Direct EPR detection of transient and continuous wave signals at 2.5 GHz

Direct detection of free induction decays and electron spin echoes, and the recording of echo-detected EPR spectra and electron spin echo envelope modulation patterns at a microwave frequency of 2.5 GHz is demonstrated. This corresponds to the measurement of the transverse magnetization in the laboratory frame, rather than in the rotating frame as usually done by down-converting the signal (homodyne detection). An oscilloscope with a 6-GHz analog bandwidth, a sampling rate of 20 GigaSamples per second, and a trigger frequency of 5 GHz for the edge trigger and 750 MHz for the advanced trigger, is used in these experiments. For signal averaging a 3-GHz microwave clock divider has been developed to synchronize the oscilloscope with the frequency of the EPR signal. Moreover, direct detection of continuous wave EPR signals at 2.5 GHz is described.     

Digital detection and processing of multiple quadrature harmonics for EPR spectroscopy

A quadrature digital receiver and associated signal estimation procedure are reported for L-band electron paramagnetic resonance (EPR) spectroscopy. The approach provides simultaneous acquisition and joint processing of multiple harmonics in both in-phase and out-of-phase channels. The digital receiver, based on a high-speed dual-channel analog-to-digital converter, allows direct digital down-conversion with heterodyne processing using digital capture of the microwave reference signal. Thus, the receiver avoids noise and nonlinearity associated with analog mixers. Also, the architecture allows for low-Q anti-alias filtering and does not require the sampling frequency to be time-locked to the microwave reference. A noise model applicable for arbitrary contributions of oscillator phase noise is presented, and a corresponding maximum-likelihood estimator of unknown parameters is also reported. The signal processing is applicable for Lorentzian lineshape under nonsaturating conditions. The estimation is carried out using a convergent iterative algorithm capable of jointly processing the in-phase and out-of-phase data in the presence of phase noise and unknown microwave phase. Cramér-Rao bound analysis and simulation results demonstrate a significant reduction in linewidth estimation error using quadrature detection, for both low and high values of phase noise. EPR spectroscopic data are also reported for illustration.     

半空间球面波函数叠加法重构声源直接辐射声场

提出了基于半空间球面波函数叠加的声场重构方法,以重构含有限声阻抗边界半空间中声源直接辐射的声场。在半空间中多极子声源声压场的解析解的基础上,构造出以边界声阻抗为参量的半空间球面波函数的正交基;通过求逆获得半空间总声压解的基函数系数,同时也获得声源直接辐射声场即自由空间中的基函数系数,进而重构出声源直接辐射的声场。在边界声阻抗已知和边界声阻抗未知两种条件下,对该方法进行了仿真验证和参数分析,并在全消声室内进行了实验验证。结果表明,所提方法能重构出半空间中典型声源即球形声源和平面声源的直接辐射声场;该方法在边界声阻抗已知时的重构精度与稳定性高于在边界声阻抗未知时的情形。     

小波尺度参数对粒子场数字全息重建图像的影响

在小波尺度参数取值范围研究的基础上,探讨了小波尺度和粒子衍射波尺度的关系（即衍射波覆盖率）,深入研究了小波尺度对重建图像分辨率、景深、信噪比以及粒子图像灰度分布的影响.研究结果表明：当小波函数尺度能够覆盖颗粒衍射波的中心和二环区域时,重建图像的分辨率高、景深小和信噪比高,否则,重建图像质量将无法保证.但是,较大的小波尺度将使重建图像的灰度分布在光轴方向产生振荡,不利于颗粒的空间定位.     

小波尺度参数对粒子场数字全息重建图像的影响

在小波尺度参数取值范围研究的基础上,探讨了小波尺度和粒子衍射波尺度的关系(即衍射波覆盖率),深入研究了小波尺度对重建图像分辨率、景深、信噪比以及粒子图像灰度分布的影响.研究结果表明:当小波函数尺度能够覆盖颗粒衍射波的中心和二环区域时,重建图像的分辨率高、景深小和信噪比高,否则,重建图像质量将无法保证.但是,较大的小波尺度将使重建图像的灰度分布在光轴方向产生振荡,不利于颗粒的空间定位.     

Derivation of the Evans Wave Equation from the Lagrangian and <Emphasis Type="Italic">Action</Emphasis>: Origin of the Planck Constant in General Relativity

No Heading The Evans wave equation is derived from the appropriate Lagrangian and action, identifying the origin of the Planck constant in general relativity. The classical Fermat principle of least time, and the classical Hamilton principle of least action, are expressed in terms of a tetrad multiplied by a phase factor exp(iS/), where S is the action in general relativity. Wave (or quantum) mechanics emerges from these classical principles of general relativity for all matter and radiation fields, giving a unified theory of quantum mechanics based on differential geometry and general relativity. The phase factor exp(iS/) is an eigenfunction of the Evans wave equation and is the origin in general relativity and geometry of topological phase effects in physics, including the Aharonov-Bohm class of effects, the Berry phase, the Sagnac effect, related interferometric effects, and all physical optical effects through the Evans spin field B⁽³⁾ and the Stokes theorem in differential geometry. The Planck constant is thus identified as the least amount possible of action or angular momentum or spin in the universe. This is also the origin of the fundamental Evans spin field B⁽³⁾, which is always observed in any physical optical effect. It originates in torsion, spin and the second (or spin) Casimir invariant of the Einstein group. Mass originates in the first Casimir invariant of the Einstein group. These two invariants define any particle.