Ray-trace in three dimensions through reflective confocal prolate spheroids

1996 ◽  
Author(s):  
Gonzalo Paez ◽  
Marija Strojnik
Keyword(s):  
Three Dimensions ◽  
Prolate Spheroids ◽  
Ray Trace

scholarly journals Compressible potential flows around round bodies: Janzen–Rayleigh expansion inferences

2021 ◽  
Vol 932 ◽  
Author(s):  
Idan S. Wallerstein ◽  
Uri Keshet
Keyword(s):  
Three Dimensional ◽  
Two Dimensions ◽  
Three Dimensions ◽  
Four Dimensions ◽  
Potential Flows ◽  
Prolate Spheroids ◽  
Flow Potential ◽  
Inverse Radius ◽  
Rayleigh Expansion ◽  
Simply Connected

The subsonic, compressible, potential flow around a hypersphere can be derived using the Janzen–Rayleigh expansion (JRE) of the flow potential in even powers of the incident Mach number ${\mathcal {M}}_\infty$ . JREs were carried out with terms polynomial in the inverse radius $r^{-1}$ to high orders in two dimensions, but were limited to order ${\mathcal {M}}_\infty ^{4}$ in three dimensions. We derive general JRE formulae for arbitrary order, adiabatic index and dimension. We find that powers of $\ln (r)$ can creep into the expansion, and are essential in the three-dimensional (3-D) sphere beyond order ${\mathcal {M}}_\infty ^{4}$ . Such terms are apparently absent in the 2-D disk, as we verify up to order ${\mathcal {M}}_\infty ^{100}$ , although they do appear in other dimensions (e.g. at order ${\mathcal {M}}_\infty ^{2}$ in four dimensions). An exploration of various 2-D and 3-D bodies suggests a topological connection, with logarithmic terms emerging when the flow is simply connected. Our results have additional physical implications. They are used to improve the hodograph-based approximation for the flow in front of a sphere. The symmetry-axis velocity profiles of axisymmetric flows around different prolate spheroids are approximately related to each other by a simple, Mach-independent scaling.

Particle Shape Analysis Using Digital Image Processing

2019 ◽  
pp. 377-391
Author(s):  
Katia Tannous ◽  
Fillipe de Souza Silva
Keyword(s):  
Image Processing ◽  
Aspect Ratio ◽  
Digital Image Processing ◽  
Shape Analysis ◽  
Processing Technique ◽  
Solid Particles ◽  
Three Dimensions ◽  
Image Processing Technique ◽  
Prolate Spheroids

This chapter will discuss new software, Particles and Geometric Shapes Analyzer (APOGEO), aiming the determination of aspect ratio and sphericity of solid particles by image processing technique without any manual work. This software can quantify the major and minor axes correlating two or three dimensions of particles (e.g., biomass, mineral, pharmaceutical, and food products) to obtain their shape. The particles can be associated with different geometries, such as rectangular parallelepiped, cylinder, oblate and prolate spheroids, and irregular. The results are presented in histograms and tables, but also can be saved in a spreadsheet.

Particle Shape Analysis Using Digital Image Processing

2018 ◽  
pp. 1331-1343
Author(s):  
Katia Tannous ◽  
Fillipe de Souza Silva
Keyword(s):  
Image Processing ◽  
Aspect Ratio ◽  
Digital Image Processing ◽  
Shape Analysis ◽  
Processing Technique ◽  
Solid Particles ◽  
Three Dimensions ◽  
Image Processing Technique ◽  
Prolate Spheroids

This chapter will discuss new software, Particles and Geometric Shapes Analyzer (APOGEO), aiming the determination of aspect ratio and sphericity of solid particles by image processing technique without any manual work. This software can quantify the major and minor axes correlating two or three dimensions of particles (e.g.: biomass, mineral, pharmaceutical and food products) to obtain their shape. The particles can be associated with different geometries such as, rectangular parallelepiped, cylinder, oblate and prolate spheroids, and irregular. The results are presented in histograms and tables, but also can be saved in a spreadsheet.

