Slicing

The stylus of the planimeter is guided around the depth to be measured and the respective area contained within this contour can then be read off. The area is now plotted for each depth as shown in Figure 6.2 and entered onto the area - depth graph. Since the structure is basically cut into slices of increasing depth the area measured for each depth will also increase. 

Fig. 2 Single slice of porosity in ferritic weld (a) original image, (b) image recontruction without noise, (c) image reconstruction with noise.

Simulations of the adaptive reconstruction have been performed for a single slice of a porosity in ferritic weld as shown in Fig. 2a [11]. The image matrix has the dimensions 230x120 pixels. The number of beams in each projection is M=131. The total number of projections K was chosen to be 50. For the projections the usual CT setup was used restricted to angels between 0° and 180° with the uniform step size of about 3.7°. The diagonal form of the quadratic criteria F(a,a) and f(a,a) were used for the reconstruction algorithms (5) and (6). 

It is known and widely applied a method, when the spatial model of object is formed by a set of plane sections or tomographic slices. An experienced sample, created in Californian University and reffered to as Dynamic Cardiac 3D densitometer, is constructed by this principle [2]. The serial model of this tomograph of the company Imatron Associates appeared on the market in the end 1983r.[13]. On this basis a line of computer tomographs has been created. 

Systems, based on a method of inspection of slice by slice, in a number of cases allow to solve put problems. But for obtaining of higher resolution it is necessary to have an opportunity to increase number of inspected slices. It results in significant increasing of collection data time that is inadmissible in some applications. Besides this, the maximum allowable number of researched slices is rigidly limited by hardware opportunities of tomographs, and also by level of emission of x-ray sources. 

The analysis of a plenty of references shows applicability for creating tomographs of a method of slice by slice scatming and method of the simultaneous collecting of data by cone beam. The second method has many advantages. 

CT offers the opportunity to examine slices through the sample non-destructively and is therefor the only method for measuring exterior and also interior part coordinates without mechanical cutting of the object. 

Typical tomographic 2D-reconstruction, like the filtered backprojection teelinique in Fan-Beam geometry, are based on the Radon transform and the Fourier slice theorem [6]. 

The data volume, which can be imported as data block or single slices, can be cutted or rebinned (e.g. if the data set is very large) and interpolated (e.g. interpolating intermediate slices between measured CT cuts in the case of 2D-CT). 

With 3D-CTVicwer the export of slice-contours from parts inside the data volume is possible via the DXF-format. From these contours a two-dimensional comparison to the CAD geometry is possible if the coordinate system and the absolute scaling between both methods are well known. 

In case of some samples besides the cross sectional CT-slice also a projectional image is of interest. In these cases the test mode Digital Radiography (DR) is applied. In the DR-mode the object is not turned, but scanned horizontally and vertically. Again the very high dynamic of the detector and the mechanical accuracy of the complete system are of large benefit to the image quality. 

Of course it is possible to calculate a complete three dimensional visualisation of the object on the base of many adjacent two-dimensional CT- sUces. By this method very detailed results can be achieved. But the total time of data acquisition increases proportional with the number of slices. 

A broad-band (standard) echographic shot in direction n gives a slice of amplitude ... 

And a rotation of the emitter-receiver transducer around the "object" (or a rotation of the object) gives a annulus of center O and radii [Km, Km] [2]. The situation is identical to that of X-ray tomography (slice-by-slice spectral coverage), but with a band-pass spectral filter instead of a low-pass spectral filter. ... 

As the cursor is moved over the rendered 3D data, the eo-ordinates and amplitude of the eell giving rise to the pixel under the cursor are displayed in the status bar. This provides a basic method for measuring the location and dimensions of flaws. However, it is more convenient and accurate to perform sizing operations on 2-dimensional slices, so several slicing and sizing tools are incorporated. 

A two-dimensional slice may be taken either parallel to one of the principal co-ordinate planes (X-Y, X-Z and Y-Z) selected from a menu, or in any arbitrary orientation defined on screen by the user. Once a slice through the data has been taken, and displayed on the screen, a number of tools are available to assist the operator with making measurements of indications. These tools allow measurement of distance between two points, calculation of 6dB or maximum amplitude length of a flaw, plotting of a 6dB contour, and textual aimotation of the view. Figure 11 shows 6dB sizing and annotation applied to a lack of fusion example. 

