Extended fractional Fourier transforms

The concept of an extended fractional Fourier transform (FRT) is suggested. Previous PBT's and complex FRT's are only its subclasses. Then, through this concept and its method, we explain the physical meaning of any optical Fresnel diffraction through a lens: It is just an extended FRT; a lens-cascaded system can equivalently be simplified to a simple analyzer of the FRT; the two-independent-parameter FRT of an object illuminated with a plane wave can be readily implemented by a lens of arbitrary focal length; when cascading, the Function of each lens unit and the relationship between the adjacent ones are clear and simple; and more parameters and fewer restrictions on cascading make the optical design easy. (C) 1997 Optical Society of America.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Dynamic full-range Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We propose a technique for dynamic full-range Fourier-domain optical coherence tomography by using sinusoidal phase-modulating interferometry, where both the full-range structural information and depth-resolved dynamic information are obtained. A novel frequency-domain filtering algorithm is proposed to reconstruct a time-dependent complex spectral interferogram from the sinusoidally phase-modulated interferogram detected with a high-rate CCD camera. By taking the amplitude and phase of the inverse Fourier transform of the complex spectral interferogram, a time-dependent full-range cross-sectional image and depth-resolved displacement are obtained. Displacement of a sinusoidally vibrating glass cover slip behind a fixed glass cover slip is measured with subwavelength sensitivity to demonstrate the depth-resolved dynamic imaging capability of our system. (c) 2007 Society of Photo-Optical Instrumentation Engineers.

Two-dimensional photonic crystals with a large photonic band gap designed by a rapid genetic algorithm

We used Plane Wave Expansion Method and a Rapid Genetic Algorithm to design two-dimensional photonic crystals with a large absolute band gap. A filling fraction controlling operator and Fourier transform data storage mechanism had been integrated into the genetic operators to get desired photonic crystals effectively and efficiently. Starting from randomly generated photonic crystals, the proposed RGA evolved toward the best objectives and yielded a square lattice photonic crystal with the band gap (defined as the gap to mid-gap ratio) as large as 13.25%. Furthermore, the evolutionary objective was modified and resulted in a satisfactory PC for better application to slab system.

Improved digital processing method used for image motion measurement based on hybrid opto-digital joint transform correlator

Hybrid opto-digital joint transform correlator (HODJTC) is effective for image motion measurement, but it is different from the traditional joint transform correlator because it only has one optical transform and the joint power spectrum is directly input into a digital processing unit to compute the image shift. The local cross-correlation image can be directly obtained by adopting a local Fourier transform operator. After the pixel-level location of cross-correlation peak is initially obtained, the up-sampling technique is introduced to relocate the peak in even higher accuracy. With signal-to-noise ratio >= 20 dB, up-sampling factor k >= 10 and the maximum image shift <= 60 pixels, the root-mean-square error of motion measurement accuracy can be controlled below 0.05 pixels.

Discrete wavelets transform for signal denoising in capillary electrophoresis with electrochemiluminescence detection

Discrete wavelets transform (DWT). was applied to noise on removal capillary electrophoresis-electrochemiluminescence (CE-ECL) electropherograms. Several typical wavelet transforms, including Haar, Daublets, Coiflets, and Symmlets, were evaluated. Four types of determining threshold methods, fixed form threshold, rigorous Stein's unbiased estimate of risk (rigorous SURE), heuristic SURE and minimax, combined with hard and soft thresholding methods were compared. The denoising study on synthetic signals showed that wave Symmlet 4 with a level decomposition of 5 and the thresholding method of heuristic SURE-hard provide the optimum denoising strategy. Using this strategy, the noise on CE-ECL electropherograms could be removed adequately. Compared with the Savitzky-Golay and Fourier transform denoising methods, DWT is an efficient method for noise removal with a better preservation of the shape of peaks.

