基于微波迈克耳孙干涉仪的傅里叶变换光谱分析实验

基于近代物理实验中微波的迈克耳孙干涉实验方法,在分析傅里叶变换光谱分析原理的基础上,利用微波分光仪首先分离了2个已知微波源的谱分布,并定量分析了最大分辨率与最大光程差、最大测量范围与采样间距之间的关系.     

Four-quadrant spatial phase-shifting Fourier transform digital holography for recording of cosine transform coefficients

A new one-step four-quadrant spatial phase-shifting Fourier transform digital holography is presented for recording of cosine transform coefficients, because cosine transform is a real-even symmetric Fourier transform. This approach implements four quadrant spatial phase shifting at a time using a special phase mask, which is located in the reference arm, and the phase distributions of its four-quadrants are 0, π/2, π,and 3π/2 respectively. The theoretical analysis and computer simulation results show that cosine transform coefficients of real-valued image can be calculated by capturing single four-quadrant spatial phase-shifting Fourier transform digital hologram.     

Identification and treatment approach for spectral baseline distortion in processing of gas analysis online by Fourier transform infrared spectroscopy

Addressing the problem of baseline drift or distortion in Fourier transform infrared spectra when analyzing gas continuously at scene, a novel and simple method is proposed to identify and treat spectral baseline drift. Firstly, the spectral baseline was corrected with the common approach followed by standard gas analysis. Then, absorbance of analytes was reconstructed and reduced from the corrected spectrum. Finally, a Fourier transform was performed with the difference spectrum, and the first four-line strengths were used as feature variables to determine if baseline distortion occurred. In the end of this paper, this approach has been applied in the field of wellhead gas logging with Fourier transform infrared. The application results showed that all the spikes had been removed from the raw logging curves, confirming that this approach could be used to identify spectral baseline distortion accurately.     

基于空域非均匀傅里叶变换的傅里叶望远镜

为了在稀疏发射阵列下清晰重构目标图像,提出了一种基于空域非均匀傅里叶变换(NDFT)的傅里叶望远镜信号处理方法。依据傅里叶望远镜的发射器位置与抽取的目标空间频率关系,结合MATLAB程序特点,完成了空域非均匀傅里叶逆变换,重构了目标图像。稀疏发射阵列配置方式为:T型阵列单臂放置11个发射望远镜,连续抽取目标的8个低频信息,再抽取3个高频分量。选择不同形状和灰度分布的4个卫星作为成像目标。与补零均匀快速傅里叶变换(FFT)方法重构的图像对比发现:信噪比为100 dB时,相比补零均匀FFT方法, NDFT方法重构图像的Strehl比都有所提升,最高提升了0.159 8。     

基于空域非均匀傅里叶变换的傅里叶望远镜

为了在稀疏发射阵列下清晰重构目标图像,提出了一种基于空域非均匀傅里叶变换(NDFT)的傅里叶望远镜信号处理方法。依据傅里叶望远镜的发射器位置与抽取的目标空间频率关系,结合MATLAB程序特点,完成了空域非均匀傅里叶逆变换,重构了目标图像。稀疏发射阵列配置方式为：T型阵列单臂放置11个发射望远镜,连续抽取目标的8个低频信息,再抽取3个高频分量。选择不同形状和灰度分布的4个卫星作为成像目标。与补零均匀快速傅里叶变换(FFT)方法重构的图像对比发现：信噪比为100 dB时,相比补零均匀FFT方法, NDFT方法重构图像的Strehl比都有所提升,最高提升了0.159 8。     

Fourier transform spectral analysis of the cyclotron radiation from the PLT Tokamak

A Fourier transform spectrometer system, assembled from commercially available components, has been installed on the PLT device as part of a joint University of Maryland Princeton Plasma Physics Laboratory project for studying cyclotron radiation from tokamaks. The system consists of a polarizing Michelson interferometer with a rapidly reciprocating scanning mirror, a multi-element low pass transmission filter, a fast composite germanium bolometer, and a dedicated minicomputer for digitizing the interferogram and computing the spectrum. The system can acquire up to about 12 successive interferograms, at a rate of 2 per 100 msec, during a single PLT discharge. The transformation of an interferogram and the display of the resulting spectrum are accomplished in a few seconds. Analysis of the preliminary data suggests that the system can become a useful diagnostic of the electron temperature and density in PLT.     

The extended Fourier transform for 2D spectral estimation.

We present a linear algebraic method, named the eXtended Fourier Transform (XFT), for spectral estimation from truncated time signals. The method is a hybrid of the discrete Fourier transform (DFT) and the regularized resolvent transform (RRT) (J. Chen et al., J. Magn. Reson. 147, 129-137 (2000)). Namely, it estimates the remainder of a finite DFT by RRT. The RRT estimation corresponds to solution of an ill-conditioned problem, which requires regularization. The regularization depends on a parameter, q, that essentially controls the resolution. By varying q from 0 to infinity one can "tune" the spectrum between a high-resolution spectral estimate and the finite DFT. The optimal value of q is chosen according to how well the data fits the form of a sum of complex sinusoids and, in particular, the signal-to-noise ratio. Both 1D and 2D XFT are presented with applications to experimental NMR signals.     

