Pseudomodulation: A computer-based strategy for resolution enhancement

Pseudomodulation is defined as computer simulation of the effect on a magnetic resonance spectrum that would be obtained if a sinusoidal field modulation were applied followed by phase-sensitive detection at the fundamental frequency or at one of its harmonics. Since it is done by computer, it is not necessary that it actually be possible to modulate the field. The algorithm is developed here for EPR spectroscopy, but can be applied to any function or to any digitized signal, including an NMR signal, and there can be more than one independent parameter, as, for example, an MR image or a 2D NMR spectrum where there are two. Pseudomodulation transforms and filters a digitized spectrum. Subtraction or addition of various amounts of the even harmonics of the digitized spectral data from or to the original spectrum results in resolution enhancement. Other resolution-enhancement algorithms that use pseudomodulation are also presented. Resolution enhancement by pseudomodulation is tested on simulated spectra to which computer-generated noise has been added and is applied to the EPR S-band spectrum of the blue copper protein azurin.     

Microwave frequency modulation in CW EPR at W-band using a loop-gap resonator

Loop-gap resonator (LGR) technology has been extended to W-band (94GHz). One output of a multiarm Q-band (35GHz) EPR bridge was translated to W-band for sample irradiation by mixing with 59 GHz; similarly, the EPR signal was translated back to Q-band for detection. A cavity resonant in the cylindrical TE011 mode suitable for use with 100 kHz field modulation has also been developed. Results using microwave frequency modulation (FM) at 50 kHz as an alternative to magnetic field modulation are described. FM was accomplished by modulating a varactor coupled to the 59 GHz oscillator. A spin-label study of sensitivity was performed under conditions of overmodulation and gamma2H1(2)T1T2<1. EPR spectra were obtained, both absorption and dispersion, by lock-in detection at the fundamental modulation frequency (50 kHz), and also at the second and third harmonics (100 and 150 kHz). Source noise was deleterious in first harmonic spectra, but was very low in second and third harmonic spectra. First harmonic microwave FM was transferred to microwave modulation at second and third harmonics by the spins, thus satisfying the "transfer of modulation" principle. The loaded Q-value of the LGR with sample was 90 (i.e., a bandwidth between 3 dB points of about 1 GHz), the resonator efficiency parameter was calculated to be 9.3 G at one W incident power, and the frequency deviation was 11.3 MHz p-p, which is equivalent to a field modulation amplitude of 4 G. W-band EPR using an LGR is a favorable configuration for microwave FM experiments.     

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.     

Using of Digital Demodulation of Multiharmonic Overmodulated EPR Signals to Improve EPR Oximetry Reliability

Overmodulation of electron paramagnetic resonance (EPR) lines is routinely used in EPR oximetry in order to increase the signal-to-noise ratio and thus to improve the accuracy with which the line width of a spin probe can be measured. For a known probe type, the line width is easily translated into the oxygen partial pressure. A standard EPR spectrometer uses the analog phase-sensitive detection (PSD) to demodulate the EPR signal. PSD imposes the restriction that only one spectrum is measured at a time, which is normally the first-harmonic EPR line. Information about EPR signals centered at the other harmonics of the modulation frequency is irreversibly destroyed by PSD. The question is raised whether this information can be utilized for EPR oximetry, for overmodulation enhances the second- and the other harmonic spectra, so that they approach the first-harmonic spectrum in intensity. To find an answer, numerical simulation and experimental measurements have been conducted. The experiment required modification of the detection scheme, so that all EPR-related information in the overmodulated signal is preserved. This permits measuring of the multiharmonic EPR spectrum, which when fitted to a set of the corresponding theoretical lines produces more accurate results in comparison with the standard overmodulation method.     

