Chemistry Reference
In-Depth Information
The curves defining the projection of each undistorted pixel to the distorted image can
be interpolated from the distortion of the surrounding fiducial spots as shown in
Figure 6.3(c). In Figure 6.3(c), P
0
j
is a pixel in the distorted image, which can be
represented by the shaded square. The shaded area surrounded by four curves is the
projection of the area of pixel, P
i
, from the corrected image to the distorted image.
This area may have overlapping areas with several pixels in the distorted image. In this
case, the intensity of pixel P
i
contains the contributions from four pixels, labeled as 1,
2, 3, and 4. In general, the intensity of pixel P
i
is given as
p
i
¼
X
l
p
0
j
r
ij
ð6
:
5Þ
j¼k
where k is the number of the first contributing pixel in the distorted image to P
i
and l is
the number of the last contributing pixel; p
0
j
is the intensity of the contributing pixel
P
0
j
and r
ij
is the ratio of the contributing area to the whole pixel area; and p
i
is the
intensity of the pixel P
i
.Ther
ij
values for all pixels can be calculated from the spatial
correction lookup table. Assuming the detector behaves the same in the real diffrac-
tion frame data collection, the lookup table generated from the fiducial image can then
apply to the real diffraction frames. Calculating the contributing area for each pixel is
not a programmer friendly approach. The pixels in the undistorted image may be
mapped to rectangular pixels in the distorted image [12]. The curve edged pixels
are approximated by the rectangular pixels. For a given pixel in the undistorted image,
the projected position of the center of each edge is calculated. A rectangular region
can be defined by these four points in the distorted image. The r
ij
values can then be
determined from the contributing pixels in rectangular shaped overlap regions. The
intensities of the corrected pixels can then be calculated with Eq. (6.5). This algorithm
may reduce programming effort and computing time, but also introduce errors since
the actual edges are typically curved.
An alternative approach is to redistribute the counts of each pixel into a set of
identical subpixels as shown in Figure 6.3(d). The subpixels are discrete points evenly
distributed inside the pixel area marked by the blank circles or dark spots. The total
number of subpixels within each pixel is M. The contributing subpixels are those that
fall into the gray area and labeled by the dark spots. The number of contributing
subpixels in pixels 1, 2, 3, and 4 are the m
i1;
m
i2
;
m
i3
, andm
i4
, respectively. In general,
the intensity of pixel P
i
is given as
p
i
¼
X
M
X
l
l
m
ij
M
¼
1
p
0
j
p
0
j
m
ij
ð6
:
6Þ
j¼k
j¼k
The m
ij
values for all pixels can be calculated from the spatial correction
lookup table.
The spatial calibration must be done at the same sample-to-detector distance as the
diffraction data collection. A common practice is to collect several spatial calibration
files at different distances and then use them as needed. Figure 6.4(a) is a raw frame
used for spatial correction. It is collected with a fiducial plate fastened to a Bruker
