Numerical experiments on one-dimensional model of turbulence

The initial-value problem of a forced Burgers equation is numerically solved by the Fourier expansion method. It is found that its solutions finally reach a steady state of 'laminar flow' which has no randomness and is stable to disturbances. Hence, strictly speaking, the so-called Burgers turbulence is not a turbulence. A new one-dimensional model is proposed to simulate the Navier-Stokes turbulence. A series of numerical experiments on this one-dimensional turbulence is made and is successful in obtaining Kolmogorov's (1941) k exp(-5/3) inertial-range spectrum. The (one-dimensional) Kolmogorov constant ranges from 0.5 to 0.65.

Singularity criteria for perturbation series

This paper is concerned with some mathematical aspects of the Van Dyke method inperturbation theory, i.e. the singularity criteria of perturbation series. The author suggestsa sign criterion and a Domb-syke plot for the cases with complex conjugate singularities, thussucceeding in extending the conclusions of Van Dyke's. Subsequently. effects of singularitiesof the lower order upon the criteria are taken into account. In addition, a method of locat-ing singular points is developed by analysing the new perturbation series derived by the Eulertransformation.

用Fourier变换莫尔法测量流体自由表面微幅波的振幅

采用一种非接触的光学方法——傅立叶变换莫尔法（Fourier transform method），结合数字图像处理技术，对微幅振荡的水表面波的振幅进行测量。它是对全场中每一个像素点进行测量，比接触测量法具有更高的灵敏度。它为微幅水表面波振幅的测量提供了一种手段。通过将计算机生成的周期性光栅图像经投影机直接投影到被测物体的参考平面，经CCD摄像头、图像板捕捉存储形成数字化的光栅图像，利用傅立叶变换莫尔法处理光栅图像，从而获得包含有水表面波的振幅的相位信息，再经适当的几何变换获得振幅信息。我们在生趣振荡装置上进行了不同激励频率和不同振幅的表面波的振幅测量。

Complex Transition of Double-Diffusive Convection in a Rectangular Enclosure with Height-to-Length Ratio Equal to 4: Part I

This is the first part of direct numerical simulation (DNS) of double-diffusive convection in a slim rectangular enclosure with horizontal temperature and concentration gradients. We consider the case with the thermal Rayleigh number of 10^5, the Pradtle number of 1, the Lewis number of 2, the buoyancy ratio of composition to temperature being in the range of [0,1], and height-to-width aspect ration of 4. A new 7th order upwind compact scheme was developed for approximation of convective terms, and a three-stage third-order Runge-Kutta method was employed for time advancement. Our DNS suggests that with the buoyancy ratio increasing form 0 to 1, the flow of transition is a complex series changing fromthe steady to periodic, chaotic, periodic, quasi-periodic, and finally back to periodic. There are two types of periodic flow, one is simple periodic flow with single fundamental frequency (FF), and another is complex periodic flow with multiple FFs. This process is illustrated by using time-velocity histories, Fourier frequency spectrum analysis and the phase-space rajectories.

A two-step phase-retrieval method in Fourier-transform ghost imaging

A two-step phase-retrieval method, based on Fourier-transform ghost imaging, was demonstrated. For the complex objects, the phase-retrieval process was divided into two steps: first got the complex object's amplitude from the Fourier-transform patterns of the squared object function, then combining with the Fourier-transform patterns of the object function to get the phase. The theoretical basis of this technique is outlined, and the experimental results are presented. (C) 2008 Elsevier B.V. All rights reserved.

Observing the fractional Fourier transform by free-space Fresnel diffraction

The fractional Fourier transform of an object can be observed in the free-space Fresnel diffraction pattern of the object. (C) 1997 Optical Society of America

Scaled fractional Fourier transform and its optical implementation

The scaled fractional Fourier transform is suggested and is implemented optically by one lens for different values of phi and output scale. In addition, physically it relates the FRT with the general lens transform-the optical diffraction between two asymmetrically positioned planes before and after a lens. (C) 1997 Optical Society of America.

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.

Optical multichannel-scale range-tunable Fourier-transforming system: experiment

The authors have demonstrated the principle of a novel optical multichannel-scale range-tunable Fourier-transforming system. The experimental results show good agreement with the theoretical analysis.

Quantitative measurement of domain inversion in RuO2 : LiNbO3 crystal by digital holographic interferometry

We quantitatively study the domain inversion in a RuO2:LiNbO3 crystal wafer by the digital holographic interferometry. The crystal wafer is placed into one arm of a Mach-Zehnder-type interferometer to record a series of holograms. Making use of the angular spectrum backward propagation algorithm, we reconstruct the optical wave field in the crystal plane. The extracted phase difference from the reconstructed optical wave field is a well linear function of the applied external voltage. We deduce that the linear electro-optic coefficient of the detected RuO2:LiNbO3 crystal sample is 9.1x10(-12) m/V. An unexpected phase contrast at the antiparallel domain wall is observed and the influence of the applied external voltage on it is studied in detail. Also the built-in internal field is quantitatively measured as 0.72 kV/mm. (c) 2006 American Institute of Physics.

Time domain synthesis of electro-optical birefringent system for optical waveform generation

In this paper is described a novel technique for producing an electro-optical intensity synthesizer which can generate different periodic time domain waveforms through only sine or cosine wave applied-voltages. The synthesizer presented here consists of a series of stages between two polarizers, with each stage consisting of an electro-optic element and a compensator. Every electro-optical element has the same applied-voltage function but different azimuth angles and ratios between the longitudinal and transverse lengths. The main principle is the synthesis of an electro-optic effect and a polarization interference effect in the time domain. This technique is based on an expanded Fourier positive-direction searching algorithm, which can not only simplify the calculation process but also produces many choices of structural parameters for different waveforms generation. A three-stage synthesis of an electro-optical birefringent system for continuous square waveform is undertaken to prove the principle.

Full-range parallel Fourier-domain optical coherence tomography using sinusoidal phase-modulating interferometry

We demonstrate a full-range parallel Fourier-domain optical coherence tomography (FD-OCT) in which a tomogram free of mirror images as well as DC and autocorrelation terms is obtained in parallel. The phase and amplitude of two-dimensional spectral interferograms are accurately detected by using sinusoidal phase-modulating interferometry and a two-dimensional CCD camera, which allows for the reconstruction of two-dimensional complex spectral interferograms. By line-by-line inverse Fourier transformation of the two-dimensional complex spectral interferogram, a full-range parallel FD-OCT is realized. Tomographic images of two separated glass coverslips obtained with our method are presented as a proof-of-principle experiment.

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.