Moduli and twisted sector dependence of ZN×ZM orbifold couplings

We derive the four point correlation function involving four twist fields for arbitrary even dimensional Z_N×Z_M orbifold compactifications. Using techniques from the conformal field theory the three point correlation functions with twist fields are determined. Both the choice of the modular background (compatible with the twists) and of the (higher) twisted sectors involved are fully general. Our results turn out to be target space duality invariant.     

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

A scheme for implementing discrete quantum Fourier transform is proposed via quantum dots embedded in a microcavity, and then some of its applications are investigated, i.e., Deutsch 3ozsa. algorithm and Shor＇s quantum factoring. In particular, the detailed process of implementing one~qubit Deutsch Jozsa algorithm and the factorization of N = 15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemes would be an important step to fabricate a solid quantum computer.     

Implementation of Quantum Fourier Transform and Its Applications via Quantum-Dot Spins and Microcavity

A scheme for implementing discrete quantum Fourier transform isproposed via quantum dots embedded in a microcavity, and then someof its applications are investigated, i.e., Deutsch-Jozsa algorithm and Shor's quantum factoring. In particular, the detailed process of implementing one-qubit Deutsch-Jozsa algorithm and the factorization of N=15 are given. The microcavity mode is only virtually excited in the whole interaction, so the effective decoherent has slight effect on the current scheme. These schemeswould be an important step to fabricate a solid quantum computer.     

A geometric nonuniform fast Fourier transform

An efficient algorithm is presented for the computation of Fourier coefficients of piecewise-polynomial densities on flat geometric objects in arbitrary dimension and codimension. Applications range from standard nonuniform FFTs of scattered point data, through line and surface potentials in two and three dimensions, to volumetric transforms in three dimensions. Input densities are smoothed with a B-spline kernel, sampled on a uniform grid, and transformed by a standard FFT, and the resulting coefficients are unsmoothed by division. Any specified accuracy can be achieved, and numerical experiments demonstrate the efficiency of the algorithm for a gallery of realistic examples.     

Comments on the complete generalized fractional Fourier transform

In this research, we thoroughly investigate the complete generalized fractional Fourier transform (CGFRFT) and draw the following conclusions that are different from the original literature: (1) The CGFRFT is not a generalized version, but a special case that ignores the marginal postulate; (2) If the period parameter is not a multiple of four, the CGFRFT can never perform a Fourier transform regardless of the value of the transform order. The simulation results of a rectangular signal support the above conclusions.     

Fourier transform emission spectroscopy of the FΔ-XΦ system of TiF

The emission spectra of TiF have been reinvestigated in the 4200-15 000 cm⁻¹ region using the Fourier transform spectrometer associated with the National Solar Observatory at Kitt Peak. TiF was formed in a microwave discharge lamp operated with 2.5 Torr of He and a trace of TiF₄ vapor, and the spectra were recorded at a resolution of 0.02 cm⁻¹. The TiF bands observed in the 12 000-14 000 cm⁻¹ region have been assigned to a new transition, F⁴Δ-X⁴Φ. Each band consists of four sub-bands assigned as, ⁴Δ_1/2-⁴Φ_3/2, ⁴Δ_3/2-⁴Φ_5/2, ⁴Δ_5/2-⁴Φ_7/2, and ⁴Δ_7/2-⁴Φ_9/2. A rotational analysis of the 0-1, 0-0, and 1-0 bands has been obtained and spectroscopic constants have been extracted.     

不对称离散分数傅里叶变换实现数字图像的加密变换

利用不对称分数傅里叶变换的特性,提出了一种图像加密变换的新方法。对图像的x,y方向分别实施不同级次的一维分数傅里叶变换,得到加密图像。解密方法就是对变换后的图像实施对应级次的分数傅里叶逆变换,只有当x,y方向的逆变换级次分别与原变换级次都相同或者满足周期条件时,才能恢复原图像。加密变换有效地提高了图像加密和防伪力度。数值计算验证了方法的正确性和可行性。     

Laser and Fourier transform emission spectroscopy of TaCl

The emission spectrum of TaCl has been recorded at high resolution in the 3000-35 000 cm⁻¹ region using a Fourier transform spectrometer. The bands were observed by microwave excitation of a mixture of TaCl₅ vapor and 3.0 Torr of He. Several TaCl bands have also been recorded using the laser ablation/molecular beam source at the University of New Brunswick. A rotational analysis of a number of bands has been obtained and the majority of the stronger bands have been classified into three groups with different lower state spectroscopic constants. The three lower states have been identified as having Ω″ = 0⁺, Ω″ = 2, and (tentatively) Ω″ = 3. The Ω″ = 0⁺ and Ω″ = 2 states are very close in energy and one of these two states is the ground state of TaCl.     