消除采集脚印的处理方法研究

Seismic technique is in the leading position for discovering oil and gas trap and searching for reserves throughout the course of oil and gas exploration. It needs high quality of seismic processed data, not only required exact spatial position, but also the true information of amplitude and AVO attribute and velocity. Acquisition footprint has an impact on highly precision and best quality of imaging and analysis of AVO attribute and velocity. Acquisition footprint is a new conception of describing seismic noise in 3-D exploration. It is not easy to understand the acquisition footprint. This paper begins with forward modeling seismic data from the simple sound wave model, then processes it and discusses the cause for producing the acquisition footprint. It agreed that the recording geometry is the main cause which leads to the distribution asymmetry of coverage and offset and azimuth in different grid cells. It summarizes the characters and description methods and analysis acquisition footprint’s influence on data geology interpretation and the analysis of seismic attribute and velocity. The data reconstruct based on Fourier transform is the main method at present for non uniform data interpolation and extrapolate, but this method always is an inverse problem with bad condition. Tikhonov regularization strategy which includes a priori information on class of solution in search can reduce the computation difficulty duo to discrete kernel condition disadvantage and scarcity of the number of observations. The method is quiet statistical, which does not require the selection of regularization parameter; and hence it has appropriate inversion coefficient. The result of programming and tentat-ive calculation verifies the acquisition footprint can be removed through prestack data reconstruct. This paper applies migration to the processing method of removing the acquisition footprint. The fundamental principle and algorithms are surveyed, seismic traces are weighted according to the area which occupied by seismic trace in different source-receiver distances. Adopting grid method in stead of accounting the area of Voroni map can reduce difficulty of calculation the weight. The result of processing the model data and actual seismic demonstrate, incorporating a weighting scheme based on the relative area that is associated with each input trace with respect to its neighbors acts to minimize the artifacts caused by irregular acquisition geometry.

HHT在电磁信号处理中的应用

In modem signal Processing，non－linear，non－Gaussian and non－stable signals are usually the analyzed and Processed objects，especially non－stable signals. The convention always to analyze and Process non－stable signals are： short time Fourier transform，Wigner－Ville distribution，wavelet Transform and so on. But the above three algorithms are all based on Fourier Transform，so they all have the shortcoming of Fourier Analysis and cannot get rid of the localization of it. Hilbert－Huang Transform is a new non－stable signal processing technology，proposed by N. E. Huang in 1998. It is composed of Empirical Mode Decomposition (referred to as EMD) and Hilbert Spectral Analysis (referred to as HSA). After EMD Processing，any non－stable signal will be decomposed to a series of data sequences with different scales. Each sequence is called an Intrinsic Mode Function (referred to as IMF). And then the energy distribution plots of the original non－stable signal can be found by summing all the Hilbert spectrums of each IMF. In essence，this algorithm makes the non－stable signals become stable and decomposes the fluctuations and tendencies of different scales by degrees and at last describes the frequency components with instantaneous frequency and energy instead of the total frequency and energy in Fourier Spectral Analysis. In this case，the shortcoming of using many fake harmonic waves to describe non－linear and non－stable signals in Fourier Transform can be avoided. This Paper researches in the following parts： Firstly，This paper introduce the history and development of HHT，subsequently the characters and main issues of HHT. This paper briefly introduced the basic realization principles and algorithms of Hilbert－Huang transformation and confirms its validity by simulations. Secondly, This paper discuss on some shortcoming of HHT. By using FFT interpolation, we solve the problem of IMF instability and instantaneous frequency undulate which are caused by the insufficiency of sampling rate. As to the bound effect caused by the limitation of envelop algorithm of HHT, we use the wave characteristic matching method, and have good result. Thirdly, This paper do some deeply research on the application of HHT in electromagnetism signals processing. Based on the analysis of actual data examples, we discussed its application in electromagnetism signals processing and noise suppression. Using empirical mode decomposition method and multi-scale filter characteristics can effectively analyze the noise distribution of electromagnetism signal and suppress interference processing and information interpretability. It has been founded that selecting electromagnetism signal sessions using Hilbert time-frequency energy spectrum is helpful to improve signal quality and enhance the quality of data.

