783620H / 1013 5. MENU COMMANDS
5.4.3.1. Calculation
The program subtracts the calculated background, channel by channel, and attempts a leastsquares fit of a Gaussian function to the remaining data. If unsuccessful, it displays “Could Not
Properly Fit Peak.” If successful, the centroid is based on the fitted function. The reported widths are linearly interpolated between the background-subtracted channels. The spectrum components used in the background calculation are illustrated in see Fig. 131.
The background on the low channel side of the peak is the average of the first n channels of the ROI, where n is the number of background points selected on the dialog under Calculate/Settings... (Section 5.4.1).
The channel number for this background point is the midpoint fractional channel of the n points. The background on the high channel side of the peak is the average of the last n channels of the ROI. The channel number for this background point is also the midpoint fractional channel of the n points.
These (n
!1) points on each side of the peak form the end points of the straight-line background.
The background is given by the following:
Fig. 131. Calculation Details.
(15)
where:
B
= the background area
l
= the ROI low limit
h
= the ROI high limit
C i
= the contents of channel i
n
= the number of background points
The gross area is the sum of all the channels marked by the ROI according to the following:
(16)
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where:
A g
= the gross counts in the ROI
l
= the ROI low limit
h
= the ROI high limit
C i
= the contents of channel i
The adjusted gross area is the sum of all the channels marked by the ROI but not used in the background according to the following:
(17)
where:
A ag
= the adjusted gross counts in the ROI
l
= the ROI low limit
h
= the ROI high limit
C i
= the contents of channel i
n
= the number of background points
The net area is the adjusted gross area minus the adjusted calculated background, as follows:
(18)
The uncertainty in the net area is the square root of the sum of the squares of the uncertainty in the adjusted gross area and the weighted error of the adjusted background. The background uncertainty is weighted by the ratio of the adjusted peak width to the number of channels used to calculate the adjusted background. Therefore, net peak-area uncertainty is given by:
(19)
where:
A ag
= the adjusted gross area
A n
= the net area
B = the background area
l = the ROI low limit
h = the ROI high limit
n
= the number of background points
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