Slit-Collimation

Integrating over the whole range of the primary beam intensity distribution W(t), we find 

Stated in words, Equation (5.169) expresses that a ray in the primary beam, proceeding toward a position in the detector plane that corresponds to an angle t, is actually scattered at an angle y/q2 + t2 before it is registered at the nominal scattering angle q9 and that the smeared intensity I(q) is the weighted sum of contributions from all such rays contained in the primary beam. 

The counter is attached directly to the camera avoiding an additional window. This change of the original design [71] is important because a window and a gap between the camera housing and the counter would cause considerable parasitic 

The distance between the sample holder and the one-dimensional counter is 41.4 cm, which is approximately twice the value of the conventional design (23.6 cm) [70]. In principle, an enhancement of the distance sample-to-detector does not improve the resolution. For a given q-range the increased distance of the detector to the sample, however, leads to approximately twice the number of charmels of the position-sensitive counter as compared to the conventional design. Hence, the region of smallest angles in which the measured intensity displays the strongest decrease may be measured and corrected much more accurately. As a consequence of this, the minima and maxima can be resolved clearly. 

Besides these advantages the enhanced distance of the sample and the detector leads to an improvement of the angular resolution of the SAXS-device. This will become more evident when considering the principal sources of smearing for a slit-coUimation system (cf. Fig. 9) [1,72]  

The finite dimensions of the primary beam lead to a smearing of the measured intensity i m) which may be expressed through the relation [1,72] 

Here P(t) is the virtual profile in the t-direction in the plane of the sample which takes into account the finite divergence of the primary beam as well as the length of the detector in the plane of registration. The function Q(x) gives the profile of the primary beam in the direction perpendicular to the slit length as measured in the plane of detection. For the block collimation system under consideration here, this profile is asynunetric and determines the smallest q-value accessible by the SAXS-camera. It results from the convolution of the intensity along the x-direction and the resolution function characterizing the finite resolution of the counter. 

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The Bra -Brentano geometry is used widely for preferentially and randomly oriented polycrystalline films. In this geometry (Figure 3a), slits collimate the inci-... 

There are many methods of X-ray topography, though the most popitlar are the Lang method with slit-collimated radiation and the double-crystal methods, which may be thought of as high resolution diffractometry with an imaging... 

CdTe buffer layer on GaAs. Slit collimated -2 scan. (Courtesy C.D.Moore) ... 

Figure 13.9—Schematic of a sequential, crystal-based spectrometer and the spectrum obtained using the sequential method with an instrument having a goniometer. The Soller slit collimator, made of metallic parallel sheets, collimates the primary X-ray beam emitted by a high power source (SRS 300 instrument, reproduced by permission of Siemens). A typical spectrum of an alloy, obtained by an instrument of this category, having an LiF crystal (200) with 26 angle in degrees as the abscissa and intensity in Cps as the ordinate). Model Philips PW2400 Spectrum, reproduced with permission of VALDI-France.

Thus, the interactions with double slits, collimators, etc. signal the source of quantum states located inside the setup, but only one material system sustains quantum states a rubidium atom. The physical quantum states address all possibilities the material system may express. Therefore, the state does not address to the material system as particle so that its whereabouts are not an issue. We summarize the situation by saying that presence of the material system in laboratory space is sufficient yet not its being localized. The concept of presence is required to articulate physical quantum states to the extent they are sustained by material systems. 

Dingenouts N, Ballauff M (1998) Structural investigation of latexes by small-angle X-ray scattering in slit-collimation. Measurements and evaluation of data. Acta Polym 49 178-183... 

Remove the circular cover, and lay it down, inside surface upward, in a safe place. Remove the two slits (collimator and beam stop), and lay them down inside the cover. 

The fibers were annealed at 200 C for 5 min. in N2, wound parallel on a sample holder and flat plate X-ray photographs taken by exposing the fibers for 1 h (WAXS) to a beam collimated at 90° to the fiber axis, uatorial diffractometer traces of uniaxially oriented fibers were taken uring slit collimation. WAXS patterns were obtained on polaroid film and the difoctometer traces with a Siemens X-ray system. Nickel filtered CuKa radiation was used. The X-ray unit was operated at 30 KV and 20 mA. The sample to film distance was 71.4 mm. 