The long-range van der Waals interaction provides a cohesive pressure for a thin film that is equal to the mutual attractive force per square centimeter of two slabs of the same material as the film and separated by a thickness equal to that of the film. Consider a long column of the material of unit cross section. Let it be cut in the middle and the two halves separated by d, the film thickness. Then, from one outside end of one of each half, slice off a layer of thickness d insert one of these into the gap. The system now differs from the starting point by the presence of an isolated thin layer. Show by suitable analysis of this sequence that the opening statement is correct. Note About the only assumptions needed are that interactions are superimposable and that they are finite in range. 

Certain materials, most notably semiconductors, can be mechanically cleaved along a low-mdex crystal plane in situ in a UFIV chamber to produce an ordered surface without contamination. This is done using a sharp blade to slice tire sample along its preferred cleavage direction. For example. Si cleaves along the (111) plane, while III-V semiconductors cleave along the (110) plane. Note that the atomic structure of a cleaved surface is not necessarily the same as that of the same crystal face following treatment by IBA. 

The barrier on the surface in figure A3,7,1 is actually a saddle point the potential is a maximum along the reaction coordinate but a minimum along the direction perpendicular to the reaction coordinate. The classical transition state is defined by a slice tlirough the top of tire barrier perpendicular to the reaction coordinate. 

Shearing of the data is perfonned to obtam isotropic spectra in the FI dimension and to facilitate easy extraction of the ID slices for different peaks. Shearing is a projection of points that lie on a line with a slope equal to the anisotropy axis onto a line that is parallel to the F2 axis [24]- Shearing essentially achieves the same as the split-t experiment or delayed acquisition of the echo. Although sheared spectra may look more attractive, they do not add any extra infomiation and they are certainly not necessary for the extraction of QIS and values. 

Figure Bl.14.1. Spin warp spin-echo imaging pulse sequence. A spin echo is refocused by a non-selective 180° pulse. A slice is selected perpendicular to the z-direction. To frequency-encode the v-coordinate the echo SE is acquired in the presence of the readout gradient. Phase-encoding of the > -dimension is achieved by incrementmg the gradient pulse G...

The integral describes the spatial amplitude modulation of the excited magnetization. It represents the excitation or slice profile, g(z), of the pulse in real space. As drops to zero for t outside the pulse, the integration limits can be extended to infinity whereupon it is seen that the excitation profile is the Fourier transfonn of the pulse shape envelope ... 

A sine-shape has side lobes which impair the excitation of a distinct slice. Other pulse envelopes are therefore more commonly used. Ideally, one would like a rectangular excitation profile which results from a sine-shaped pulse with an infinite number of side lobes. In practice, a finite pulse duration is required and therefore the pulse has to be truncated, which causes oscillations in the excitation profile. Another frequently used pulse envelope is a Gaussian frmction ... 

For a given half width at half maximum in the time domain, Ar,.n =2, /, the slice width A decreases with increasing gradient strength G. ... 

Closer examination of equation B 1,14,3 reveals that, after the slice selection pulse, the spin isocln-omats at different positions in the gradient direction are not in phase. Rather they are rotated by i exp jyC. )tind... 

Once a slice has been selected and excited, it is necessary to encode the ensuing NMR signal with the coordinates of nuclei within the slice. For each coordinate (x andy) this is achieved by one of two very closely related means, frequency encoding or phase encoding [1]. In this section we consider the fonner and in the next, the latter. In tlie section after that we show how the two are combined in the most coimnon imaging experiment. 

As before, we note that the resonance frequency of a nucleus at position r is directly proportional to the combined applied static and gradient fields at that location. In a gradient G=G u, orthogonal to the slice selection gradient, the nuclei precess (in the usual frame rotating at coq) at a frequency ciD=y The observed signal therefore contains a component at this frequency witli an amplitude proportional to the local spin density. The total signal is of the fomi... 

There is of course no requirement to confine the slice selection to the z-gradient. The gradients may be used in any combination and an image plane selected in any orientation without recourse to rotating the sample. 

Figure Bl.14.2. Gradient-recalled echo pulse sequence. The echo is generated by deliberately dephasing and refocusing transverse magnetization with the readout gradient. A slice is selected in the z-direction and v- and y-dimension are frequency and phase encoded, respectively.

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