Geometry normal transmission

In practice, for SAXS and USAXS experiments carried out in normal-transmission geometry the set of equations... 

The example is valid for the most simple case SAXS or USAXS in normal-transmission geometry. 27The same line of code evaluates curves, images or data structures of higher dimensionality (imagine time as an additional coordinate)... 

Figure 4.1. Typical X-ray setup with 2D detector in normal-transmission geometry. The intensity of the incident X-ray beam is measured in an ionization chamber (a). Thereafter it penetrates the sample which is subjected to some process. At a distance R (cf. Table 2.1 on p. 7) behind the sample the detector is recording the scattering pattern. In its center (b) the detector is protected by a beam stop. It is equipped with a pin-diode which records the intensity of the attenuated beam...

Figure 4.2. Sketch of a laboratory setup comprising a rotating anode, conventional beam shaping optics, and an X-ray camera with the sample in normal-transmission geometry...

Some experiments are aiming at the study of structure evolution. In general, the studied material is isotropic or exhibits simple anisotropy (e.g., fiber symmetry). Most frequently the material is irradiated in normal-transmission geometry. A synchrotron beamline is necessary, because in situ recording during the materials processing is requested with a cycle time of seconds between successive snapshots (time-resolved measurements). 

For USAXS and SAXS studies in normal-transmission geometry it is more convenient to carry out this step later - after the absorption and background correction. 

Figure 7.2. Absorption in normal-transmission geometry. The path of the photon through a sample of thickness t before and after its scattering about the angle 20... 

General Routes. If a SAXS beamline in normal transmission geometry is used, calibration to absolute intensity is, in general, carried out indirectly using secondary standards. Direct methods require direct measurement of the primary beam intensity under consideration of the geometrical setup of the beamline. On a routine basis such direct calibration was commercially available for the historic Kratky camera equipped with zero-dimensional detector and moving slit device 14. 

This is the differential definition of the absolute intensity. The total absolute intensity can be deduced by integration from Eq. (7.19) and Eq. (7.20) for any normal transmission geometry. Geometries are discriminated by the shape and size of the irradiated volume, the image of the primary beam in the registration plane17 of the detector, and the dimensions of the detector elements18. 

Direct calibration to absolute intensity is not a usual procedure at synchrotron beamlines. Nevertheless, the technical possibilities for realization are improving. Therefore the basic result for the total scattering intensity measured in normal transmission geometry is presented. At a synchrotron beamline point-focus can be realized in good approximation and the intensity /(s) is measured. Then integration of Eq. (7.19) results in... 

CDFs are computed from scattering data which are anisotropic and complete in reciprocal space. Thus the minimum requirement is a 2D SAXS pattern of a material with fiber symmetry taken in normal transmission geometry (cf. p. 37, Fig. 4.1). Required pre-evaluation of the image is described in Chap. 7. 

Figure 7.3. Effect of absorption in normal-transmission geometry. The total transmitted scattering intensity, It, as a fnnction of the rednced sample thickness. The highest scattering signal is obtained at utopt/cos (26) = 1 with tgpt being the optimum sample thickness...

In normal transmission geometry any mathematical treatment of calibration to absolute units [87-90] starts from the basic differential relation among the scattering intensity in the detector, the primary intensity and the structure... 

Fig. 3.19 Schematic illustration of the measurement geometry for Mossbauer spectrometers. In transmission geometry, the absorber (sample) is between the nuclear source of 14.4 keV y-rays (normally Co/Rh) and the detector. The peaks are negative features and the absorber should be thin with respect to absorption of the y-rays to minimize nonlinear effects. In emission (backscatter) Mossbauer spectroscopy, the radiation source and detector are on the same side of the sample. The peaks are positive features, corresponding to recoilless emission of 14.4 keV y-rays and conversion X-rays and electrons. For both measurement geometries Mossbauer spectra are counts per channel as a function of the Doppler velocity (normally in units of mm s relative to the mid-point of the spectrum of a-Fe in the case of Fe Mossbauer spectroscopy). MIMOS II operates in backscattering geometry circle), but the internal reference channel works in transmission mode...

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