Mosource—A novel simple seismic source

Geophysics ◽  
1984 ◽  
Vol 49 (10) ◽  
pp. 1798-1799
Author(s):  
M. H. Safar
Keyword(s):  
Fourier Transform ◽  
Transfer Function ◽  
Seismic Source ◽  
Calibration Method ◽  
Comparison Method ◽  
Sensitivity Factor ◽  
Popular Method ◽  
Comparison Calibration ◽  
The Fourier Transform ◽  
Marine Seismic

One very popular method used for calibrating pressure detectors (hydrophones) in the seismic band is the comparison method. The comparison calibration method, which is widely used (Safar and Newman, 1981) in calibrating marine seismic streamers, can be briefly described as follows. A seismic source is placed at some distance from a standard hydrophone with known transfer function [Formula: see text] and sensitivity factor [Formula: see text]. The pressure detector under test is placed as near as possible to the standard hydrophone so that the Fourier transform of the incident pressure, [Formula: see text], generated by the seismic source at the pressure detector and the standard hydrophone, can be assumed to be the same. Thus the Fourier transform of the output voltages [Formula: see text] and [Formula: see text] of the standard hydrophone and the pressure detector are given as [Formula: see text], (1) and [Formula: see text], (2) where [Formula: see text] and [Formula: see text] are the transfer function and sensitivity factor of the pressure detector. Elimination of [Formula: see text] between equations (1) and (2) gives [Formula: see text]. (3)

On-line electron-optical correlation computing in the CTEM

1978 ◽  
Vol 36 (1) ◽  
pp. 88-89 ◽  
Author(s):  
R. Guckenberger ◽  
W. Hoppe
Keyword(s):  
Fourier Transform ◽  
Correlation Function ◽  
Transfer Function ◽  
Inverse Fourier Transform ◽  
Main Peak ◽  
Optical Correlation ◽  
Auto Correlation ◽  
Auto Correlation Function ◽  
On Line ◽  
The Fourier Transform

Light diffractograms of electron micrographs are frequently used to study the transfer function of the microscope. In order to utilize diffractograms for control operations in the microscope, several attempts have been undertaken to obtain on-line diffractograms /1 - 3/. Alternatively correlation functions (CF) may be used /4-8/. In this paper we describe an electron-optical device for the computation of such CF and its on-line operation in a microscope.The auto-correlation function (ACF) is the inverse Fourier transform of the squared modulus of the Fourier transform (diffractogram) of an image. Therefore it also contains the transfer function. It is its zero peak (main peak) which is of particular interest. In noisy images the main ACF-peak of the noise contributes in an unwanted way to the main ACF-peak of the image. This can be avoided if the ACF will be computed of two images which are identical except for noise /9/ (noise-reduced ACF= NRACF).

On the Simulation of EEL Spectra Corresponding to Solid and Gaseous Samples

1990 ◽  
Vol 48 (2) ◽  
pp. 18-19
Author(s):  
G. Zanchi ◽  
Y. Kihn ◽  
J. Sévely
Keyword(s):  
Fourier Transform ◽  
Transfer Function ◽  
Energy Loss ◽  
Electron Interaction ◽  
Fourier Space ◽  
Angular Scattering ◽  
The Fourier Transform ◽  
Image Position ◽  
Electron Energy Loss ◽  
Electron Energy Loss Spectra

The electron energy loss spectra can be considered as the result of the convolution of elementary inelastic scattering processes (1, 2). We have developed a procedure which allows to write the intensity of the spectrum as a function of the energy loss.These calculations take the electron angular scattering into account.The probability for an electron to suffer an energy loss E and to be deviated through an angle after a single electron-electron interaction of any kind is given by a normalized function D(E, ), which can be written with a good approximation as a product of two functions g(E) and f(), separately normalized. Assuming that the excitation probabilities of any interaction follows a Poisson distribution, for a collection angle θd the intensity of the spectrum can be written in the Fourier space :Gs(ω) is the Fourier transform of GS(E) which characterizes the transfer function of the experimental device.

Point Resolution Below 1 Å by Means of Electron Holography?