基于傅里叶变换光谱技术的Zoom-FFT算法研究

在分析经典的Zoom-FFT算法基础上,提出一种基于傅里叶变换光谱技术的Zoom-FFT算法,用matlab仿真常规FFT算法和Zoom-FFT算法,对不同采样步长的干涉条纹进行数据处理,通过反演出的光谱曲线图和原始光谱曲线图可以看出:采样步长小于20 m时,FFT和Zoom-FFT算法都可以反演出光谱;而当采样步长大于20 m且小于33.3 m时,FFT算法未能反演出光谱,而Zoom-FFT算法仍然可以反演出光谱。     

A simple phase unwrapping approach based on filtering by windowed Fourier transform

Phase unwrapping is an interesting yet challenging problem in optical interferometry. In this paper, we limit our interest to unwrapping noisy phase maps as it is a common but difficult task. Our aim is to propose a simple solution to phase unwrapping. We first remove the noise by a novel windowed Fourier transform approach and then use sequential line scanning method for phase unwrapping. This simple approach is verified to be very effective.     

Fourier transform profilometry based on defocusing

Sinusoidal fringe patterns are popularly used in conventional Fourier transform profilometry. There are numerous harmonics in the Fourier spectrum, so as to avoid spectrum overlapping; the maximum range of measurement is limited. The present paper studies FTP based on properly defocusing a binary square wave. There are only odd harmonics in the Fourier spectrum of a binary square wave, and the maximum range of measurement is expanded 1.5 times. Defocusing has a low-pass filtering effect and higher-order odd harmonics are suppressed. Therefore, the fundamental spectrum is easy to extract. The proposed method overcomes the filtering problem of conventional FTP. Measurement experiments show that the proposed method has a good measurement result and the measurement accuracy is improved.     

Photonic approach to microwave frequency measurement with extended range based on phase modulation

We propose and demonstrate a photonic approach to instantaneous frequency measurement with an extended range based on phase modulation.In the measurement system,two optical wavelengths and two dispersion fiber segments are used to construct the frequency-dependent amplitude comparison functions(ACFs).Several ACFs can be utilized jointly to determine the microwave frequency without ambiguities beyond a monotonic region of the lone conventional ACF.The measurable range of microwave frequency can be extended and the accuracy can be improved by selecting an ACF with a large slope.The experimental results show that the errors are limited within ±140 MHz of a frequency measuremental range from 8 to 20 GHz.     

Image encryption based on the multiple-order discrete fractional cosine transform

A novel scheme for image encryption based-on the multiple-order discrete fractional cosine transform (MODFrCT) is proposed. The DFrCT has a similar relationship with the discrete fractional Fourier transform (DFrFT). Not only has the DFrCT many useful properties similar to the conventional discrete cosine transform, but it also has another property, namely its fraction, or its transform order. The image to be encrypted is transformed with the multiple-order DFrCT using a random row cipher key vector and a random column key vector successively, and the corresponding cipher key vectors of decryption are also very sensitive. The transmission of the encrypted image with the algorithm of the multiple-order DFrCT is faster due to its reality. The digital simulation results proved the validity and safety of this algorithm.     

基于离散余弦变换与二维Ushiki混沌的图像加密

提出了一种基于离散余弦变换与混沌随机相位掩模的图像加密方法。起密钥作用的两块混沌随机相位掩模由二维Ushiki混沌系统生成,Ushiki混沌系统的初值和控制参数可以替代随机相位掩模作为加解密过程中的密钥,因此便于密钥管理和传输。通过对密钥敏感性、图像相邻像素间的相关性、抗噪声攻击及抗剪切攻击等分析表明,图像加密方法具有较强的抵抗暴力攻击、统计攻击、噪声攻击和剪切攻击能力。     

Photonic quasicrystals treated by Fourier analysis

A photonic quasicrystal as quasi-periodic structure is studied by expanding its wavelength-dependent index of refraction and group index in Fourier series. This Fourier analysis of quasi-periodic systems is a generalization of the Fourier analysis for periodic ones.     

Fourier transform microwave spectroscopy of aluminum hydrosulfide, AlSH

Pure rotational transitions of three isotopic species of aluminum hydrosulfide, AlSH, have been measured with a cavity pulsed jet Fourier transform microwave spectrometer. AlSH was prepared by the reaction of laser ablated Al metal with H₂S, and was stabilized in pulsed supersonic free jets of Ar. For each species the transition 1₀₁-0₀₀ was measured; hyperfine structure due to the nuclear spin of ²⁷Al was observed for the first time and analyzed. For Al³²SH and Al³²SD, the rotational constants are in excellent agreement with published values. For the third species, Al³⁴SH, this is the first observation, and its rotational constants are consistent with the published geometry. Information on the electronic structure of the molecule has been obtained using the ²⁷Al nuclear quadrupole coupling constants and nuclear spin-rotation constants. The latter have been used to evaluate ²⁷Al NMR shielding parameters, which are compared with those of other ²⁷Al compounds. These shieldings have been found to be in excellent agreement with theoretical predictions. The results should also help facilitate astrophysical searches for the molecule.     

