Pattern Correction
The figure on the left shows a typical fiber pattern of polypropylene before mapping it into reciprocal space. The mirror axis in the pattern is rotated by the angle with respect to the vertical direction. This shortcoming is compensated by simple rotation of the picture. 4 straight arrows point at 4 reflexion images of a chosen reference reflexion. Their positions are used to determine the fiber tilt angle . The image has been recorded on a CCD detector. It shows the logarithmic intensitity in pseudo-color representation. Here bright colors represent high intensity.
After determination of the distance between sample and detector is computed using known crystallographic data of the reference reflexion, a uniformly gridded map for the representative fiber plane in reciprocal space is constructed and the diffraction data are fed into this map. The figure on the right shows the result. Change of scattering intensity has been considered in the unwarping process. Because of the curvature of the surface of the Ewald sphere there remain white spots at the meridian, in which structure information is missing. Only in the center of the image and at a s-value related to the scattering angle there is structure information on the meridian. Of course, there is now 4-quadrant symmetry. This means that in the example pattern part of the missing information may be copied "from the lower half to the upper half" into the white areas. Thus, it frequently makes sense to tilt the fiber intentionally.
The three-dimensional sketch demonstrates that in the example experiment the collected information on the molecular structure of the polypropylene fiber is almost complete. By rotation of the plane pattern about the meridian the scattering data collected in 4 s fill an almost spherical volume of s-space. In the example the 4-quadrant symmetry has not yet been considered to fill part of the white spots. For clarity a quarter of the sphere has been cut out, but keeping the equatorial plane itself.
Read more about this topic: Fiber Diffraction
Famous quotes containing the words pattern and/or correction:
“It is a very true and expressive phrase, “He looked daggers at me,” for the first pattern and prototype of all daggers must have been a glance of the eye.... It is wonderful how we get about the streets without being wounded by these delicate and glancing weapons, a man can so nimbly whip out his rapier, or without being noticed carry it unsheathed. Yet it is rare that one gets seriously looked at.”
—Henry David Thoreau (1817–1862)
“There are always those who are willing to surrender local self-government and turn over their affairs to some national authority in exchange for a payment of money out of the Federal Treasury. Whenever they find some abuse needs correction in their neighborhood, instead of applying the remedy themselves they seek to have a tribunal sent on from Washington to discharge their duties for them, regardless of the fact that in accepting such supervision they are bartering away their freedom.”
—Calvin Coolidge (1872–1933)