Formulation of Zeeman modulation as a signal filter

The Bloch equation containing a Zeeman modulation field is solved analytically by treating the Zeeman modulation frequency as a perturbation. The absorption and dispersion signals at both 0 degrees and 90 degrees modulation phase are obtained. The solutions are valid to first order in the modulation frequency, but are otherwise valid for any value of modulation amplitude or microwave amplitude. A first order treatment of modulation frequency is shown to be a valid approximation over a wide range of typical experimental EPR conditions. The solutions derived from the Bloch equation suggest that the effect of over-modulation on first and second harmonic EPR spectra can be formulated as a mathematical filter that smoothes and broadens the under-modulated signal. The only adjustable filter parameter is a width that is equivalent to the applied peak-to-peak modulation amplitude. The true spin-spin and spin-lattice relaxation rates are completely determined from the under-modulated spectrum. The filters derived from the analytic solutions of the Bloch equation in the linear limit of modulation frequency are tested against numerical solutions of the Bloch equation that are valid for any modulation frequency to show their applicability. The filters are further tested using experimental EPR spectra. Experimental under-modulated spectra are mathematically filtered and compared with the experimental over-modulated spectra. The application of modulation filters to STEPR spectra is explored and limitations are discussed.     

The continuous wave electron paramagnetic resonance experiment revisited

When the modulation frequency used in continuous wave electron paramagnetic resonance (cw EPR) spectroscopy exceeds the linewidth, modulation sidebands appear in the spectrum. It is shown theoretically and experimentally that these sidebands are actually multiple photon transitions, sigma(+)+kxpi, where one microwave (mw) sigma(+) photon is absorbed from the mw radiation field and an arbitrary number k of radio frequency (rf) pi photons are absorbed from or emitted to the modulation rf field. Furthermore, it is demonstrated that both the derivative shape of the lines in standard cw EPR spectra and the distortions due to overmodulation are caused by the unresolved sideband pattern of these lines. The single-photon transition does not even give a contribution to the first-harmonic cw EPR signal. Multiple photon transitions are described semiclassically in a toggling frame and their existence is proven using second quantization. With the toggling frame approach and perturbation theory an effective Hamiltonian for an arbitrary sideband transition is derived. Based on the effective Hamiltonians an expression for the steady-state density operator in the singly rotating frame is derived, completely describing all sidebands in all modulation frequency harmonics of the cw EPR signal. The relative intensities of the sidebands are found to depend in a very sensitive way on the actual rf amplitude and the saturation of single sidebands is shown to depend strongly on the effective field amplitude of the multiple photon transitions. By comparison with the analogous solutions for frequency-modulation EPR it is shown that the field-modulation and the frequency-modulation technique are not equivalent. The experimental data fully verify the theoretical predictions with respect to intensities and lineshapes.     

Detection of undistorted continuous wave (CW) electron paramagnetic resonance (EPR) spectra with non-adiabatic rapid sweep (NARS) of the magnetic field

A continuous wave (CW) electron paramagnetic resonance (EPR) spectrum is typically displayed as the first harmonic response to the application of 100 kHz magnetic field modulation, which is used to enhance sensitivity by reducing the level of 1/f noise. However, magnetic field modulation of any amplitude causes spectral broadening and sacrifices EPR spectral intensity by at least a factor of two. In the work presented here, a CW rapid-scan spectroscopic technique that avoids these compromises and also provides a means of avoiding 1/f noise is developed. This technique, termed non-adiabatic rapid sweep (NARS) EPR, consists of repetitively sweeping the polarizing magnetic field in a linear manner over a spectral fragment with a small coil at a repetition rate that is sufficiently high that receiver noise, microwave phase noise, and environmental microphonics, each of which has 1/f characteristics, are overcome. Nevertheless, the rate of sweep is sufficiently slow that adiabatic responses are avoided and the spin system is always close to thermal equilibrium. The repetitively acquired spectra from the spectral fragment are averaged. Under these conditions, undistorted pure absorption spectra are obtained without broadening or loss of signal intensity. A digital filter such as a moving average is applied to remove high frequency noise, which is approximately equivalent in bandwidth to use of an integrating time constant in conventional field modulation with lock-in detection. Nitroxide spectra at L- and X-band are presented.     

