Random fractional Fourier transform

We propose a novel random fractional Fourier transform by randomizing the transform kernel function of the conventional fractional Fourier transform. The random fractional Fourier transform inherits the excellent mathematical properties from the fractional Fourier transform and can be easily implemented in optics. As a primary application the random fractional Fourier transform can be directly used in optical image encryption and decryption. The double phase encoding image encryption schemes can thus be modeled with cascaded random fractional Fourier transformers.     

Transparent Fourier transform spectrometer

We realized a transparent Fourier transform spectrometer and investigated its operating principle. The spectrometer consists of a low-reflectivity Fabry-Perot interferometer and a partially transparent photodetector, which allows for the operation of the spectrometer in transmission. By changing the distance between the low-reflectivity mirrors of the Fabry-Perot interferometer, the light intensity that reaches the partially transparent photodetector is modulated and the spectral information of the incident light is determined by the Fourier transform of the generated photocurrent. This transparent Fourier transform spectrometer allows easy miniaturization and integration into any kind of optical system.     

Randomization of the Fourier transform

We have investigated the multiplicity and complexity in eigenvalues of the fractional Fourier transform and found that the ambiguity of the eigenvalues may indicate randomness. We have therefore proposed a method to randomize the Fourier transform. Such a random Fourier transform can be applied in the field of image encryption and decryption.     

Fourier transform spectroscopy of NbS

Emission bands attributed to the NbS radical have been observed in the near infrared and visible regions with FTS techniques using an electrodeless 2450 MHz discharge as a source. Transitions within the doublet and quartet manifolds were recorded at high resolution. The present paper gives the first rotational analysis of this molecule. Numerous bands within the doublet and quartet manifolds have been analyzed, resulting in the characterization of seven different electronic states, three in the doublet and four in the quartet manifold. The states have been labeled in analogy with NbO. The analyzed electronic states are: X⁴Σ⁻, C⁴Σ⁻, A′⁴Φ, D⁴Δ, a²Δ, c²Π, and e²Φ. Four additional substates in the doublet manifold have also been analyzed. In all, 27 vibrational sublevels have been included in the analysis, the total number of rotational lines being about 18 000. The positions of the analyzed transitions are: C⁴Σ⁻ → X⁴Σ⁻ near 15 670 cm⁻¹, D⁴Δ → A′⁴Φ near 7740 cm⁻¹, c²Π → a²Δ near 5850 cm⁻¹ and e²Φ → a²Δ near 8500 cm⁻¹. The overall picture is consistent with the corresponding analysis of NbO. However, three energy separations could not be derived from the experimental data in the case of NbS, i.e., the a²Δ− X⁴Σ⁻, A′⁴Φ− X⁴Σ⁻ and a²Δ_5/2-a²Δ_3/2 splittings. These were set to 4992, 5490, and 992 cm⁻¹, respectively, from preliminary ab initio calculations. In this way, a tentative energy level scheme could be drawn. The first order spin-orbit parameter of the A′⁴Φ state was indeterminable from the experimental data and was set to the value 170 cm⁻¹, derived from the same calculations.     

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。     

Fast Fourier transform processor architecture

This paper describes a VLSI architecture used for implementation offast Fourier transform,of which the computation cell(CC)implement the com-putation of 4-point DFT and multiplication of twiddle factors using radix-4pipeline computation method,and the address generator(AG)gives the ad-dresses of both transform data and twiddle factors simultaneously.In addition,this paper also presents the recursive and cascade circuit configurations usingthe CC,AG and BFP overflow preventing scheme.Up to 64K-point FFT canbe computed quickly and flexibly by using these two circuit configurations.     

Microcomputers in Fourier transform spectroscopy

With the rapid advancement of VLSI technologies, microcomputer systems with relatively fast CPU processing time and electronic memory (RAM) of 1 Mbyte are now available at a reasonably low cost. We discuss the interfacing of microcomputers with 6502, 8086 and 68000 CPU to an FTS system. The performance of some A/D converters and microcomputer-controlled micropositioners available commercially are also discussed.     

Improved discrete fractional Fourier transform

The fractional Fourier transform is a useful mathematical operation that generalizes the well-known continuous Fourier transform. Several discrete fractional Fourier transforms (DFRFT's) have been developed, but their results do not match those of the continuous case. We propose a new DFRFT. This improved DFRFT provides transforms similar to those of the continuous fractional Fourier transform and also retains the rotation properties.     

