Chemistry Reference
In-Depth Information
FIGURE 2.9 Relationship between a pixel P and detector position in the laboratory
coordinates, X
L
Y
L
Z
L
.
calibration, and spatial correction. The diffraction space coordinates (2u, g) for a pixel
at P(x,y) are given by
2u ¼ arccos
x sin a
þ
D cos a
p
D
2
ð0
<
2u
< pÞ
ð2
:
8Þ
þx
2
þ y
2
x cos a
D sin a
jx cos a D sin aj
y
y
2
g ¼
arccos
q
ðp < g pÞ
2
þðx cos a D sin aÞ
ð2
:
9Þ
h
3
g in the sample coordinates
S
1
S
2
S
3
corresponding to each pixel can then be calculated by Eq. (2.19). In
Eq. (2.9), when x cos a D sin a ¼ 0, the division by zeromay cause the computer
calculation to terminate or return an error value. In this case, the equation can be
expressed as
The unit diffraction vector components fh
1
;
h
2
;
8
<
y
y
2
arccos
q
if x cos a D sin a
2
þðx cos a D sin aÞ
g ¼
ð2
:
10Þ
y
y
2
:
arccos
q
if x cos a
<
D sin a
2
þðx cos a D sin aÞ
