Experimental Consideration of Two-Dimensional Fourier Transform Spectroscopy

Two-dimensional Fourier transform(2D FT) spectroscopy is an important technology that developed in recent decades and has many advantages over other ultrafast spectroscopy methods. Although 2D FT spectroscopy provides great opportunities for studying various complex systems, the experimental implementation and theoretical description of 2D FT spectroscopy measurement still face many challenges, which limits their wide application.Recently, the 2D FT spectroscopy reaches maturity due to many new developments which greatly reduces the technical barrier in the experimental implementation of the 2D FT spectrometer. There have been several different approaches developed for the optical design of the 2D FT spectrometer, each with its own advantages and limitations. Thus, a procedure to help an experimentalist to build a 2D FT spectroscopy experimental apparatus is needed.This tutorial review is intending to provide an accessible introduction for a beginner to build a 2D FT spectrometer.

Numerical Approximation of Real Finite Nonnegative Function by the Modulus of Discrete Fourier Transform

The numerical algorithms for finding the lines of branching and branching-off solutions of nonlinear problem on mean-square approximation of a real finite nonnegative function with respect to two variables by the modulus of double discrete Fourier transform dependent on two parameters, are constructed and justified.

Numerical Solution of Mean-Square Approximation Problem of Real Nonnegative Function by the Modulus of Double Fourier Integral

A nonlinear problem of mean-square approximation of a real nonnegative continuous function with respect to two variables by the modulus of double Fourier integral dependent on two real parameters with use of the smoothing functional is studied. Finding the optimal solutions of this problem is reduced to solution of the Hammerstein type two-dimensional nonlinear integral equation. The numerical algorithms to find the branching lines and branching-off solutions of this equation are constructed and justified. Numerical examples are presented.

Calibration Algorithm of Surface Charge Density on Insulating Materials Measured by Pockels Technique

Surface charges greatly affect the discharge/flashover development process across an insulator. The relationship between surface charge distribution on insulating materials and measurement data based on Pockels technique is discussed, and an improved algorithm is built to calculate the real surface charge density from original data. In this algorithm, two-dimensional Fourier transform technique and Wiener filter are employed to reduce the amount of numerical calculation and improve the stability of computation, Moreover, this algorithm considers not only the influence of sample＇s thickness and permittivity, but also the impact of charges at different positions. The achievement of this calibration algorithm is demonstrated in details. Compared with traditional algorithms, the improved one supplies a better solution in the calibration of surface charge distribution on different samples with different thickness.

Quantitative Rectangular Notch Detection of Laser-induced Lamb Waves in Aluminium Plates with Wavenumber Analysis

It is difficult to quantitatively detect defects by using the time domain or frequency domain features of Lamb wave signals due to their dispersion and multimodal characteristics.Therefore,it is important to discover an intrinsical parameter of Lamb waves that could be used as a damage sensitive feature.In this paper,quantitative defect detection in aluminium plates is carried out by means of wavenumber analysis approach.The wavenumber of excited Lamb wave mode is a fixed value,given a frequency,a thickness and material properties of the target plate.When Lamb waves propagate to the structural discontinuity,new wavenumber components are created by abrupt wavefield change.The new wavenumber components can be identified in the frequency-wavenumber domain.To estimate spatially dependent wavenumber values,a short-space two-dimensional Fourier transform(FT)method is presented for processing wavefield data of Lamb waves.The results can be used to determine the location,size and depth of rectangular notch.The analysis techniques are demonstrated using simulation examples of an aluminium plate with a rectangular notch.Then,the wavenumber analysis method is applied to simulation data that are obtained through a range of notch depths and widths.The results are analyzed and rules of the technique with regards to estimating notch depth are determined.Based on simulation results,guidelines for using the technique are developed.Finally,experimental wavefield data are obtained in aluminium plates with rectangular notches by a full noncontact transceiving method,i.e.,laser-laser method.Band-pass filtering combined with continuous wavelet transform is used to extract a certain frequency component from the full laser-induced wavefield with wide band.Shortspace two-dimensional FT method is used for further processing full wavefield data at a certain frequency to estimate spatially dependent wavenumber values.The consistency of simulation and experimental results shows the effectiveness of proposed wavenumber method for quantitative rectangular notch detection.

