A STATISTICAL THEORY OF APERTURE SYNTHESIS

1967 ◽  
Vol 45 (6) ◽  
pp. 2041-2052
Author(s):  
Ralph J. Gagnon
Keyword(s):  
Point Source ◽  
Random Noise ◽  
Circular Disk ◽  
Brightness Distribution ◽  
Source Distribution ◽  
Base Line ◽  
Fourier Inversion ◽  
Visibility Function ◽  
The Fourier Transform ◽  
Infinite Set

The usual methods of interferometry make use of the Fourier transform relationship which holds between a radio-noise brightness distribution and the complex visibility function which is measured with a pair of antennas. The visibility function is a function of the distance or base line between the antennas. If it were known for all base lines, then the brightness distribution could be found by Fourier inversion. Unfortunately, the visibility function is not known for all base lines and the Fourier inversion is not unique. If the observer wishes to interpret his data by displaying a single possible brightness distribution, then he must choose from the infinite set of brightness distributions which could have produced his data. Previously, the author suggested that this be accomplished by representing the set of possible distributions as a statistical ensemble, and making the choice on a statistical basis so as to minimize the expected mean-square error.In the present communication, the results of the previous paper are presented for the two-dimensional case. The inversion formulas are worked out in detail for the cases of uniform point-source distributions in a square (or rectangle) and in a circular disk, and also for a point-source distribution with a Gaussian envelope taper. It is shown how to extend the point-source results to a distribution of nonpoint sources, and as an example the inversion equations are computed for the case of a distribution of Gaussian-shaped sources distributed with a Gaussian amplitude or density envelope. Finally, the appropriate inversion equations are derived for an observed visibility function which is contaminated with additive zero-mean Gaussian random noise, uncorrelated with the true visibility function.

Pulmonary impedance in dogs measured by forced random noise with a retrograde catheter

1982 ◽  
Vol 52 (3) ◽  
pp. 725-733 ◽  
Author(s):  
J. M. Fullton ◽  
D. A. Hayes ◽  
R. L. Pimmel
Keyword(s):  
Endotracheal Tube ◽  
Airway Resistance ◽  
Random Noise ◽  
Peripheral Resistance ◽  
Base Line ◽  
The Mean ◽  
The Difference ◽  
Central Airway

Retrograde catheter and forced random noise techniques were combined to study the distribution of resistance and compliance in dogs following the inhalation of aerosols containing 2.5 and 5.0 mg/ml of histamine. Mean base-line peripheral resistance was 0.367 cmH2O . l'1 . s, agreeing with previous estimates. After correction for the endotracheal tube, the mean central airway resistance was 0.040 cmH2O . l'1 . s, considerably lower than previous estimates. This discrepancy was attributed to an overcorrection for the endotracheal tube resistance. The lower histamine dose caused a substantial increase in peripheral resistance, a relatively small increase in central resistance, and substantial decreases in total and peripheral compliance. After the higher histamine dose, changes in peripheral resistance and both compliances were similar to those obtained with the lower dose; however, the increase in central resistance was much larger than at the lower dose. The difference between total and peripheral compliance yielded estimates of airway compliance of 0.00306 l/cmH2O before and 0.00104 l/cmH2O after 2.5 mg/ml of histamine.

Energy Eigenvalues and Periodic Orbits for the Circular Disk or Annular Infinite Well

1998 ◽  
Vol 05 (02) ◽  
pp. 519-526 ◽  
Author(s):  
R. W. Robinett
Keyword(s):  
Periodic Orbits ◽  
Mechanical Energy ◽  
Level Density ◽  
Circular Disk ◽  
Energy Eigenvalues ◽  
Inner Radius ◽  
Path Lengths ◽  
The Fourier Transform ◽  
Effective Path ◽  
Quantum Mechanical Energy

We compute the Fourier transform [ρ(L)] of the quantum-mechanical energy level density for the problem of a particle in an annular infinite well (or circular disk) of outer (inner) radius R max =RR min =fR. For various values of f=R min /R we then explicitly compare ρ(L) to the lengths of the classical periodic orbits. We also comment on the diffraction peak seen by Reimann et al. in this system, noting that at least one recurrence of that feature is present in the spectrum, and discussing the corresponding effective path lengths for these features.