Frequently, SAXS experiments are performed with slit collimated systems. We assume that the conditions are such that the incident beam can be regarded as infinite and of constant intensity in the direction of the Xj-axis and inifmitely narrow in the direction of the Xj-axis of a cartesian coordinate system (Xf, X2, X3) The cylinder axis is supposed to be parallel to the xj-axis and the intensity measurements are performed parallel to the X2-axis. In the small-angle region we have, by replacing sin 0 by its argument in Equation (22)... 

We note that T(x2) is proportional to Ip(Sr), therefore, Ipfs ) is directly obtained by measuring with a slit collimated system. It should be realized that an equivalent relationship does not exist if the intensity is measured along the cylinder-axis with the incident beam being infinitely perpendicular to this axis. 

Lang (1956a,b) attempted a complete map of the diffracted intensity, but was handicapped by the low resolution inherent in the use of counter techniques with fibrous materials. Although quantitative data are highly desirable, they are very difficult to obtain from fibrous materials of large period. Measurements of meridional intensities in various keratins reported by Onions et al. (1960) are of considerable interest in comparative studies, but cannot be used to check structures because the slit collimation used does not differentiate between meridional and near-meridional reflections. The same difficulty applies to the intensities quoted by Bear (1944). 

For measuring Tc and other gamma emitters, a Nal(Tl) scintillation detector is used. The resolution of the scanner is dependent on the width of the slit-collimator, the distance between chromatogram and detector, and the window settings on the scaler. Artificial results may be obtained if the peaks are not symmetrical and comparable. 

A basic concern in experimental measurements at small angles is the spatial proximity of the scattered rays to the incident beam transmitted unmodified through the sample. The flux of the transmitted primary beam is usually at least several orders of magnitude higher than the scattered beam flux, and consequently even a minor intrusion of the tail of the primary beam can seriously degrade the observed data. To eliminate such contamination the incident beam must be very carefully collimated. A very fine collimation, irrespective of how it is achieved, is always accompanied by a proportionate reduction in the incident beam flux. To alleviate this difficulty, a slit collimation has often been employed. Some problems associated with the use of slit collimation, both in the measurement itself and in the analysis of the data, are discussed in Section 5.6. This collimation-vs.-flux dichotomy has become less... 

Fig 12 is a conceptual sketch of what a CT expls detection system might look like. The objects to be examined are placed on a conveyor belt, 2 to 3 meters long, which passes between an X-ray source on one side and an array of column detectors on the other. The design speed for the conveyor is 30cm/sec. The column detectors are 60cm hi with vertical slit collimators focused on the extended-anode X-ray source. Source and detector collimation will vary depending on the distance from the source to the detector, so that the spatial dispersion of the X-ray pencil beams thru the examined olqect will be the same for ail projection angles... 

A survey of different cameras used for small-angle analysis has been given by Pedersen [69] which provides a practically complete overview of all systems used up to now for SANS and SAXS. Here we shall focus on devices used for SAXS-measurements. In particular, an extended discussion of the Kratky-cam-era [70,71] will be given because this device allows very accurate SAXS-measurements using an ordinary X-ray generator. Most of the experimental investigations on polymeric latexes have been conducted using this type of SAXS-cam-era. Since this device works in slit collimation, the correction of the data will be discussed in detail. 

With slit collimation, higher resolution may be obtained with much less loss of intensity. Such cameras are, for example, of the Rigaku-Denki and Kratky type, the latter employing an ingenious U-bar collimating system which permits resolution up to several thousand angstroms. While slit cameras may not readily be used to characterise degrees of partial orientation, a compromise is possible with cameras of... 

The Fan Beam Reconstruction. With a slit collimated fan beam of x-rays, a projection is formed by the illumination of a fixed line of detector cells. A common detector structure in this respect is the equally spaced collinear array. The projection data for this geometry is represented by the function P ), where )3 is the projection angle of a typical ray path SB and p is the distance along the detector line D,D2 to a point at B (Fig. 26.22). To simplify the algebra, the fan beam projection R ) is referred to the detector plane moved to DJ/Dj. The ray path integral along SB is now associated with the point A on this imaginary detector line aXp = OA (Fig. 26.23). 

Commercial instruments use multiple tube or multiple slit collimator arrangements, often both before the analyzing crystal (the primary collimator) and before the detector (the secondary collimator). The collimator positions in a sequential WDXRF spectrometer are shown schematically in Figure 8.30. In many wavelength-dispersive (WD) instruments, two detectors are used in tandem, and a third auxiliary collimator may be required. Such an arrangement is shown in Figure 8.31. 

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