Image encryption and decryption using fractional Fourier transform and radial Hilbert transform

A technique for image encryption using fractional Fourier transform (FRT) and radial Hilbert transform (RHT) is proposed. The spatial frequency spectrum of the image to be encrypted is first segregated into two parts/channels using RHT, and image subtraction technique. Each of these channels is encrypted independently using double random phase encoding in the FRT domain. The different fractional orders and random phase masks used during the process of encryption and decryption are the keys to enhance the security of the proposed system. The algorithms to implement the proposed encryption and decryption scheme are discussed, and results of digital simulation are presented.     

用小型全息设备做傅里叶变换全息图存储资料实验

阐述了用小型全息设备做傅里叶变换全息图存储资料实验所采用的光路、详细的操作步骤和实验中的关键问题.     

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.     

Displacement measurement based on joint fractional Fourier transform correlator

A displacement measurement technology based on joint fractional Fourier transform is firstly proposed. Contrast to conventional displacement measurement based on joint Fourier transform correlator, the position of cross correlation peak in the proposed technology could be fixed arbitrarily according to the order of fractional Fourier transform. The optical setup in the proposed technology is more flexible and easier to implement. Simulation and experiment results are given out to verify the analysis.     

基于分数阶Fourier变换的数字图像实值加密方法

构造了一种新的保实化的分数阶Fourier变换,提出了一种基于该变换的数字图像实值加密方法。利用保实分数阶Fourier变换的保实特性和阶数可加性等完成了数字图像的加密与解密,明文和密文分别位于空域和由密钥决定的保实分数阶Fourier变换域中,具有较强的抗统计破译能力。密图是一个实值图像,便于显示和存储。仿真实验结果表明,该加密方法密钥简单,无数据膨胀,对参数敏感度高,具有一定的鲁棒性和安全性。在信息安全领域具有良好的研究前景和实用价值。     

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.     

Fractional Fourier transform of an elliptical dark-hollow beam

The fractional Fourier transform (FRT) of an elliptical dark-hollow beam (EDHB) is studied in detail. Based on the definition of FRT in the rectangular coordinate system, analytical formulae are derived for the FRT of an EDHB with the help of a tensor method. The properties of an EDHB in the FRT plane are illustrated numerically by use of the derived formulae. The results show that the properties of the EDHB in the FRT plane are closely related to the parameters of the beam and to the fractional order. The derived formula provides a convenient way for analyzing and calculating the FRT of an EDHB.     

Fractional Fourier transform for off-axis dark-hollow beams

Based on the definition of fractional Fourier transform (FRT) in the rectangular coordinate system, the FRT for off-axis circular and elliptical dark-hollow beams (DHB) is studied in detail, and analytical formulae are derived for the FRT for off-axis circular and elliptical DHB. The properties of off-axis DHB in the FRT plane are illustrated numerically by use of the derived formulae. The results show that the properties of the off-axis DHB in the FRT plane are closely related with the parameters of the beam and fractional order. The derived formula provides a convenient way for analyzing and calculating the FRT of off-axis DHBs.     

Free-space Fresnel diffraction for the approximation of fractional Fourier transform

Fractional Fourier transformation of an object can be approximated by the object's free-space Fresnel diffraction pattern under some restricted conditions and plane wave illumination according to Hua's method. A better approximation is achieved under least-squared conditions developed in this paper. Simulation results verify that our theoretical development works for any fractional order a compared with the previous approach.     

Characterizing Young's fringes’ orientation and spacing by Fourier transform and Radon transform

Orientation and spacing are important features of fringe patterns, especially in speckle photography when the displacement information of the object is determined by pointwisely filtering the double-exposure specklegram. The Fourier transform and Radon transform are both simple and effective tools for solving this problem, which extract the information in spectral domain and spatial domain, respectively. A hybrid method combining Radon transform and Fourier transform is also possible. The results can be further improved by enhanced Fourier transform and enhanced Radon transform. The theories, as well as real applications, are given in this paper.