A THEOREM ON NEUTRON MULTIPLICATION

1947 ◽  
Vol 25a (4) ◽  
pp. 276-292 ◽  
Author(s):  
G. Placzek ◽  
G. Volkoff
Keyword(s):  
Point Source ◽  
Asymptotic Form ◽  
Homogeneous Medium ◽  
Integral Form ◽  
Exact Expression ◽  
Neutron Distribution ◽  
Chain Reaction ◽  
Neutron Multiplication ◽  
Fission Neutrons ◽  
The Fourier Transform

The asymptotic behaviour of the neutron distribution due to a point source in an infinite homogeneous medium in which a convergent chain reaction (multiplication constant k<1) takes place is investigated without special assumptions about the properties of the medium and the mechanism of neutron diffusion. It is shown under very general assumptions that at large distances r from the point source the neutron distribution always has the form[Formula: see text]General expressions for the constants μ and A of this asymptotic form of the distribution are given for any k<1 in terms of the Fourier transform of the spatial distribution of primary fission neutrons. These expressions reduce to particularly simple form for (1 − k) << 1. The exact expression for the neutron distribution throughout the medium is given in integral form. Four special frequently occurring cases are discussed as illustrations of the general result.

Reflection technique in time‐frequency domain using multicomponent acoustic emission signals and application to geothermal reservoirs

Geophysics ◽  
2002 ◽  
Vol 67 (3) ◽  
pp. 928-938 ◽  
Author(s):  
Nobukazu Soma ◽  
Hiroaki Niitsuma ◽  
Roy Baria
Keyword(s):  
Acoustic Emission ◽  
Wavelet Transform ◽  
Frequency Domain ◽  
Random Noise ◽  
Spherical Shape ◽  
Source Distribution ◽  
S Wave ◽  
Spectral Matrix ◽  
Time Frequency ◽  
Reflected Wave

We have developed a reflection technique for estimating deep geothermal reservoir structures using acoustic emission signals as a source, which is useful when there is no proper estimating technique because of high temperature, high pressure, and great depth. Because its resolution is not high enough for comparison with methods such as well logging, we have enhanced the technique by developing a time–frequency‐domain analysis of multicomponent acoustic emission signals using a wavelet transform. The reflected wave is separated from an incoherent coda by analyzing the shape of a 3‐D hodogram: a linear shape indicates the arrival of a coherent signal such as a reflected wave, and an incoherent signal such as a coda makes a spherical shape. We construct a spectral matrix of 3‐D particle motion using a wavelet transform, as is done in a time–frequency domain. We evaluate the linearity of the 3‐D hodogram for each time and frequency by using the eigenvalues of the spectral matrix. Three‐dimensional inversion of the distribution of hodogram linearity in the time–frequency domain lets us image the deep subsurface structure. The inversion is based on the diffraction stack. We reduce the uncertainties by investigating S‐wave polarization direction, and we compensate for inhomogeneous source distribution to get reliable estimates with high resolution. We then evaluate our methods with synthetic signals. We discriminate a coherent wave from incoherent random noise in the presence of an S/N ratio of −3.7 dB and detect reflectors at correct depths with a small number of detectors. We apply the method to data from the European hot, dry rock site in Soultz‐sous‐Forêts, France, and compare our estimates with those from a number of borehole observations. The detected reflectors agree with the location of fracture zones. We demonstrate the feasibility of the method for detecting reflectors at great depths.

scholarly journals STUDY OF CHANGES IN THE CONCENTRATION OF A POLLUTANT IN THE SPACE OF EMISSIONS FROM A POINT SOURCE

2020 ◽  
Vol 2020 (1) ◽  
pp. 9-14
Author(s):  
Oksana Blaschinskaya ◽  
Vladimir Kobozev ◽  
Konstantin Patrushev
Keyword(s):  
Point Source ◽  
Emission Source ◽  
Standard Approach ◽  
Source Distribution

A standard approach to modeling the concentration of a pollutant in the system “emission source - distribution of pollutant in space” is considered.

