A formula for the ray density over a caustic surface for variable index media

1982 ◽  
Vol 72 (S1) ◽  
pp. S58-S58
Author(s):  
Donald G. Burkhard
Keyword(s):  
Author(s):  
R. W. Carpenter ◽  
I.Y.T. Chan ◽  
J. M. Cowley

Wide-angle convergent beam shadow images(CBSI) exhibit several characteristic distortions resulting from spherical aberration. The most prominent is a circle of infinite magnification resulting from rays having equal values of a forming a cross-over on the optic axis at some distance before reaching the paraxial focal point. This distortion is called the tangential circle of infinite magnification; it can be used to align and stigmate a STEM and to determine Cs for the probe forming lens. A second distortion, the radial circle of infinite magnification, results from a cross-over on the lens caustic surface of rays with differing values of ∝a, also before the paraxial focal point of the lens.


2020 ◽  
Vol 24 (4) ◽  
pp. 108-118
Author(s):  
A. V. Petraikin ◽  
A. K. Smorchkova ◽  
N. D. Kudryavtsev ◽  
K. A. Sergunova ◽  
Z. R. Artyukova ◽  
...  

Rationale. Quantitative CT (QCT) bone densitometry with asynchronous calibration not require a phantom during the scan procedure. Based on calibration data it converts X-ray density in HU to bone mineral density (BMD). Given the large number of CT studies performed on patients at risk of osteoporosis, there is a need for a hands-on method capable of assessing BMD in a short period of time without tailored software or protocols.Goal. To develop a method for QCT bone densitometry using an PHK (PHantom Kalium), to compare the volume BMD measurements with the QCT data with asynchronous calibration provided by software from a reputable developer.Methods. The studies were performed at 64-slice CT unit with body scanning parameters. The BMD was measured using two techniques: 1) QCT with asynchronous calibration using software from a reputable developer; 2) QCT using a PHK phantom (QCT-PHK). For convert the HU to BMD values, we scanned the PHK phantom and calculate correction factor. Phantom contains “vertebrae” filled with potassium hydrogen phosphate in different concentrations. In both methods, the BMD values measured for LI–II, and sometimes for ThXII, LIII.Results. The study enrolled 65 subjects (11 male and 54 female patients); median age 69.0 years. A comparison of the vertebrae BMD measured by QCT and QCT-PHK revealed a significant linear Pearson correlation r = 0.977 (p < 0.05). The Bland–Altman analysis demonstrated a lack of relationship between the difference in measurements and the average BMD and a systematic BMD; bias of +4.50 mg/ml in QCT vs. QCT-PHK. Differences in the division into groups osteoporosis / osteopenia / norm according to the ACR criteria for the two methods were not significant.Conclusion. The developed asynchronous QCT-PHK method measure BMD comparable to the widely used QCT with asynchronous calibration. This method can be used for opportunistic screening for osteoporosis.


2007 ◽  
Vol 63 (2) ◽  
pp. 296-302 ◽  
Author(s):  
Mikhail A. Strzhemechny ◽  
Vyacheslav N. Baumer ◽  
Anatoli A. Avdeenko ◽  
Oleg S. Pyshkin ◽  
Roman V. Romashkin ◽  
...  

A combination of single-crystal and powder X-ray diffractometry was used to study the structure of two polymorphs of 4-bromobenzophenone over the temperature range from 100 to 300 K. One of the polymorphs of the title compound was known previously and its structure has been determined at room temperature [Ebbinghaus et al. (1997). Z. Kristallogr. 212, 339–340]. Two crystal growth methods were employed, one of which (a modification of the Bridgman–Stockbarger technique) resulted in single crystals of a previously unknown structure. The basic physical properties of the stable polymorph are: growth method, from 2-propanol solutions or gradient sublimation; space group, monoclinic P21/c; melting point, T m = 355.2 K; X-ray density (at 100 K), Dx = 1.646 g cm−3. The same properties of the metastable polymorph (triclinic P\overline 1 ) are: growth method, modified Bridgman–Stockbarger method; X-ray density (at 100 K), Dx = 1.645 g cm−3; T m = 354 K. Thermograms suggest that the melting of the metastable form is accompanied by at least a partial crystallization presumably into the monoclinic form; the transformation is therefore monotropic. Analysis of short distances in both polymorphs shows that numerous weak hydrogen bonds of the C—H...π type ensure additional stabilization within the respective planes normal to the longest dimension of the molecules. The strong temperature dependence of the lattice constants and of the weak bond distances in the monoclinic form suggest that the weak bond interactions might be responsible for both the large thermal expansion within plane bc and the considerable thermal expansion anisotropy.


2002 ◽  
Vol 17 (1) ◽  
pp. 41-43 ◽  
Author(s):  
Rashmi ◽  
U. Dhawan

ZnGa2Te4 was found to crystallize in a defect tetrahedral structure with possible space group I4(82) with Z=2. Complete X-ray powder diffraction data were obtained and the unit cell parameters a and c and X-ray density were calculated. These were a=0.5930(1) nm, c=1.1859(3) nm, and Dx=5.7×103 kg/m3.


Author(s):  
John E. Hoel ◽  
Thomas W. Novitsky
Keyword(s):  

2018 ◽  
Vol 8 (2) ◽  
pp. 75
Author(s):  
Edi Suharyadi ◽  
Lintang Griyanika ◽  
Joko Utomo ◽  
Ayu Kurnia Agustina ◽  
Takeshi Kato ◽  
...  

Nanocrystalline mixed spinel ferrite of Co0.5Ni0.5Fe2O4 magnetic nanoparticles (MNPs) has been successfully synthesized by coprecipitation method and encapsulated by PEG-4000 with various concentrations. X-Ray Diffraction (XRD) patterns showed that nanoparticles contained Co0.5Ni0.5Fe2O4 spinel ferrite with crystallite size of 14.9 nm. After PEG-4000 encapsulation particles size decreased became 7.7 nm. Interaction Co0.5Ni0.5Fe2O4 nanoparticles with long chain PEG-4000 caused the crystal growth trap. Lattice parameter and X-Ray density have no significant difference after encapsulated PEG-4000. The coercivity (𝐻𝑐) of Co0.5Ni0.5Fe2O4 was 214 Oe. The 𝐻𝑐 decreased after PEG-4000 encapsulation became 127 Oe, which is due to the decrease of crystallite size. The maximum magnetization (Mmax) of Co0.5Ni0.5Fe2O4 was 12.0 emu/g, and decreased after PEG-4000 encapsulation to 11.7 emu/g, because PEG-4000 is paramagnetic. After the concentration of PEG-4000 increased, then the amount of paramagnetic material increase which lead maximum magnetization decrease.


Geophysics ◽  
1960 ◽  
Vol 25 (4) ◽  
pp. 891-904 ◽  
Author(s):  
J. J. Pickell ◽  
J. G. Heacock

This review of density logging is primarily a compilation of information presented in the petroleum industry literature. It includes a brief discussion of some of the theory involved in gamma‐ray density logging, various calibration curves, comparisons of density‐log and core data, and comments on density‐log interpretation. Conclusions are that the density log, under good borehole conditions, provides an accurate means for measuring bulk density of the formation adjacent to the borehole. If grain density is known, valid estimates of porosity can also be made. Because of the response characteristics of the system, accuracy in determining porosity is best when formation densities are low and porosities are high.


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