Room temperature chirped-pulse Fourier transform microwave spectroscopy of anisole

The room-temperature rotational spectrum of anisole from 8.7 to 18.3 GHz was collected with a waveguide-based chirped-pulse Fourier transform microwave spectrometer whose operating principles are described. Three spectra were assigned, corresponding to the vibrational ground state and the first and second excited states of the lowest frequency torsional mode. Results for the ground state and first excited state are in agreement with prior millimeter wave studies of this molecule. Microwave–microwave double resonance measurements also confirm these assignments.     

Fourier transform microwave spectrum of the CO-dimethyl sulfide complex

The rotational spectrum of the CO-dimethyl sulfide (DMS) complex was measured in the frequency region from 4.8 up to 25 GHz by Fourier transform microwave spectroscopy. For the normal species 27 a-type and 57 c-type transitions were observed, while 16 and 8 c-type transitions were assigned for the species with ³⁴S and ¹³C in the DMS moiety, respectively, in natural abundance. In addition, 7 a-type and 48 c-type transitions were assigned for the complex with the ¹³CO enriched species as a component and 9 a-type and 42 c-type transitions for the complex with enriched C¹⁸O. No splitting was observed, which could be ascribed to the tunneling motion of the CO between two possible potential minima around DMS, while many transitions were split by the internal-rotation of the two methyl tops of the DMS unit. In cases where the K-type splitting was close to the methyl internal-rotation splitting, forbidden transitions were observed which apparently followed b-type selection rules. All of the observed transition frequencies for the normal species were analyzed simultaneously using a two-top internal-rotation and rotation Hamiltonian. The potential barrier height V₃ to internal rotation of the methyl groups of the DMS was determined to be 745.5 (30) cm⁻¹. The transition frequencies observed for all the isotopomers were analyzed using an asymmetric-rotor rotational Hamiltonian, to determine rotational and centrifugal distortion constants. The r_s coordinates calculated from the observed rotational constants led to the conclusion that the CO moiety was located in a plane perpendicular to the skeletal plane of the DMS and bisecting its CSC angle. This structure of the CO-DMS is very much different from that of the CO-DME, in which the CO is located in the DME skeletal plane. The distance between the centers of gravity of the two moieties, R_cm, was calculated to be 3.789 Å for the CO-DMS, which is longer by only 0.11 Å than that in the CO-DME complex: 3.68 Å, in spite of the fact that the van der Waals radius of the S atom is much larger than that of the O atom. The small difference in R_cm is, in part, ascribed to the location of the CO relative to the DMS/DME. The more important reason is that the intermolecular bonding of the CO-DMS is stronger than that of CO-DME; by assuming a Lennard-Jones-type potential, the force constant of the van der Waals stretching mode and the dissociation energy were estimated to be 2.7 Nm⁻¹ and 3.3 kJ mol⁻¹, respectively, which were larger than those of the CO-DME: 1.4 Nm⁻¹ and 1.6 kJ mol⁻¹.     

傅里叶变换光谱成像仪光谱传递函数研究

根据光学传递函数理论,定义了光谱成像仪的光谱传递函数. 针对基于Michelson干涉仪的时间调制傅里叶变换（FT）光谱成像仪,基于Sagnac干涉仪、Fresnel干涉仪、Lloyd干涉仪的空间调制FT光谱成像仪,推导出相应的光谱调制传递函数和光谱相位传递函数解析表达式,并分析了其物理意义. 光谱传递函数为评价相应光谱成像仪在光谱域的性能提供了一种量化的判据. 与空间域的光学传递函数相结合,成为反映光谱成像仪综合性能的客观依据. 关键词： 傅里叶变换 光谱成像仪 光谱传递函数     

Accurate carrier-removal technique based on zero padding in Fourier transform method for carrier interferogram analysis

Based on interferogram zero padding and fast Fourier transform (FFT) methods, an effective, straightforward and stable carrier-removal approach in Fourier transform (FT) based method for carrier interferogram analysis is proposed. The spatial carrier interferogram is firstly extrapolated by zero padding method, and the carrier-frequency values within a small fraction of an integral (or a pixel) are estimated from the extrapolation interferogram with FFT method. Then the carrier-phase component is removed by subtracting a pure carrier-frequency phase constructed by the estimated carrier-frequencies in the spatial domain. Numerical simulations and experiments are given to demonstrate the performance of the proposed method and the results show that the proposed method is effective and stable for suppressing the carrier-removal error in the FT method for carrier interferogram analysis.