Measuring Structural Parameters of Knitted Fabrics by Digital Image Processing Techniques

In the knitting industry the measurements of the stitch density and the stitch length are usually done manually, which may lead to lower efficiency and less definition and also bring subjective ideas into the test results. In order to improve the effect we can measure with Digital Image Processing Techniques. A piece of sample is scanned into computer and changed into a digital image, which is processed with media filtering. To acquire the power spectrum, the image in the spatial domain is converted into the frequency domain. Picking up the characteristic points describing the stitch density and the stitch length separately in the power spectra and reconstructing them, the values of the stitch density and the stitch length could be calculated. When measuring the stitch length, we should establish a geometric model of the stitch based en the digital image processing, which provides a method to transform the stitch length in the two-dimensien space into the three-dimensien space and to measure the value of the stitch length more accurately. This method also provides a new way to measure the stitch length without damaging the fabric.

DECONVOLUTION METHOD BASED ON THE DOUBLE PASS THROUGH THE HUMAN EYE

The Paper Presents a deconvolution method based on the double passthrough the human eye By using an optical-digital-computer. S system, the methodsolves the point-spread function and the optical transfer function of the optical systemof eye from the reflective image of retina, reconstructs the retinal image.As the double pass feature says, in the Positive direction and negative direction ofthe light propagation, the amplitude spread function is the same along the same media ofeye. If He-Ne laser beam is used as a short-time point impulse source, the incident lightcan be referred to as coherent light. Because the surface of retina is not fine smooth,usually the reflection is in company with the scattering, the reflective light beam is considered as incoherent light. After many times of flashings, samplings and averagings,the reflective ratio of retina will approximate to a constant and be neglected. Therefore,the conclusion is: the light intensity distribution outside of eye is the auto-convolution ofthe light intensity distribution of the renal image, i. e. the auto-convolution of thePOint-spread function. By the convolution theorem in the spatial frequency domain,two-dimensional Fourier transform of the point-spread runction, i. e. the optical transfer runction (OTF), can be calculated. Sequentially, by inverse Fourier transform, thePOint-spead function (PSF) is obtained. Thus the de-auto-convolution is accomplished.If a real picture replaces the point light source, the picture image on the fovea near thelight axis and then is reflected incoherently, the intensity distribution of the receivedimage outside of eye is equal to the crossconvolution between the intensity distribution ofretina and the point-spread function. By doing deconvolution once more. i. e. once decross-convolution, the retinal image of the picture can be reconstructed. The results ofthe experiments show that the hybrid system is advanced at the objectivity, auto-calibration and dynamic recording.

Fe_3O_4 nano-whiskers by ultrasonic-aided reduction in concentrated NaOH solution

Fe3O4 nano-whiskers were synthesized via ultrasonic-aided reduction of FeCl2.4H2O with N2H4-H2O in concentrated NaOH solution. Phase identification and morphology observation were conducted by X-ray diffraction （XRD） analysis, transmission electron microscopy （TEM） and field emission scanning electron microscopy （FE-SEM）. Face scanning energy dispersive spectrum （face scanning EDS） and twodimensional fast Fourier transform （2DFFF） for element distribution were carried out for confirming composition homogeneity. From XRD and TEIVI, the synthesized Fe304 nano-whiskers are of cubic phase with average dimension of 20 nm~ 200 nm （average aspect ratio of 10）. FE-SEM shows that the nanowhiskers without dispersion are interconnected into a network at a scale of 20μm. 2DFFT of the distribution of Fe and O from face scanning EDS confirms the composition homogeneity of the synthesized Fe3O4. Hydrazine hydrate determines the formation of the nano-whiskers, while the possible mechanism is the preferred growth along certain orientation with the aid of ultrasonic treatment.