一维多原子分子离子与超短激光场作用产生的高次谐波

从经典方程出发，采用克兰克-尼科尔森中心差分法对一维多原子分子离子与一维超短强激光场相互作用产生的高次谐波进行了数值模拟计算，发现激光场的初始相位对高次谐波辐射谱有明显影响；通过进一步研究，给出了初步解释。从而，可以通过调节适当的激光初始相位和选取适当的系统来改善高次谐波的相位匹配，产生清晰的高次谐波辐射谱。     

相对论激光在Maxwell分布等离子体中产生的高次谐波

 研究了强激光与具有初始速度分布的等离子体作用产生的高次谐波。结果表明，对于Maxwell速度分布的等离子体，由于电子初始时刻的无规则热运动，在一定程度上抹平了辐射功率在谐波谱上的分布，使得高次谐波的辐射增强，低次谐波的辐射有所减弱，有利于高次谐波的产生。     

渐变折射率传感气室中干涉噪声的数值模拟与分析

在直接红外吸收式光纤气体传感器中，由渐变折射率（Graduated Refractive Index，GRIN）棒透镜构成的微型传感气室有着广泛的应用。分析了GRIN气室中的干涉噪声信号和甲烷信号，并利用MATLAB对干涉噪声信号的幅值与分布反馈式半导体激光器（DFBLD）的频率调制幅度之间的关系以及干涉噪声对气体检测灵敏度的影响进行了数值模拟与分析。当前谐波检测技术是气体检测的一种非常重要的技术，这种技术需要检测气体吸收信号的一次、二次或更高次谐波。而GRIN气室的二次干涉噪声对浓度信号有很大的影响，研究发现当频率调制幅度达到某些特定频率值时，二次干涉噪声信号的幅值变为零，通过调整气室参数和DFBLD的调制频率可以削减干涉噪声的影响从而提高谐波检测技术的检测灵敏度。     

Spectral modulation of higher harmonic spontaneous emission from an optical klystron

Higher harmonics of spontaneous emission from an optical klystron have been observed. The modulation factor of the spontaneous emission spectrum for the higher harmonics can be described by considering the observation system. When the dispersive gap of the optical klystron was fixed, the microstructure interval of the spontaneous emission spectrum at a certain resonant wavelength became narrower as the order of the higher harmonic became larger. Some unique characteristics of the higher harmonics have been clarified, and these studies are likely to contribute to the development of free‐electron lasers using higher harmonics of an optical klystron in the shorter‐wavelengths region.     

Phase-Drift-Suppression Method Using Higher Order Harmonics in Heterodyne Detection

The theory of phase-drift-suppression method and simulated results using sinusoidal and triangular phase modulation have been described. The computed signal intensity is defined as the square root of the sum of squares of each harmonic intensity in the heterodyne beat signal. The relations between the computed signal intensity, its relative standard deviation, and the modulation indexes are shown through simulations. Modulation indexes that suppress the phase drifts were obtained, including up to the eighth harmonic. The stability of the beat signal in sinusoidal and triangular phase modulation was confirmed to increase 245 times using harmonics from the fundamental to the fourth order and a modulation index of 2.8 rad, and to increase 490 times using harmonics from the fundamental to the second order and 2.9 rad.     

Dynamics of the critical surface in high-intensity laser-solid interactions: modulation of the XUV harmonic spectra

The generation of harmonics from the interaction of an intense (I>or=10(18) W cm(-2)) laser with a solid surface is investigated. Modulation of the harmonic emission spectrum with a periodicity of 2 to 4 harmonics is observed at higher laser intensities. A similar modulation is predicted by a particle-in-cell simulation. The modulation is shown to be caused by the higher modes of oscillation of the critical surface during the interaction. As a result, the dynamics of the critical surface can be inferred from the shape of the harmonic spectrum.     

光调制技术用于提高光谱法舌诊的测量信噪比

为了解决光谱采集受环境光干扰严重的问题,首次将光调制技术用于提高光谱法舌诊测量的信噪比。系统采用调制盘对参考光信号强度进行调制,运用此装置采集同一被测体在分别叠加绿色、紫色、红色激光以及自然环境光干扰情况下的反射光谱,对采集来的数据运用离散傅里叶变换进行解调,提取最大谐波分量,然后对提取的最大谐波分量进行归一化,绘制解调后的光谱曲线,通过比较发现,不同干扰情况下所测同一被测体经过调制解调后的反射光谱曲线走向基本一致,结果表明光调制技术能够去除舌体反射光谱采集中环境杂散光的干扰,为高信噪比舌诊光谱数据采集提供了一种新途径。     

调控空间非均匀啁啾场获得孤立阿秒脉冲

通过调节二阶啁啾参数和空间非均匀效应对高次谐波光谱进行了优化.结果表明：在长脉宽负向啁啾和负向非均匀效应组合下,谐波光谱截止能量和强度得到最佳增大,并获得X射线范围内的光谱连续区.最后,通过叠加光谱连续区上的部分谐波可获得一个脉宽仅为23 as的孤立脉冲.     

