Beam profile

In traditional Fan-Beam CT the radiation emitted from the X-ray tube is collimated to a planar fan, and so most of the intensity is wasted in the collimator blades (Fig. 2a). Cone-Beam CT, where the X-rays not only diverge in the horizontal, but also in the vertical direction, allows to use nearly the whole emitted beam-profile and so makes best use of the available LINAC photon flux (Fig. 2b). So fast scanning of the samples three-dimensional structure is possible. For Cone-Beam 3D-reconstruction special algorithms, taking in consideration the vertical beam divergence of the rays, were developed. 

A commercial fs-laser (CPA-10 Clark-MXR, MI, USA) was used for ablation. The parameters used for the laser output pulses were central wavelength 775 nm pulse energy -0.5 mj pulse duration 170-200 fs and repetition rate from single pulse operation up to 10 Hz. In these experiments the laser with Gaussian beam profile was used because of the lack of commercial beam homogenizers for femtosecond lasers. 

Near field beam profile fo check the spatial and intensity profiles. 

It is useful for illustrative purposes to consider a laser beam with a Gaussian spatial profile and a square pulse time profile. If the laser has a Gaussian spatial beam profile the temperature at the surface of the Irradiated solid (z=0) at a time t after the laser pulse is started is given by(4) ... 

The cross-section of the primary X-ray beam is extended and not an ideal point. This fact results in a blurring of the recorded scattering pattern. By keeping the cross-section tiny, modern equipment is close to the point-focus collimation approximation - because, in general, the features of the scattering patterns are relatively broad. Care must be taken, if narrow peaks like equatorial streaks (cf. p. 166) are observed and discussed. The solution is either to desmear the scattering pattern or to correct the determined structure parameters for the integral breadth of the beam profile (Sect. 9.7). 

Smearing. Because scattering is emanating from every point of the irradiated volume, the recorded scattering pattern is smeared by the shape of the effective cross-section of the primary beam measured in the detector plane. In terms of mathematics this smearing is accomplished by convolution (Eq. (2.17)) with the primary beam profile. 

Measure the Beam Profile. Deconvolution is possible if the primary beam profile has been recorded. Recording of the beam profile is readily accomplished during the adjustment of the beamline prior to the experiment as long as the beam stop has not yet been mounted. Damage to the detector is avoided1 either by short exposure or by attenuation of the primary beam itself. 

Here the observed scattering pattern Iobs (x) is considered a digital image in 2D coordinates x = (xi,X3). W (x) is the measured primary beam profile. Similar application... 

The primary beam profile is reasonably measured during adjustment of the optics just before the beam stop is inserted. If overexposure of the detector can be avoided by choosing a short exposure interval this method is to be favored. Instead, attenuation of the primary beam by an absorber must be considered. 

Figure 7.1. Variation of a primary beam profile caused by multiple scattering, (a) Unaffected primary beam, (b) Moderate multiple scattering, (c) Strong multiple scattering... 

A Practical Hint20. In order to most accurately determine PI in Eq. (7.21), a mathematical theorem concerning convolution of a function with a shape function are helpful. The measured primary beam profile of the Kratky camera... 

It is thus reasonable to make the slit height H of the detector slit wider than the integral breadth of the intrinsic primary beam profile. In this case the observed integral breadth equals H - and can be accurately determined from the measured primary beam profile. 

Direct measurement of the primary beam profile may be carried out in the fields of MAXS and SAXS (cf. Sect. 6.4.3). 

A model-free method for the analysis of lattice distortions is readily established from Eq. (8.13). It is an extension of Stokes [27] method for deconvolution and has been devised by Warren and Averbach [28,29] (textbooks Warren [97], Sect. 13.4 Guinier [6], p. 241-249 Alexander [7], Chap. 7). For the application to common soft matter it is of moderate value only, because the required accuracy of beam profile measurement is rarely achievable. On the other hand, for application to advanced polymeric materials its applicability has been demonstrated [109], although the classical graphical method suffers from extensive approximations that reduce its value for the typical polymer with small crystal sizes and stronger distortions. 

Distribution of Rod Lengths. If the distribution of rod lengths shall be studied, the smearing of the equatorial streak by the primary beam profile must be eliminated99. After that the ID scattering intensity is computed by means of Eq. (8.56) and fitted to the respective ID model (e.g., Eq. (8.80)) from Sect. 8.7.1.1. Be careful. The rods may, in fact, not be stretched out perfectly but only resemble long worms instead. 

Many industrial semi-crystalline polymer materials like polypropylene, polyamides, or polyesters contain nucleating agents or clarifiers which form needle-shaped aggregates already in the polymer melt. "For this purpose the pattern is desmeared using the measured primary beam. For a less involved treatment it may be sufficient to know the integral width of the primary beam profile in fiber direction. 

We need Bp in the perpendicular direction with respect to the direction in which the streak is extending. The beam profile has (hopefully) been measured after the adjustment of the instrument and before installation of the beam stop. Before being used in Eq. (9.27) or Eq. (9.28) Bp is converted to reciprocal space units. 

Croitoru N., Inberg A., Dahan R. and Ben David M., Scattering and beam profile measurements of plastic, silica, andmetal radiation waveguides, J. Biomedical Optics, 1997 2 (2) 235-242. 

Ion beam profiling techniques have been used to determine the total content and concentration versus depth of hydrogen in a-Si H (Lanford et al., 1976 Brodsky et al., 1977b Ziegler et al., 1978 Milleville et al., 1979). An a-Si H sample is bombarded with 15N ions, which can undergo a resonant reaction. 

Recently, an interesting correlation between the laser pulse polarization and the ellipticity of the electron beam profile has been observed [71]. However, no major influence of laser polarization on the efficiency of the electron acceleration processes has been observed so far, nor this influence has been predicted by theory and simulations, differently from the proton acceleration. For proton acceleration, a great improvement on bunch charge and quality are expected by using circularly polarized laser pulses focused on thin foils at ultra-high intensities [72-74]. 

Fig. 12.10 (a) SEM image of the circular Bragg nanocavity designed to support the m 0 mode in the 300 nm wide central pillar, (b) The evolution of the emitted spectrum from the device shown in Fig. 12.9a as a function of the pump intensity. Inset L L curve, indicating a lasing threshold of Pth 900 pW. (c) Calculated modal intensity profile of the nanocavity, (d) IR image of the emitted beam profile... 

Fig. 17. Angular LEED beam profiles plotted for various values of the coverage for H on Fe(llO) at a temperature T = 200 K. From Imbihl et ol. .)...

Dreisewerd, K. Schiirenberg, M. Karas, M. Hillenkamp, F. Influence of the Laser Intensity and Spot Size on the Desorption of Molecules and Ions in MALDI With a Uniform Beam Profile. Int. J. Mass Spectrom. Ion Proc. 1995, 747, 127-148. 

It is possible to compensate for curvature in theoretical simulation of the rocking curve. If the beam profile is square, then the rocking curve is simply correlated with... 

---