Improved composite Fourier transform profilometry

An improved composite Fourier transform profilometry (ICFTP) is proposed through optimizing the composite grating. Compared with the composite Fourier transform profilometry (CFTP), the frequencies of the two sinusoidal images modulated along the orthogonal direction in the optimized composite grating are not equal. The overlapping degree of Fourier spectrum of the optimized grating is lowered. The measuring accuracy is improved because two frequencies are used to calculate phase more accurately. By using a more advantageous flat image extracted ingeniously from the optimized grating, the zero component of the lower frequency sinusoidal image in the Fourier spectrum can be eliminated. So the measuring range is extended the same as that by the π phase shifting technique. Both numerical simulation and experiment demonstrate the feasibility and validity of the proposed method.     

Fourier transform emission lifetime spectrometer

We report a rapid and low cost Fourier transform spectrometer that uses a path length modulated Michelson interferometer to simultaneously measure excitation spectra and excitation wavelength-dependent emission lifetimes. Excitation spectra and lifetimes of excited tris(2,2'-bipyridyl) ruthenium(II) measured using this technique corresponded to values known in the literature. Excitation-dependent lifetimes of porous silicon measured with this technique suggest the influence of quantum confinement effects. This method may be useful for measuring mixtures of emitting species with closely spaced lifetimes as well as studying excitation wavelength-dependent emission phenomena.     

Field-compensated birefringent Fourier transform spectrometer

A field-compensation method applied for Savart birefringent Fourier transform spectrometer is presented. By using a combination of Savart plates fabricated from positive and negative birefringent materials, the useful solid angle of field of view can be increased by a large amount in broad spectral coverage. Compared to the conventional Fourier transform spectrometers, the compensated field angle has optical throughput higher by one order in magnitude. To demonstrate the effectiveness, a design example operating at 400-1100 nm with a large solid angle exceeding ± 40° is presented in detail.     

Nilpotent Fourier transform and applications

We study the nilpotent Fourier transform on spaces of distributions. We use it to prove the equivalence between ^*-products on g^* for nilpotent g.     

Infrared Fourier transform spectroscopy of PH

The infrared vibration-rotation spectrum of the PH radical was observed in emission using a high-resolution Fourier transform spectrometer. The observation of five bands (1-0, 2-1, 3-2, 4-3, and 5-4) allowed the first six vibrational energy levels of the ground X³Σ⁻ state to be characterized. An RKR potential curve for the ground state was computed.     

Fractional Fourier transform of Lorentz beams

This paper introduces Lorentz beams to describe certain laser sources that produce highly divergent fields. The fractional Fourier transform (FRFT) is applied to treat the propagation of Lorentz beams. Based on the definition of convolution and the convolution theorem of the Fourier transform, an analytical expression for a Lorentz beam passing through a FRFT system has been derived. By using the derived formula, the properties of a Lorentz beam in the FRFT plane are illustrated numerically.     

Fractional Fourier transform of Airy beams

An analytical expression of an Airy beam passing through a fractional Fourier transform (FRFT) system is presented. The effective beam size of the Airy beam in the FRFT plane is also derived. The influences of the order of FRFT, the modulation parameter, and the transverse scale on the normalized intensity distribution and the effective beam size of an Airy beam in the FRFT plane are examined. The order of FRFT controls the effective beam size and the orientation of the beam spot. The modulation parameter affects the effective beam size and the number of lateral side lobes. The normalized intensity distribution and the effective beam size are both proportional to the transverse scale.     

Implementation of the quantum Fourier transform

A quantum Fourier transform (QFT) has been implemented on a three qubit nuclear magnetic resonance (NMR) quantum computer to extract the periodicity of an input state. Implementation of a QFT provides a first step towards the realization of Shor's factoring and other quantum algorithms. The experimental implementation of the QFT on a periodic state is presented along with a quantitative measure of its efficiency measured through state tomography. Experimentally realizing the QFT is a clear demonstration of the ability of NMR to control quantum systems.     

Fourier transform properties of acousto-optic lens

A rf pulse of 4 μs swept linearly over 10 MHz, about a center frequency of 100 MHz, has been compressed to 110 ns. Fourier and Mellin transforms property of the surface acousto-optic lens has been discussed.     

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。