Conic/receiving slit intersection

In a special case there is only one intersection of the line and the conics. This can occur if the line is parallel to the main axis of the conic (in the case of a parabola), or the line is parallel to the asymptote of the hyperbola. Only the intersection points x y, lying on the receiving slit boundary are of interest. 

Suppose points = xi,yi,0 and Xj = x2,y2,0 represent the intersections of the conic and receiving slit boundary. The registered intensity is proportional to the dihedral angle 4> between two planes containing points Ai, A2, Xi and A, 2, This angle is the angle between the two normals Ni and N2 to the plane in question ... 

Figure 6.6 Possible intersections of the conics and receiving slit (20 < 90°).

Absorption. An absorption correction is important for thick specimens with small absorption coefficient for X-rays. Consideration of absorption means that point A2 has a non-zero y component. As a consequence of this there is another conic that is important for considering the absorption. This conic is the intersection of the diffraction cone and the surface plane of the sample. Figure 6.16 shows schematically a part of the diffraction cone and a cross-section of the latter with the sample surface plane (plane in coordinate system CSl.). Points Dip (i= 1-4) are point projections of the receiving slit from point A2. Points Pap are projections of the intersection points P of the receiving slit and conic in the receiving slit plane. 

Intersection of the Diffraction and Reflection Conics in the Receiving Slit Plane... 

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