基于信息重建技术的地震信号处理方法研究

The dissertation addressed the problems of signals reconstruction and data restoration in seismic data processing, which takes the representation methods of signal as the main clue, and take the seismic information reconstruction (signals separation and trace interpolation) as the core. On the natural bases signal representation, I present the ICA fundamentals, algorithms and its original applications to nature earth quake signals separation and survey seismic signals separation. On determinative bases signal representation, the paper proposed seismic dada reconstruction least square inversion regularization methods, sparseness constraints, pre-conditioned conjugate gradient methods, and their applications to seismic de-convolution, Radon transformation, et. al. The core contents are about de-alias uneven seismic data reconstruction algorithm and its application to seismic interpolation. Although the dissertation discussed two cases of signal representation, they can be integrated into one frame, because they both deal with the signals or information restoration, the former reconstructing original signals from mixed signals, the later reconstructing whole data from sparse or irregular data. The goal of them is same to provide pre-processing methods and post-processing method for seismic pre-stack depth migration. ICA can separate the original signals from mixed signals by them, or abstract the basic structure from analyzed data. I surveyed the fundamental, algorithms and applications of ICA. Compared with KL transformation, I proposed the independent components transformation concept (ICT). On basis of the ne-entropy measurement of independence, I implemented the FastICA and improved it by covariance matrix. By analyzing the characteristics of the seismic signals, I introduced ICA into seismic signal processing firstly in Geophysical community, and implemented the noise separation from seismic signal. Synthetic and real data examples show the usability of ICA to seismic signal processing and initial effects are achieved. The application of ICA to separation quake conversion wave from multiple in sedimentary area is made, which demonstrates good effects, so more reasonable interpretation of underground un-continuity is got. The results show the perspective of application of ICA to Geophysical signal processing. By virtue of the relationship between ICA and Blind Deconvolution , I surveyed the seismic blind deconvolution, and discussed the perspective of applying ICA to seismic blind deconvolution with two possible solutions. The relationship of PC A, ICA and wavelet transform is claimed. It is proved that reconstruction of wavelet prototype functions is Lie group representation. By the way, over-sampled wavelet transform is proposed to enhance the seismic data resolution, which is validated by numerical examples. The key of pre-stack depth migration is the regularization of pre-stack seismic data. As a main procedure, seismic interpolation and missing data reconstruction are necessary. Firstly, I review the seismic imaging methods in order to argue the critical effect of regularization. By review of the seismic interpolation algorithms, I acclaim that de-alias uneven data reconstruction is still a challenge. The fundamental of seismic reconstruction is discussed firstly. Then sparseness constraint on least square inversion and preconditioned conjugate gradient solver are studied and implemented. Choosing constraint item with Cauchy distribution, I programmed PCG algorithm and implement sparse seismic deconvolution, high resolution Radon Transformation by PCG, which is prepared for seismic data reconstruction. About seismic interpolation, dealias even data interpolation and uneven data reconstruction are very good respectively, however they can not be combined each other. In this paper, a novel Fourier transform based method and a algorithm have been proposed, which could reconstruct both uneven and alias seismic data. I formulated band-limited data reconstruction as minimum norm least squares inversion problem where an adaptive DFT-weighted norm regularization term is used. The inverse problem is solved by pre-conditional conjugate gradient method, which makes the solutions stable and convergent quickly. Based on the assumption that seismic data are consisted of finite linear events, from sampling theorem, alias events can be attenuated via LS weight predicted linearly from low frequency. Three application issues are discussed on even gap trace interpolation, uneven gap filling, high frequency trace reconstruction from low frequency data trace constrained by few high frequency traces. Both synthetic and real data numerical examples show the proposed method is valid, efficient and applicable. The research is valuable to seismic data regularization and cross well seismic. To meet 3D shot profile depth migration request for data, schemes must be taken to make the data even and fitting the velocity dataset. The methods of this paper are used to interpolate and extrapolate the shot gathers instead of simply embedding zero traces. So, the aperture of migration is enlarged and the migration effect is improved. The results show the effectiveness and the practicability.

Detection and Characterization of Long-Pulse Low-Velocity Impact Damage in Plastic Bonded Explosives

Damage not only degrades the mechanical properties of explosives, but also influences the shock sensitivity, combustion and even detonation behavior of explosives. The study of impact damage is crucial in the vulnerability evaluation of explosives. A long-pulse low-velocity gas gun with a gas buffer was developed and used to induce impact damage in a hot pressed plastic bonded explosive. Various methods were used to detect and characterize the impact damage of the explosive. The microstructure was examined by use of polarized light microscopy. Fractal analysis of the micrographs was conducted by use of box counting method. The correlation between the fractal dimensions and microstructures was analyzed. Ultrasonic testing was conducted using a pulse through-transmission method to obtain the ultrasonic velocity and ultrasonic attenuation. Spectra analyses were carried out for recorded ultrasonic signals using fast Fourier transform. The correlations between the impact damage and ultrasonic parameters including ultrasonic velocities and attenuation coefficients were also analyzed. To quantitatively assess the impact induced explosive crystal fractures, particle size distribution analyses of explosive crystals were conducted by using a thorough etching technique, in which the explosives samples were soaked in a solution for enough time that the binder was totally removed. Impact induces a large extent of explosive crystal fractures and a large number of microcracks. The ultrasonic velocity decreases and attenuation coefficients increase with the presence of impact damage. Both ultrasonic parameters and fractal dimension can be used to quantitatively assess the impact damage of plastic bonded explosives.

Interferometric Measurement of Density in Nonstationary Shock Wave Reflection Flow and Comparison with CFD

We present density measurements from the application of interferometry and Fourier transform fringe analysis to the problem of nonstationary shock wave reflection over a semicircular cylinder and compare our experimental measurements to theoretical results from a CFD simulation of the same problem. The experimental results demonstrate our ability to resolve detailed structure in this complex shock wave reflection problem, allowing visualization of multiple shocks in the vicinity of the triple point, plus visualization of the shear layer and an associated vortical structure. Comparison between CFD and experiment show significant discrepancies with experiment producing a double Mach Reflection when CFD predicts a transitional Mach reflection.

