Braun Appendix 2 MCA166-USB algorithm, formulas, Area and the Area Uncertainty Function

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 =

(ROIend

−

ROIbegin + 1)

* (∑

ROIbegin

Spectrum + ∑

ROIend + 3Spectrum )

i= ROIbegin − 3

8

i

i= ROIend

i

ROIend

Integral = ∑

Spectrumi

i= ROIbegin

Area Uncertainty =

⎛

⎛

ROIbegin

ROIend + 3

⎞

⎛

( ROIend −

ROIbegin + 1) ⎞

2

⎞

⎜

⎟

Integral +

⎜

⎜

∑

Spectrum +

∑

Spectrum ⎟

∗ ⎜

⎟

⎟

⎜

i= ROI

− 3

i

ROI

i ⎟

⎜

8

⎟

⎜

⎝

⎠

⎟

⎝

begin

end

⎝

⎠

⎠

where,

Spectrumi

= the absolute number of counts in channels i

ROIbegin

= the ROI’s start channel

ROIend

= the ROI’s stop channel

32