Digital Image Processing of High Resolution 500KV Micrographs

1981 ◽  
Vol 39 ◽  
pp. 234-235
Author(s):  
E.J. Kirkland ◽  
B.M. Siegel ◽  
N. Uyeda ◽  
Y. Fujiyoshi
Keyword(s):  
Phase Contrast ◽  
Transfer Functions ◽  
Spherical Aberration ◽  
Random Noise ◽  
Image Plane ◽  
Partial Coherence ◽  
Thin Specimen ◽  
The Fourier Transform ◽  
Image Position ◽  
Contrast Image

The predominate linear components of a defocus series of bright field phase contrast electron micrographs of a thin specimen may be represented in Fourier space as;(1)If there are m micrographs in the series then are m dimensional vectors, each component of which represents one micrograph. is the Fourier transform of the recorded defocus series and is the random noise content of is an mx2 matrix representing the transfer functions of the microscope (including spherical aberration, defocus, and partial coherence). is a two component vector representing the two components (real and imaginary) of the ideal unaberrated phase contrast image, is a two dimensional spatial frequency vector in the image plane.

scholarly journals HIGH-RESOLUTION AUTORADIOGAPHY

1962 ◽  
Vol 15 (2) ◽  
pp. 189-199 ◽  
Author(s):  
Lucien G. Caro
Keyword(s):  
Bacillus Subtilis ◽  
Point Source ◽  
Cross Sections ◽  
Source Distribution ◽  
Silver Bromide ◽  
Photographic Emulsion ◽  
Nuclear Region ◽  
Electron Microscopic ◽  
Beta Particles ◽  
Extended Sources

The resolution obtainable in electron microscopic autoradiographs, using a photographic emulsion consisting of a monolayer of silver bromide crystals, was investigated theoretically and experimentally. The expected distribution of exposed crystals around a point source was calculated from the geometry of the preparation and from the range distribution of the beta particles emitted by tritium. From such a distribution an autoradiographic resolution of the order of 1000 A can be predicted. From the point source distribution, the expected distribution of grains around bacteriophages labeled with tritium was calculated. This distribution was also measured experimentally in electron microscopic autoradiographs of bacteriophages T-2 labeled with thymidine-H3. The two distributions agreed closely. It was also verified, using the nuclear region in thin cross-sections of Bacillus subtilis labeled with thymidine-H3, that resolutions of the same order were obtained for extended sources. It was concluded that an autoradiographic resolution of 1000 A could be achieved with a presently available commercial emulsion, although emulsions with finer grains might be desirable in some circumstances.

Correlation of airway resistance with forced random noise resistance parameters

1981 ◽  
Vol 51 (1) ◽  
pp. 33-39 ◽  
Author(s):  
R. L. Pimmel ◽  
J. M. Fullton ◽  
J. F. Ginsberg ◽  
M. J. Hazucha ◽  
E. D. Haak ◽  
...  
Keyword(s):  
Airway Resistance ◽  
Random Noise ◽  
Linear Regression Analysis ◽  
Base Line ◽  
Regression Equations ◽  
Noise Resistance ◽  
Peripheral Airways ◽  
Average Resistance ◽  
Serial Measurements ◽  
Central Airway

The correlation between airway resistance (Raw) measured in a plethysmograph and three respiratory resistance parameters measured by forced random noise was evaluated. Forced random noise resistance parameters were the average resistance between 5 and 9 hz (R5–9), the average resistance between 20 and 24 Hz (R20–24), and the extrapolated resistance at 1 Hz (R1). We studied 22 healthy, nonsmoking subjects, 10 of whom had a history suggesting childhood asthma. Serial measurements were made after inhalation of aerosols containing increasing concentrations of methacholine of aerosols containing increasing concentrations of methacholine to obtain data in various stages of bronchoconstriction. There was a broad range of responsiveness to methacholine; the ratio of the peak to base-line values of Raw ranged from 1.1 to 6.3. R1, R5–9, and R20–24 were related to Raw by linear regression analysis. R1 and R5–9 showed excellent correlation with Raw (r = 093 and 4=0.91, respectively); R20–24 showed much poorer correlation (r = 0.62). The slopes of the regression equations for R1 and R5–9 were 1.56 and 0.51, respectively; thus neither provided an exact measure of Raw. The data appear to be consistent with a model in which most of the methacholine-induced increase in resistance occurred in the peripheral airways and only a small fraction in the central airway.

Sign in / Sign up

Export Citation Format

Share Document