Numerical simulation of an adaptive optics system with laser propagation in the atmosphere

A comprehensive model of laser propagation in the atmosphere with a complete adaptive optics (AO) system for phase compensation is presented, and a corresponding computer program is compiled. A direct wave-front gradient control method is used to reconstruct the wave-front phase. With the long-exposure Strehl ratio as the evaluation parameter, a numerical simulation of an AO system in a stationary state with the atmospheric propagation of a laser beam was conducted. It was found that for certain conditions the phase screen that describes turbulence in the atmosphere might not be isotropic. Numerical experiments show that the computational results in imaging of lenses by means of the fast Fourier transform (FFT) method agree well with those computed by means of an integration method. However, the computer time required for the FFT method is 1 order of magnitude less than that of the integration method. Phase tailoring of the calculated phase is presented as a means to solve the problem that variance of the calculated residual phase does not correspond to the correction effectiveness of an AO system. It is found for the first time to our knowledge that for a constant delay time of an AO system, when the lateral wind speed exceeds a threshold, the compensation effectiveness of an AO system is better than that of complete phase conjugation. This finding indicates that the better compensation capability of an AO system does not mean better correction effectiveness. (C) 2000 Optical Society of America.

Abel Inversion of Axially-Symmetric Shock Wave Flows

Finite-fringe interferograms produced for axisymmetric shock wave flows are analyzed by Fourier transform fringe analysis and an Abel inversion method to produce density field data for the validation of numerical models. For the Abel inversion process, we use basis functions to model phase data from axially-symmetric shock wave structure. Steady and unsteady flow problems are studied, and compared with numerical simulations. Good agreement between theoretical and experimental results is obtained when one set of basis functions is used during the inversion process, but the shock front is smeared when another is used. This is because each function in the second set of basis functions is infinitely differentiable, making them poorly-suited to the modelling of a step function as is required in the representation of a shock wave.

Transition to Chaos in the Floating Half Zone Convection

The transition process from steady convection to chaos is experimentally studied in thermocapillary convections of floating half zone. The onset of temperature oscillations in the liquid bridge of floating half zone and further transitions of the temporal convective behaviour are detected by measuring the temperature in the liquid bridge. The fast Fourier transform reveals the frequency and amplitude characteristics of the flow transition. The experimental results indicate the existence of a sequence of period-doubling bifurcations that culminate in chaos. The measured Feigenbaum numbers are delta(2) = 4.69 and delta(4) = 4.6, which are comparable with the theoretical asymptotic value delta = 4.669.

The interaction between poly(vinylpyrrolidone) and reversed micelles of water/AOT/n-heptane

The interactions between poly(vinylpyrrolidone) (PVP) and the reversed micelles composed of water, AOT, and n-heptane are investigated with the aid of phase diagram, measurements of conductivity and viscosity, Fourier transform infrared (FTIR) spectrum, and dynamic light scattering (DLS). The phase diagrams of water/AOT/heptane in the presence of and absence of PVP are given. The conductivity of the water/AOT/heptane reversed micelle without PVP initially increases and then decreases with the increase of water content, ω0 (the molar ratio of water to AOT), while the plots of conductivity (K) versus ω0 of the reversed micelle in the presence of PVP depend on the PVP concentrations. The plot of K versus ω0 with 2.0%wt PVP is similar to that without PVP. Only the ω0,max (the water content that the maximum conductivity corresponds to) is larger than that without PVP. Nevertheless, the conductivity of the reversed micelle containing more than 4%wt PVP always rises with the increase of the water content in the measured range. The DLS results indicate that the hydrodynamic radius (Rh) in the presence and absence of PVP rises with the increase of ω0. The plots with PVP and without PVP have almost the same value when ω0<17; and after that, it quickly increases with the increase of ω0. It is interesting to find that there is almost no effect of the PVP concentration on the viscosity and Rh of the reversed micelle at ω0 = 15. The FTIR results suggest that the contents of SO3--bound water and Na+-bound water both decrease with PVP added, while the content of the bulky-like water increases. However, the trapped water in the hydrophobic chain of the surfactant is nearly unaffected by PVP. It is also found from the FTIR that the carbonyl group stretching vibration of AOT is fitted into two sub-peaks, which center at 1740 and 1729 cm-1, corresponding to the trans and cis conformations of AOT, respectively.