On possibility of using the lowest odd harmonics of the phase modulation frequency in the output signal of the fiber-optic ring interferometer for detection of the sagnac effect

The possibility of using the lowest harmonics of the phase modulation frequency in the output signal of the fiber-optic ring interferometer (FRI) for detection of the FRI rotation angular velocity is considered. It is shown that the use of the third harmonic of the phase modulation frequency is optimal, since, in this case, the effect of insignificant admixture of the second harmonic of the phase modulation frequency on the FRI baseline shift can be completely eliminated. When processing the signal using the first or the fifth harmonic of the phase modulation frequency, it is possible to compensate for the FRI baseline shift because of its weak dependence on the phase modulation amplitude. Upon processing of the FRI output signal using higher odd harmonics of the phase modulation frequency, the signal-to-noise ratio noticeably decreases.     

Measurements of absolute values of electrooptic coefficients in a ferroelectric liquid crystal

Weak external electric field E causes two effects in chiral smectic liquid crystals: linear change of the optic axis direction and modification of the shape of the indicatrix. The relative changes in the light intensity consist of two components. The first component represents the modulation with the fundamental frequency f and the second one, with the doubled frequency 2f (second harmonic). We carried out measurements of the electrooptic modulation at both the first and second harmonics frequency. The applied calibration procedure allowed for expressing the experimental results as angular quantities independent of experimental conditions. Therefore we were able to determine the absolute values of the coefficients describing both effects of the electric field on the optical properties of the sample. We studied the temperature dependence of the first and second order coefficients in the ferroelectric smectic C? and paraelectric smectic A phases. The experiments delivered an information on the structure of tilted smectic liquid crystals and its dependence on the electric field.     

Optical high harmonic generation in C60

High harmonic generation (HHG) requires a strong laser field, but in C60 a relatively weak laser field is sufficient. Numerical results presented here show that, while its low order harmonics result from the laser field, its high order ones are mainly from the multiple excitations. Since high order harmonics directly correlate with electronic transitions, the HHG spectrum accurately measures transition energies. Therefore, C60 is not only a promising material for HHG, but may also present an opportunity to develop HHG into an electronic structure probing tool.     

Using Fast Fourier Transform to compute the line shape of frequency-modulated spectral profiles

An expression for the shape of spectral lines recorded by sinusoidal frequency modulation and harmonic detection is derived. It can be fast computed by means of the Fast Fourier Transform method and it holds for any modulation depth and modulation frequency. Different line shape functions, such as Voigt, Galatry, and speed-dependent Voigt, may be included in the model. In this work, the performance of the computing method is tested with experimental second harmonic rotational profiles, but it can be applied to higher harmonic spectra as well.     

The second plateau in the distribution of high harmonics generated in plasma torches

The second plateau in the intensity distribution of high harmonics generated in cadmium, chromium, manganese, and vanadium plasmas is observed. The characteristic plateau-like distribution of harmonic intensities, which was observed at comparatively low excitations of surface plasma, changes at higher energies of a prepulse that generates the plasma torch. The appearance of the second plateau is associated with harmonic generation due to the interaction with doubly charged plasma ions. The intensity of harmonics of the second plateau is either somewhat lower or comparable with the intensity of harmonics of the first order. The observed modification of the generated radiation spectrum caused by changes in the laser plasma characteristics allowed us to increase the maximum order of generated harmonics such that they fall into the far ultraviolet region. In particular, harmonics up to the 73rd (Cd), 75th (V), 83rd (Cr), and 95th (λ = 8.3 nm, Mn) orders are obtained.