1990 ◽  
Vol 48 (1) ◽  
pp. 226-227
Author(s):  
Edgar Völkl ◽  
Hannes Lichte
Keyword(s):  
Fourier Transform ◽  
Electron Microscope ◽  
Transfer Function ◽  
Optical Resolution ◽  
Object Wave ◽  
Objective Lens ◽  
Electron Holography ◽  
Resolution Limit ◽  
The Fourier Transform ◽  
Image Position

The optical resolution limit δD according to Lord Rayleigh is given by δD = 0.61 λ/α0 where an is the aperture of the objective lens and λ the wavelength. Assuming identical conditions in an electron microscope, one would obtain (depending on the accelerating voltage) a resolution of several 0.001 nm. However, the actual resolution limit is found to be worse by a factor of a hundred. This is due to the aberrations of the objective lens. Generally, the image wave if>(x,y) is given by the convolution of the object wave ψx,y) with the Fourier transform of the wave transfer function exp(ix) (assuming isoplanacy),

scholarly journals Spectral transfer function of the Fourier transform spectral imager

2009 ◽  
Vol 58 (8) ◽  
pp. 5399
Author(s):  
Xiangli Bin ◽  
Yuan Yan ◽  
Lyu Qun-Bo
Keyword(s):  
Fourier Transform ◽  
Transfer Function ◽  
The Fourier Transform ◽  
Spectral Imager

scholarly journals Strain Sensitivity Enhancement of Broadband Ultrasonic Signals in Plates Using Spectral Phase Filtering

2021 ◽  
Vol 11 (6) ◽  
pp. 2582
Author(s):  
Lucas M. Martinho ◽  
Alan C. Kubrusly ◽  
Nicolás Pérez ◽  
Jean Pierre von der Weid
Keyword(s):  
Fourier Transform ◽  
Guided Waves ◽  
Strain Level ◽  
Energy Concentration ◽  
Short Time Fourier Transform ◽  
Time Frequency ◽  
Frequency Representation ◽  
The Fourier Transform ◽  
Short Time ◽  
Sensitivity Gain

The focused signal obtained by the time-reversal or the cross-correlation techniques of ultrasonic guided waves in plates changes when the medium is subject to strain, which can be used to monitor the medium strain level. In this paper, the sensitivity to strain of cross-correlated signals is enhanced by a post-processing filtering procedure aiming to preserve only strain-sensitive spectrum components. Two different strategies were adopted, based on the phase of either the Fourier transform or the short-time Fourier transform. Both use prior knowledge of the system impulse response at some strain level. The technique was evaluated in an aluminum plate, effectively providing up to twice higher sensitivity to strain. The sensitivity increase depends on a phase threshold parameter used in the filtering process. Its performance was assessed based on the sensitivity gain, the loss of energy concentration capability, and the value of the foreknown strain. Signals synthesized with the time–frequency representation, through the short-time Fourier transform, provided a better tradeoff between sensitivity gain and loss of energy concentration.

Determination of starch crystallinity with the Fourier-transform terahertz spectrometer

2021 ◽  
Vol 262 ◽  
pp. 117928
Author(s):  
Shusaku Nakajima ◽  
Shuhei Horiuchi ◽  
Akifumi Ikehata ◽  
Yuichi Ogawa
Keyword(s):  
Fourier Transform ◽  
The Fourier Transform ◽  
Starch Crystallinity

Translation uniqueness of phase retrieval and magnitude retrieval of band-limited signals

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Lung-Hui Chen
Keyword(s):  
Fourier Transform ◽  
Entire Function ◽  
Convex Hull ◽  
Scattering Theory ◽  
Phase Retrieval ◽  
Indicator Function ◽  
Band Limited ◽  
The Fourier Transform ◽  
Complex Valued ◽  
Spectral Invariant

Abstract In this paper, we discuss how to partially determine the Fourier transform F ⁢ ( z ) = ∫ - 1 1 f ⁢ ( t ) ⁢ e i ⁢ z ⁢ t ⁢ 𝑑 t , z ∈ ℂ , F(z)=\int_{-1}^{1}f(t)e^{izt}\,dt,\quad z\in\mathbb{C}, given the data | F ⁢ ( z ) | {\lvert F(z)\rvert} or arg ⁡ F ⁢ ( z ) {\arg F(z)} for z ∈ ℝ {z\in\mathbb{R}} . Initially, we assume [ - 1 , 1 ] {[-1,1]} to be the convex hull of the support of the signal f. We start with reviewing the computation of the indicator function and indicator diagram of a finite-typed complex-valued entire function, and then connect to the spectral invariant of F ⁢ ( z ) {F(z)} . Then we focus to derive the unimodular part of the entire function up to certain non-uniqueness. We elaborate on the translation of the signal including the non-uniqueness associates of the Fourier transform. We show that the phase retrieval and magnitude retrieval are conjugate problems in the scattering theory of waves.

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