Generalized Optical Theorem and Point Sources

2021 ◽  
pp. 4-11
Author(s):  
Leon A. Apresyan
Keyword(s):  
Natural Generalization ◽  
Point Sources ◽  
Optical Theorem ◽  
Simple Derivation ◽  
Operator Approach ◽  
Small Absorption ◽  
Scattering Potential ◽  
Mathematical Literature ◽  
Energy Conservation Law ◽  
Polarized Radiation

A simple derivation of the general form of the optical theorem (GOT) is given for the case of a conservative scatterer in a homogeneous lossless medium, suitable for describing point sources and an observation region close to the scatterer. The presentation is based on the use of the operator approach and scalar wave equation in the limit of vanishingly small absorption. This approach does not require asymptotic estimates of rapidly oscillating integrals, does not use the integration of fluxes, which leads to the loss of information about the energy conservation law, and allows a natural generalization to the case of polarized radiation, as well as more complex multi-part fields. Such GOT generalizes the results known in the mathematical literature for models to the case of any conservative (real) scattering potential and arbitrary sources.

Single Atom Image Contrast in Fixed Beam Dark Field Electron Microscopy

1974 ◽  
Vol 32 ◽  
pp. 366-367
Author(s):  
Wah Chi
Keyword(s):  
Scattering Amplitude ◽  
Present Report ◽  
Dark Field ◽  
Image Contrast ◽  
Single Atom ◽  
Optical Theorem ◽  
Hartree Fock ◽  
Heavy Atoms ◽  
Beam Stop ◽  
Fixed Beam

Resolution and contrast are the important factors to determine the feasibility of imaging single heavy atoms on a thin substrate in an electron microscope. The present report compares the atom image characteristics in different modes of fixed beam dark field microscopy including the ideal beam stop (IBS), a wire beam stop (WBS), tilted illumination (Tl) and a displaced aperture (DA). Image contrast between one Hg and a column of linearly aligned carbon atoms (representing the substrate), are also discussed. The assumptions in the present calculations are perfectly coherent illumination, atom object is represented by spherically symmetric potential derived from Relativistic Hartree Fock Slater wave functions, phase grating approximation is used to evaluate the complex scattering amplitude, inelastic scattering is ignored, phase distortion is solely due to defocus and spherical abberation, and total elastic scattering cross section is evaluated by the Optical Theorem. The atom image intensities are presented in a Z-modulation display, and the details of calculation are described elsewhere.

Resistance Monitor and Control for Vacuum Evaporation of Metals and Carbon

1976 ◽  
Vol 34 ◽  
pp. 572-573
Author(s):  
Russell L. Steere ◽  
Eric F. Erbe ◽  
J. Michael Moseley
Keyword(s):  
Electronic Device ◽  
Point Sources ◽  
High Contrast ◽  
Variable Resistor ◽  
Quality Of Results ◽  
Low Contrast ◽  
Evaporation Source ◽  
And Control ◽  
At Will

We have designed and built an electronic device which compares the resistance of a defined area of vacuum evaporated material with a variable resistor. When the two resistances are matched, the device automatically disconnects the primary side of the substrate transformer and stops further evaporation.This approach to controlled evaporation in conjunction with the modified guns and evaporation source permits reliably reproducible multiple Pt shadow films from a single Pt wrapped carbon point source. The reproducibility from consecutive C point sources is also reliable. Furthermore, the device we have developed permits us to select a predetermined resistance so that low contrast high-resolution shadows, heavy high contrast shadows, or any grade in between can be selected at will. The reproducibility and quality of results are demonstrated in Figures 1-4 which represent evaporations at various settings of the variable resistor.

Modelling polarized radiation from interstellar clouds

2008 ◽  
Vol 31 ◽  
pp. 179-180
Author(s):  
M. Juvela ◽  
J. Goncalves ◽  
V.-M. Pelkonen ◽  
T. Lunttila
Keyword(s):  
Interstellar Clouds ◽  
Polarized Radiation

Operator approach for orthogonality in linear spaces

2018 ◽  
Vol 11 (4) ◽  
pp. 103-112
Author(s):  
Mahdi Iranmanesh ◽  
Maryam Saeedi Khojasteh
Keyword(s):  
Operator Approach ◽  
Linear Spaces

EVALUATION OF MOUNTAIN AREA AS NON-POINT SOURCE OF NITROGEN FOR SETO INLAND SEA: THE NORTHERN SHIKOKU REGION, JAPAN

2017 ◽  
Author(s):  
Shohei Morisawa ◽  
Shohei Morisawa ◽  
Yukio Komai ◽  
Yukio Komai ◽  
Takao Kunimatsu ◽  
...  
Keyword(s):  
Average Concentration ◽  
Point Sources ◽  
Seto Inland Sea ◽  
Mountain Streams ◽  
Unit Load ◽  
Mountain Areas ◽  
Mountain Area ◽  
The Seto Inland Sea ◽  
Unit Load Method ◽  
Important Position

The northern Shikoku region is located in the Western part of Japan and faces towards the Seto Inland Sea. The forest area, which is one of the non-point sources in the Seto Inland Sea watershed, occupies 75% of the land use in the watershed of the northern Shikoku region. The amount of loadings of nutrients and COD in the Seto Inland Sea has been estimated by the unit load method but actually the data has not been investigated. It is however, necessary to know the real concentration of nitrogen in mountain streams to evaluate the role which is the mountain area plays as non-point sources. Therefore, more water samples of mountain streams in the watershed need to be taken and the concentrations of nitrogen analyzed. The mountain streams in the northern Shikoku area were investigated from April, 2015 to November, 2015. The number of sampling sites was 283, in addition to the past data by Kunimatsu et al. The average concentration of nitrate nitrogen in Ehime, Kagawa, and Tokushima was 0.61mg/L, 0.78mg/L and 0.34mg/L, respectively. The environmental standard range for nitrogen in the Seto Inland Sea is from between less than 0.2mg/L and less than 1mg/L. Therefore, the average concentration of nitrogen in these regions was over category II, and those of mountain streams in Kagawa Prefecture exceeded category III. About 20% of mountain streams were more than 1mg/L. It has become clear that mountain areas occupy an important position as non-point sources for the Seto Inland Sea.

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