High-resolution scanning electron microscopy (HRSEM) of mitochondria from various rat tissues

1988 ◽  
Vol 46 ◽  
pp. 14-15
Author(s):  
P.J. Lea ◽  
M.J. Hollenberg
Keyword(s):  
Electron Microscopy ◽  
Pigment Epithelium ◽  
Retinal Pigment ◽  
Rat Hepatocytes ◽  
Three Dimensions ◽  
Objective Lens ◽  
Rat Tissues ◽  
Thin Sections ◽  
Reconstruction Methods ◽  
Scanning Electron

Our current understanding of mitochondrial ultrastructure has been derived primarily from thin sections using transmission electron microscopy (TEM). This information has been extrapolated into three dimensions by artist's impressions (1) or serial sectioning techniques in combination with computer processing (2). The resolution of serial reconstruction methods is limited by section thickness whereas artist's impressions have obvious disadvantages.In contrast, the new techniques of HRSEM used in this study (3) offer the opportunity to view simultaneously both the internal and external structure of mitochondria directly in three dimensions and in detail.The tridimensional ultrastructure of mitochondria from rat hepatocytes, retinal (retinal pigment epithelium), renal (proximal convoluted tubule) and adrenal cortex cells were studied by HRSEM. The specimens were prepared by aldehyde-osmium fixation in combination with freeze cleavage followed by partial extraction of cytosol with a weak solution of osmium tetroxide (4). The specimens were examined with a Hitachi S-570 scanning electron microscope, resolution better than 30 nm, where the secondary electron detector is located in the column directly above the specimen inserted within the objective lens.

Inelastic Electron Scattering from Valence Electrons in Aluminum

1976 ◽  
Vol 34 ◽  
pp. 462-463
Author(s):  
P. E. Batson ◽  
C. H. Chen ◽  
J. Silcox
Keyword(s):  
Electron Scattering ◽  
Single Scattering ◽  
Three Dimensions ◽  
Inelastic Electron ◽  
Weak Beam ◽  
Scattering Spectrum ◽  
Valence Electrons ◽  
Diffraction Patterns ◽  
Electronic Scattering

We wish to report in this paper measurements of the inelastic scattering component due to the collective excitations (plasmons) and single particlehole excitations of the valence electrons in Al. Such scattering contributes to the diffuse electronic scattering seen in electron diffraction patterns and has recently been considered of significance in weak-beam images (see Gai and Howie) . A major problem in the determination of such scattering is the proper correction for multiple scattering. We outline here a procedure which we believe suitably deals with such problems and report the observed single scattering spectrum.In principle, one can use the procedure of Misell and Jones—suitably generalized to three dimensions (qx, qy and #x2206;E)--to derive single scattering profiles. However, such a computation becomes prohibitively large if applied in a brute force fashion since the quasi-elastic scattering (and associated multiple electronic scattering) extends to much larger angles than the multiple electronic scattering on its own.

Advantages of Complementary Stereo Images as Viewed with the Low-Temperature Field-Emission SEM

1992 ◽  
Vol 50 (2) ◽  
pp. 1314-1315
Author(s):  
William P. Wergin ◽  
Eric F. Erbe
Keyword(s):  
Fold Increase ◽  
Horizontal Displacement ◽  
Three Dimensions ◽  
Stereo Image ◽  
Stereo Pair ◽  
Sem Micrograph ◽  
Left And Right ◽  
The Common ◽  
The Brain ◽  
Pair Analysis

The eye-brain complex allows those of us with normal vision to perceive and evaluate our surroundings in three-dimensions (3-D). The principle factor that makes this possible is parallax - the horizontal displacement of objects that results from the independent views that the left and right eyes detect and simultaneously transmit to the brain for superimposition. The common SEM micrograph is a 2-D representation of a 3-D specimen. Depriving the brain of the 3-D view can lead to erroneous conclusions about the relative sizes, positions and convergence of structures within a specimen. In addition, Walter has suggested that the stereo image contains information equivalent to a two-fold increase in magnification over that found in a 2-D image. Because of these factors, stereo pair analysis should be routinely employed when studying specimens.Imaging complementary faces of a fractured specimen is a second method by which the topography of a specimen can be more accurately evaluated.

convergent-beam diffraction from surfaces

1987 ◽  
Vol 45 ◽  
pp. 30-33
Author(s):  
J. A. Eades ◽  
A. E. Smith ◽  
D. F. Lynch
Keyword(s):  
Reciprocal Lattice ◽  
Three Dimensional ◽  
Grazing Incidence ◽  
Three Dimensions ◽  
Plane Figure ◽  
Transmission Electron ◽  
Convergent Beam ◽  
Beam Patterns ◽  
Beam Diffraction

It is quite simple (in the transmission electron microscope) to obtain convergent-beam patterns from the surface of a bulk crystal. The beam is focussed onto the surface at near grazing incidence (figure 1) and if the surface is flat the appropriate pattern is obtained in the diffraction plane (figure 2). Such patterns are potentially valuable for the characterization of surfaces just as normal convergent-beam patterns are valuable for the characterization of crystals.There are, however, several important ways in which reflection diffraction from surfaces differs from the more familiar electron diffraction in transmission.GeometryIn reflection diffraction, because of the surface, it is not possible to describe the specimen as periodic in three dimensions, nor is it possible to associate diffraction with a conventional three-dimensional reciprocal lattice.

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