MCA166-USB
APPENDIX 2 - MCA166-USB algorithm, formulas
This appendix lists the algorithms used by the MiniMCA for the following functions:
●
Area, Area uncertainty
●
Centroid
●
FWHM
●
Smooth
●
Strip
●
Energy Calibration
The Area and the Area Uncertainty Function:
The area algorithm calculates the number of counts above the background in a ROI. The background area is
determined by averaging 4 points on both sides of the peak (the ROI limit points and 3 outer points) and linear
fit:
Area = Integral - Background
Background =
(
)
(
)
∑
∑
+
=
−
=
+
+
−
3
3
*
8
1
end
end
begin
begin
ROI
ROI
i
i
ROI
ROI
i
i
begin
end
Spectrum
Spectrum
ROI
ROI
Integral =
Spectrum
i
i ROI
ROI
begin
end
=
∑
Area Uncertainty =
(
)
Integral
Spectrum
Spectrum
ROI
ROI
i
i
ROI
ROI
i ROI
ROI
end
begin
end
end
begin
begin
+
+
∗
−
+
+
=
−
∑
∑
3
3
2
1
8
where,
Spectrum
i
= the absolute number of counts in channels i
ROI
begin
= the ROI’s start channel
ROI
end
= the ROI’s stop channel
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