Spiral sampling

Shortcomings of Wang s method like limited pitch of the spiral and blurring in the vertical direction can be improved by the CFBP-algorithm [10], where gaps in the spiral sampling pattern are filled using X-rays measured from the opposite side. 

Spiral sampling is used mainly in MRI, where it permits reduced exploration of k-space (and thus a reduction of scan time). 

Fig. 6 (continued) five sampling lines, (e) concentric rings sampling, (f) spiral sampling, (g) purely random sampling, (h) Poisson disk sampling. Number of points in each sampling scheme is equal to 100. For panels (c)-(h) timax = = 50 ms... 

Point coordinates in the spiral sampling scheme [44] are defined as... 

Notably, both radial and LCRS schemes can be considered as special cases of the spiral sampling scheme. PSF of this distribution is the combination of the two above PSFs. The artifacts form ring-shaped ridges, but the intensity is not constant along the rings, but varies with angle (see Fig. 6f) [60]. 

Many different methods exist to sample fc-space including radial sampling spiral sampling and raster sampling. For more details see, for example, [277]. Once sufficient sampling is complete, the spin density n x) is recovered by Fourier transform. 

We have perfomied some simulations of the eddy current distribution in a test object for a spiral coil and a circular one (see Fig. 4.1). Both coils had 9 turns and the excitation current was 6 mA. Figs. 4.1 show the cross section of the sample at the location of the crack and the amplitude of the eddy current density. One observes a 1.5 higher current density at the sides of the crack for the case of the circular coil. 

Left Fig. 4.1 Excitation with spiral (top) or circular (bottom) coil. While color corresponds to a high eddy current density in the sample (9turns, 6mA). 

Using the theorem that the sufficiency condition for mathematical correctness in 3D-reconstruction is fulfilled if all planes intersecting the object have to intersect the source-trajectory at least in one point [8], it is possible to generalise Feldkamp s method. Using projection data measured after changing the sotuce-trajectory from circular to spiral focus orbit it is possible to reconstruct the sample volume in a better way with the Wang algorithm [9]. 

The temporary filling of the combustion tube D is now inserted this is in part replaced after every combustion. Sufficient wire-form copper oxide is added so that it just emerges to the left of the furnace E when the tube (not including the beak) is protruding 10-15 mm. at the beak end this constitutes the main oxidative packing of the tube. This is followed by 25 mm. of M.A.R. powder-form" copper oxide, followed by the sample suspended in more copper oxide, and backed by an oxidised copper spiral, 50 mm. in length. 

Applications The common Heliflow apphcations are tank-vent condensers, sample coolers, pump-seal coolers, and steam-jet vacuum condensers. Instant water heaters, glycoLwater seivdces, and cryogenic vaporizers use the spiral tube s ability to reduce thermally induced stresses caused in these apphcations. 

Figure 3. Different geometries for microwave conductivity measurements, (a) Sample (black square) at end of microwave guide, (b) sample in microwave resonator, and (c) sample above dielectric microwave spiral. The electrical field E of the microwave is shown schematically.

Fig. 2.1.13 Planar spiral micro-coil of 1.2 mm outer diameter (left), mounted as an exchangeable rf insert on a standard NMR microscopy probe (right) (Bruker-Biospin GmbH, Rheinstetten, Germany). The micro-coil is embedded, together with a glass sample holder, in a slotted PTFE holder.

The use of NMR for studying chemical reactions began about 30 years ago. In 1972, Asahi and Mizuta [11] reported a study of the performance of five different types of flow cells used in NMR studies of chemical reactions (a) a straight glass tube, (b) a pipette-type tube, (c) a spiral capillary in a conventional sample tube, (d) a jet in the base of a conventional tube, and (e) a conventional spinning tube with an inlet at the base and an outlet at a height of about 50 mm. The best results were... 

The course of the reaction can conveniently be followed by gas chromatography. A sample of the reaction mixture is withdrawn at intervals, neutralized with solid sodium bicarbonate, dried over magnesium sulfate, and injected directly into a gas chromatography column consisting of 15% phenyldiethanola-mine succinate (PDEAS) substrate coated on 60/80 mesh, acid-washed fire brick contained in a i in. by 5 ft. spiral-shaped copper... 

In the mixing spiral the samples are incubated with reagents and are led into... 

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