Order Fourier Coefficients Research Articles

A FOURIER SERIES APPROACH TO THE MEASUREMENT OF FLEXURAL WAVE INTENSITY IN PLATES

In regions sufficiently remote from excitation and discontinuities, the flexural motion of a plate can be expressed as the sum of plane propagating waves. In this paper this fact is used as the basis of a wave-based technique for plate intensity measurement. It is assumed that far field conditions exist, and that the displacement within a region can be described as the sum of a set of plane waves the amplitude of which is a function of propagation direction. This function is approximated using a truncated complex Fourier series. It is shown that the time-averaged intensity at the co-ordinate origin can be written in terms of the five Fourier coefficients of lowest order. The effect that the choice of measured variables and measurement locations have on systematic errors and on the conditioning of the problem is discussed. A numerical comparison, under specific conditions, between a Fourier series approach and a finite difference approach to plate intensity measurement is shown. This indicates that the Fourier series approach can offer a better compromise between systematic and random errors. Experimental intensity measurements illustrating the use of the Fourier series approach are presented and discussed.

The multitap lock-in CCD with offset subtraction

An image sensor for the two-dimensional (2-D) synchronous detection of temporal properties of modulated optical wave fields is presented. Each pixel of this multitap lock-in CCD is capable of acquiring all optical data for the extraction of modulation amplitude, relative phase, background level, and higher order Fourier coefficients. By employing the pixels' offset subtraction stages, a dynamic range of >100 dB was obtained experimentally.

A fourier analysis dynamic birefringence apparatus

AbstractMolecular motion in a polymeric system can be studied using dynamic birefringence. Computer interfacing of the dynamic birefringence apparatus and the data treatment using Fourier analysis are reported in this paper. Experiments are done under sinusoidal strain; stress, strain and birefringence signals are monitored. Birefringence is measured using the optical transmission technique. An AIM‐65 microcomputer was interfaced with this apparatus for the purposes of data acquisition and data analysis. First‐order Fourier coefficients are used to determine the real and imaginary components of the modulus, the strain optical coefficient, and the stress optical coefficient. Higher order Fourier coefficients can be used to study the nonlinear viscoelastic behavior in the polymer.

An Edge Detection Algorithm for Attenuation Correction in Emission CT

A new body edge detection algorithm is presented for attenuation compensation based on calculation in emission computed tomography. Based on the differential geometry, the edge contour on the image plane can be calculated directly from the edge detected on the projection data. A new algorithm is; (1) detect edge contour on projection data, (2) smooth noisy contour by retaining lower order Fourier coefficients and (3) transform it to the edge contour on the image. Manipulation of two dimensional array is only needed in step (1) and the rest can be done by manipulation of one dimensional array. Robustness of the algorithm was tested on the threshold level and number of Fourier coefficients. The algorithm was applied to positron emission computed tomography. It can be applied to single photon emission computed tomography as well.

Fourier transform photoelectron spectroscopy

This paper describes a new method of data acquisition and analysis for photoelectron spectroscopy (ESCA/UPS). Rather than sweeping through a preset range of energies at a constant rate accumulating count rates at each energy, nonlinear sweeps are used for each Fourier coefficient of the spectrum. Compared to conventional scan mode, this method offers two advantages: (1) The noise contents of each Fourier coefficient can be predetermined by setting the length of the sweep interval. This is very helpful for the subsequent application of deconvolution techniques because they amplify the contribution of higher order components. Using time efficiently, the noise contents of these components can be reduced more than the noise of lower order contributions. This is not possible for spectra taken by normal means because their noise spectra are flat. (2) Much time can be saved by not recording higher order Fourier coefficients whose contribution to the spectrum is negligible. A data acquisition system for ESCA has been developed to test these advantages. Spectra taken by conventional scan mode and by Fourier transform photoelectron spectroscopy (FTPS) are presented for comparison.

The structural properties of Cepheid velocity curves

Fourier decompositions are performed on the velocity curves of 11 classical Cepheids. The progression of curve shape with period is described in terms of combinations of the lower order Fourier coefficients. These quantities are shown to change with pulsation period in a manner similar to that already demonstrated for Cepheid light variations (Simon and Lee). We recommend further velocity observations, particularly in the period range 10 ~ P ~ 16 days. Subject headings: stars: Cepheids stars: pulsation

Pattern Synthesis of Linear Arrays Using Fourier Coefficient Matching

This paper presents a computer technique for synthesizing an array pattern for the practical problem in which only the magnitude of the far‐field pattern is specified. The general design problem is one in which both the currents and the spacings of the elements are allowed to be variables. The synthesis is based on a procedure which minimizes the norm of the difference between the Fourier coefficients of the desired and actual patterns. This criterion is very useful from practical design considerations since it allows one to determine a priori the highest order Fourier coefficient that can be approximated if the maximum array size is specified. Also, if no array size is specified, the procedure gives the array size necessary to obtain a given degree of approximation in the pattern.

Magnetic torque measurements on cubic manganese ferrites

Magnetic crystal anisotropy of the cubic MnxFe3−xO4 (x=0·99, 1·24 and 1·6) single crystals was measured down to liquid helium temperatures using the torque method. Fourier analysis of the torque curves in the (001), (011), and (111) crystallographic planes showed that higher order Fourier coefficients are not insignificant in this description. The anomalies observed are explained as caused by the Mn3+ ions whose5Eg electron ground states are strongly coupled to the crystal lattice.

A Technique for Recovering Doppler Line Profiles from Fabry-Perot Interferometer Fringes of Very Low Intensity

A technique for recovering doppler line profiles from Fabry-Perot interferometer fringes of very low intensity is described. The technique is based on a fourier decomposition of the data and a subsequent nonlinear least squares fit of the low order fourier coefficients to the fourier decomposition of an ideal instrument function. The ideal instrument function is expressed by the convolution of various instrument broadening functions and includes a parametric representation of the actual instrument. The method for recovering doppler temperature, emission line intensity, and mass motion of the emitting molecules is described. A theoretical analysis of errors for doppler temperature and emission line intensity is made for a statistical noise distribution superimposed upon a fringe profile of very low intensity. These errors are related to the emission line intensity, number of data points per fringe, background continuum level, and instrument parameters. As a specific example, the errors in retrieving the doppler temperature from the 6300-A atomic oxygen emission line OI((1)D - (3)P) in the nightglow are determined for the 15-cm Fabry-Perot interferometer at the University of Michigan Airglow Observatory.