Measurement of the 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). 

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. 

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. 

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. 

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. 

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. 

---