Papers by Keyword: Fourier Transformation

Abstract: We investigated the consistency of four methods by analyzing the distorted Debye rings with various stress states. Firstly, the distorted Debye rings were generated under various uni-, bi-and tri-axial stress states by using the fundamental stress-strain relationship in two dimensional X-ray stress analysis theory. Secondly, we performed reverse analysis of stress states in the frameworks of sin²ψ and cosα methods from the simulated Debye rings. Moreover, the profiles of simulated Debye rings were Fourier transformed and the stress states were calculated in accordance with the obtained 1st and 2nd order Fourier coefficients. As a result, it was confirmed that all these methods provide the same stress values. That is to say, all these methods are consistent. Therefore, we can guarantee the validity of choosing any appropriate method considering the geometrical restrictions of experiment.

Abstract: In this paper, Von Karman random media is constructed with power spectrum method. The random media with Von Karman autocorrelation cannot be constructed in time domain but in frequency domain. So power spectrum method is utilized to solve the problem. The spectrum of random function is generated in frequency domain with random field and auto-correlation function. With inverse Fourier transformation, the Von Karman random media model is constructed. With different correlation lengths, six group of Von Karman random media are constructed.

Abstract: Remote sensing technology has rapid development in the past half one century, it is widely used in various fields and society. But the clouds have affected the quality of remote sensing data, how to effectively use the modern computer science and technology to remove the cloud is a hot issue in the field. From the theory of cloud formation in the remote sensing image, we analyze the formation mechanism, and based on this we do two layers decomposition and reconstruct the structure according to wavelet transform in network communication, and establish the image degradation model. Combining Fourier transformation, we set up the removing cloud fusion model of remote sensing image. Through the simulation experiment, the effect is significant. To a certain extent, it provides technical support for theory study and practice operation.

Abstract: Based on Fresnel diffraction theory we give out the light field distribution for the definite frequency component of a femtosecond laser pulse when the laser pulse passes through a serrated aperture. Through an inverse Fourier transformation, we get the temporal diffraction field function of the femtosecond laser pulse at any distance. The temporal diffraction field function is related to the width of the laser pulse, the structure of the serrated aperture, the Fresnel number at central frequency and time. Number calculation shows when the width of the laser pulse is within a few tens of femtoseconds and Fresnel number at central frequency is much, the temporal diffraction intensity is not a Gaussian distribution. Nevertheless when Fresnel number at central frequency is less than ten, the temporal diffraction intensity can be approximately regarded as a Gaussian distribution and has a time delay effect.

Abstract: An equation is put forward to calculate the temporal diffraction intensity distribution of a chirped femtosecond laser pulse when it incites a circle aperture. In the aperture central direction an analytic expression is given to calculate the temporal intensity distribution. Many factors such as the width of the laser pulse, the radius of the circle aperture, the Fresnel number at central frequency, time and the chirped coefficient of the laser pulse affect the temporal intensity. Number calculation shows that if the width of laser pulse is within a few tens of femtoseconds and Fresnel number at central frequency is much than twenty, the temporal diffraction intensity outline is not a Gaussian curve. While when the Fresnel number is less than ten and the chirped coefficient is small, the temporal intensity is an approximate Gaussian curve. If the chirped coefficient is large, the temporal intensity is not Gaussian distribution.

Abstract: First we give the optical field function at distance z for a monochromatic light according to the Fresnel diffraction theory. The total optical field intensity is an integral of that of the monochromatic light. The total optical field intensity is not only related to the full width at half maximum, the distance, the structure of the serrated aperture, but also the radius of the ultrashort laser pulse. Numerical calculation shows that when the ratio of the averaged radius of the serrated aperture to the radius of the ultrashort laser pulse equals to 1 and the full width at half maximum is within a few tens of femtoseconds, the total optical field intensity reaches a constant along the axis direction and it is more stable than that without considering the radius of the ultrashort laser pulse in case that the Fresnel number of the laser pulse is about a hundred.

Abstract: Shape context is not rotation invariant as a local visual feature. To solve this problem, 2-D and 1-D Fourier Transformation has been performed on the feature. Based on the property of Fourier Transformation, a fast and efficient method is presented in the cost matrix computation of these improved shape context feature. The analysis shows the time complexity is much lower and the experiments show effective and efficiency of this new algorithm.

Abstract: Morphological features, such as the orientation and linearity of basal plane dislocations (BPDs) in SiC crystals, were analyzed by applying a two-dimensional fast Fourier transform (2D-FFT) to X-ray topographic images of the BPDs. An SiC crystal fabricated by an improved repeated a-face (RAF) method and an SiC crystal fabricated by an conventional RAF method discussed in a previous study were evaluated. In the 2D-FFT images of the improved crystal, streaks along the directions were observed, indicating that the BPDs were highly oriented along the directions. The degree of orientation of the BPDs, which may reflect their linearity, was calculated, and the improved RAF crystal had a much higher degree of orientation than the conventional RAF crystal.

Abstract: A no interference optical image encryption is put forward in this paper. The encrypting process is composed of a Fresnel diffraction and a Fourier transformation. A digital image coded with a random phase plate first takes a Fresnel diffraction. The diffraction function is enlarged and coded with another random phase mask. At last the enlarged function undergoes a Fourier transformation. The real part of the transformed function is defined as an encrypted image. In decrypting process, first the encrypted image takes an inverse Fourier transformation. Then the upper left corner of the transformed function is intercepted. According to the space inversion of the transformed function, if the intercepted function takes an inverse Fresnel diffraction, the original digital image can be restored from the final diffraction function. Because there is no interference process in encryption and decryption, the optical system is relatively simple and the quality of restored image is very good

Abstract: In this paper, basing on Hu haichang’s theory and using Fourier transformation, the problem is changed into solving fourth-order and second-order linear ordinary differential equations. The eigenvalue method is used for solving these equations, and then both displacement and stress with undetermined coefficients can be received. Considering the boundary conditions, the exact displacement and stress of the transversely isotropic foundation can also be gotten. Especially on the transversely isotropic elastic half space, with the aid of computer software, a more simple vertical displacement is presented. When the foundation is degenerated into isotropic elastic half space, the displacement is also degenerated into elastic half space displacement in a rectangular coordinate system which is given in the reference. And this exactly proves the result which is received from this paper is right. On this basis, we can analyze a settlement of transversely isotropic foundation and the static characteristics of rectangular plate on the transversely isotropic foundation.