectrum of the field is modulated using an amplitude mask. It is shown that the new method ensures high spatial and angular resolutions. An optical scheme for implementing the method and an algorithm for reconstructing the wave-field phase from the measurement data are developed. Computer simulation of the experiment for recording the wave field on the basis of the proposed method is performed.     

Three dimensional polarization control in 4Pi microscopy

An approach to obtain a diffraction-limited spherical focal spot with controllable three dimensional state of polarization in 4Pi microscopy is proposed. By combining the angular radiation pattern of a dipole antenna and vectorial diffraction method, input field at the pupil plane for creating a spherical focal spot with arbitrary three dimensionally oriented linear polarization is found analytically by solving the inverse problem. A diffraction-limited spherical spot with arbitrary three dimensional elliptical polarization can be realized by introducing a second dipole antenna oriented in the orthogonal plane with appropriate amplitude and phase differences.     

A radial propagator for axisymmetric pressure fields

The concept of a propagator is central to the angular spectrum formulation of diffraction theory, which expresses the pressure field diffracted by a two-dimensional aperture as a superposition of a continuum of plane waves. In the conventional form, an exponential term, known as a propagator, is multiplied by the wavenumber spectrum obtained from a two-dimensional spatial Fourier transform of the aperture boundary condition, to obtain the wavenumber spectrum in a plane parallel to the boundary, offset by some distance specified in the propagator. By repeated use of this propagator and Fourier inversion, it is possible to completely construct the homogeneous part of the pressure field in the positive half-space beyond the planar boundary containing the aperture. Drawing upon preceding work relating the boundary condition to the axial pressure [Pees, J. Acoust. Soc. Am. 127(3), 1381-1390 (2010)], it is shown in this article that when the aperture is axially symmetric, an alternative type of propagator can be derived that propagates an axial wavenumber spectrum away from the axis of the aperture. Use of this radial propagator can be computationally advantageous since it allows for field construction using one-dimensional Fourier transforms instead of Hankel transforms or two-dimensional Fourier transforms.     

重建彩色数字全息图时不同色光物光场的准确重叠研究

将数字全息检测物体表面视为散射面,球面波为参考波,使用角谱重建算法对不同波长照明情况下物平面光波场重建位置进行研究.结果表明,不考虑图像的物理意义时,衍射的一次傅里叶变换重建像中心与物光场频谱的中心相对应,以一次傅里叶变换重建像为参考,可以较好地确定物光场频谱位置,按照可变放大率的角谱重建算法实现不同色光重建场的准确重叠.     

Lensless imaging of an arbitrary object

A new class of imaging systems that do not require the use of lenses or similar optical devices is introduced and theoretically investigated. In particular, it is demonstrated that, if an arbitrary plane object is illuminated by an appropriate spherical wave front (generated from a monochromatic point source), then a magnified image of the object intensity distribution can be observed in any transversal plane along the light-propagation direction within the far-field (Fraunhofer) diffraction region. The phenomenon is based on the fact that, under certain conditions, the spherical wave front can modify the energy's angular spectrum of the field distribution in the object plane such that this spectrum replicates the spatial intensity distribution of the object.     

氧碘化学激光器的红光发射体CuCl2

通过测量、分析CuCl_2的激光诱导荧光并与氧碘化学激光器光腔中红光辐射的傅里叶变换光谱比较,认为红光辐射体是CuCl_2。     

Wave field synthesis of moving virtual sound sources with complex radiation properties

An approach to the synthesis of moving virtual sound sources with complex radiation properties in wave field synthesis is presented. The approach exploits the fact that any stationary sound source of finite spatial extent radiates spherical waves at sufficient distance. The angular dependency of the radiation properties of the source under consideration is reflected by the amplitude and phase distribution on the spherical wave fronts. The sound field emitted by a uniformly moving monopole source is derived and the far-field radiation properties of the complex virtual source under consideration are incorporated in order to derive a closed-form expression for the loudspeaker driving signal. The results are illustrated via numerical simulations of the synthesis of the sound field of a sample moving complex virtual source.     

显微数字全息中物光波前重建方法研究和比较

根据全息理论和线性系统理论,采用离轴无透镜傅里叶变换全息记录光路,对利用菲涅耳近似法、基于瑞利—索末菲衍射积分的卷积法以及角谱理论方法数值重建全息图进行了比较研究,并做了计算机模拟验证.结果表明：菲涅耳近似法和角谱方法重建像质比较好,且菲涅耳方法重建速度快;在记录距离极小的情况下,尽管记录距离不满足通常的菲涅耳近似条件,菲涅耳近似公式仍然成立;自由空间脉冲响应的快速傅里叶变换的性质与距离有关,由卷积方法得到的再现像只在某一特定距离下比较理想;对于极小物场、大孔径显微数字全息来说,菲涅耳近似重建方法是较为有效的方法.     

Reconstruction of the first-derivative EPR spectrum from multiple harmonics of the field-modulated continuous wave signal

Selection of the amplitude of magnetic field modulation for continuous wave electron paramagnetic resonance (EPR) often is a trade-off between sensitivity and resolution. Increasing the modulation amplitude improves the signal-to-noise ratio, S/N, at the expense of broadening the signal. Combining information from multiple harmonics of the field-modulated signal is proposed as a method to obtain the first derivative spectrum with minimal broadening and improved signal-to-noise. The harmonics are obtained by digital phase-sensitive detection of the signal at the modulation frequency and its integer multiples. Reconstruction of the first-derivative EPR line is done in the Fourier conjugate domain where each harmonic can be represented as the product of the Fourier transform of the 1st derivative signal with an analytical function. The analytical function for each harmonic can be viewed as a filter. The Fourier transform of the 1st derivative spectrum can be calculated from all available harmonics by solving an optimization problem with the goal of maximizing the S/N. Inverse Fourier transformation of the result produces the 1st derivative EPR line in the magnetic field domain. The use of modulation amplitude greater than linewidth improves the S/N, but does not broaden the reconstructed spectrum. The method works for an arbitrary EPR line shape, but is limited to the case when magnetization instantaneously follows the modulation field, which is known as the adiabatic approximation.     

Re-explanation of Weyl Quantization Scheme via Weyl Ordering Approach

We re-explain the Weyl quantization scheme by virtue of the technique of integration within Weyl ordered product of operators, i.e., the Weyl correspondence rule can be reconstructed by classical functions＇ Fourier transformation followed by an inverse Fourier transformation within Weyl ordering of operators. As an application of this reconstruction, we derive the quantum operator coresponding to the angular spectrum amplitude of a spherical wave.     

Limitations of superoscillation filters in microscopy applications

The idea of superresolving pupil filters comes from the concept of superoscillations that may occur in regions of a band-limited signal with small amplitude having oscillations faster than the fastest Fourier component of the signal. In optical microscopy, superresolution can be achieved by appropriate design of pupil functions where the angular aperture determines the ultimate focal spot smaller than the Abbe diffraction limit outside the evanescent field region. The angular aperture cannot be increased indefinitely and the huge sidelobes cannot be avoided that are present in superresolving filters. The limitations of using such kind of filters in microscopy applications are discussed through computational examples.