Corrigendum to “Optical radiation flux illuminating a circular disk from an off-axis point source through two different homogeneous refractive media” [Opt. Commun. 211 (2002) 15–30]

2014 ◽  
Vol 313 ◽  
pp. 392-393 ◽  
Author(s):  
Stanislaw Tryka
Keyword(s):  
Point Source ◽  
Optical Radiation ◽  
Radiation Flux ◽  
Circular Disk

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.

scholarly journals The Statistics Of Nearly On-Axis Gravitational Lensing Events

1996 ◽  
Vol 173 ◽  
pp. 371-376
Author(s):  
Yun Wang
Keyword(s):  
Point Source ◽  
Gravitational Lensing ◽  
Small Volume ◽  
Radiation Flux ◽  
Source Size ◽  
Gravitational Lens ◽  
Initial Examination ◽  
Maximum Flux ◽  
Finite Source ◽  
Approach Zero

A small volume of space, nearly on-axis behind a gravitational lens with respect to a given source, will receive a greatly increased radiation flux. In the idealized case of a point mass lens acting on a point source in complete isolation, the volume will approach zero only as the flux tends to infinity; in fact, the volume weighted rms flux is divergent. In realistic cases, finite source size and the effects of other gravitational deflections (i.e., non-zero shear) limit the maximum flux and considerably complicate the physics, but very large fluxes are still produced in small volumes. We consider the physics and statistics of these Extreme Gravitational Lensing Events (EGLE) and present an initial examination of their possible astrophysical effects for various known and putative populations of lensing objects and sources, with particular attention to the case in which finite source size is important but shear is not.

scholarly journals The effect of mesh division of a volume source on calculated radiation flux distribution

2015 ◽  
Vol 30 (1) ◽  
pp. 55-60
Author(s):  
Kyung-O Kim ◽  
Chul-Gyo Seo ◽  
Chul Lee
Keyword(s):  
Point Source ◽  
Radiation Flux ◽  
Kernel Method ◽  
Mesh Size ◽  
Approximate Equation ◽  
Radiation Shielding ◽  
Significant Error ◽  
Representative Point ◽  
Volume Source ◽  
Calculation Results

A sensitivity analysis of a point kernel code was performed to investigate the effect of mesh division of a volume source on the radiation flux at points of interest. The QAD-CGGP, known as a representative point kernel code, was employed for a series of calculations and these calculation results compared with the reference data obtained from the MCNP5-1.60 code. The spherical volume source widely used in radiation shielding was also considered in this work and the mesh division along the radius was performed in two ways (regular and irregular). In addition, an approximate equation was defined to correct the significant error that occurs as an outcome of the point source assumption. As a result, in the case of a regular mesh division, a minimum mesh size of 1 cm is required to produce accurate results in comparison to the MCNP ones, while in the other instance, a half-level mesh division is sufficient to obtain the same result from the standpoint of the level of accuracy. In addition, by introducing the approximate equation presented in this paper, a significant error resulting from the point source assumption is exponentially reduced from a maximum of ~30% to a maximum of ~11%. Therefore, it is to be expected that the appropriate level of mesh division is required so as to increase the accuracy of the calculation using a point kernel method.

XRMF applications of a monolithic, polycapillary, focusing x-ray optic

1996 ◽  
Vol 54 ◽  
pp. 240-241
Author(s):  
D. A. Carpenter ◽  
Ning Gao ◽  
G. J. Havrilla
Keyword(s):  
Trace Elements ◽  
Point Source ◽  
Focal Spot ◽  
Fluorescence Analysis ◽  
X Rays ◽  
Focal Distance ◽  
Spot Diameter ◽  
X Ray ◽  
Focal Spot Diameter

A monolithic, polycapillary, x-ray optic was adapted to a laboratory-based x-ray microprobe to evaluate the potential of the optic for x-ray micro fluorescence analysis. The polycapillary was capable of collecting x-rays over a 6 degree angle from a point source and focusing them to a spot approximately 40 µm diameter. The high intensities expected from this capillary should be useful for determining and mapping minor to trace elements in materials. Fig. 1 shows a sketch of the capillary with important dimensions.The microprobe had previously been used with straight and with tapered monocapillaries. Alignment of the monocapillaries with the focal spot was accomplished by electromagnetically scanning the focal spot over the beveled anode. With the polycapillary it was also necessary to manually adjust the distance between the focal spot and the polycapillary.The focal distance and focal spot diameter of the polycapillary were determined from a series of edge scans.

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