Biomedical Engineering Reference
In-Depth Information
x10
2
100
D
p
8
80
spectrum 2
spectrum 1
60
4
40
20
0
1
2
3
4
5
6
7
x 10
5
p
2
p
1
6.37
6.38
p
2
Time
x 10
5
x10
3
x10
2
spectrum 2
before
alignment
spectrum 1
spectrum 2
before
alignment
spectrum 2
after alignment
8
1.5
spectrum 2
after alignment
spectrum 1
1.0
4
0.5
0
0
8.33
8.34
8.35
x 10
4
6.37
6.38
Time
Time
x 10
5
Fig. 2. Illustration of alignment: (a) shift of arrival time for the same peak in two
spectra; (b) the linear trend of the shifts with respect to peak arrival time; (c) and (d)
after alignment the shift is corrected.
be the estimated peak positions of the rst isotopic peak in the two spectra
as indicated in Fig. 2(a), then the shift between this peak pair p = p
1
p
2
is readily computed. Specically, using the estimated peak positions, the
shifts between all paired peaks in the two spectra are easily calculated and
are found to increase as peaks arrive at the detector later, as shown in Fig.
2(b), where the shifts are plotted versus peak positions. It is evident from
Fig. 2(b) that the shifts, at least to a rst order approximation, increase
linearly with peak position. A possible cause for this linearly increasing shift
may be the dierence(s) in surface morphology which aects the kinetic
energy that the ejected ions gain during the acceleration stage. There are,
of course, many other possible reasons. Nevertheless, the observed linear
dependence implies that we can align one spectrum to another by a simple
linear operation. An example would be aligning spectrum 2 in Fig. 2(a) to
spectrum 1. More specically, using the least squares method, p
i
is t to
a linear function of p
2
as p
i
= ap
2
+ b, where the superscript i means the
i
th
peak pair. The resulting a and b give the information about how the
time axis of spectrum 2 should be scaled and shifted to match spectrum 1.
This simple linear operation is found to eectively enable global alignment
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