LB Thesis SNR

Background Analysis

In order to find the SNR at [math]\displaystyle{ t_{Beam Off} }[/math], the background was analyzed to check if it remained constant from [math]\displaystyle{ t_{Beam Off} }[/math] until [math]\displaystyle{ t_{Measure} }[/math]. First, the background was plotted for each concentration of Se/Soil and was overlaid with the the background in the pure sample for each respective target.

The clearest exponential behavior is seen in the 1% sample. The background rate dropped by 62% between the first and second measurements ([math]\displaystyle{ \Delta t }[/math] = 7.5 minutes). This indicated that considering the background to be constant from [math]\displaystyle{ t_{Beam Off} }[/math] until [math]\displaystyle{ t_{Measure} }[/math], which was an average of 23.3 [math]\displaystyle{ \pm }[/math] 2.67 minutes would not be sufficient. Since this was the case, an exponential fit was attempted on the 1% mixture data to find the half life of the background (even though this is still just an estimate).

50% Fit Parameters: Constant = 2.11 [math]\displaystyle{ \pm }[/math] 0.004 , Slope = 1.99 [math]\displaystyle{ \pm }[/math] 0.002 [math]\displaystyle{ \times 10^{-4} }[/math]

10% Fit Parameters: 3.22 [math]\displaystyle{ \pm }[/math] 0.008, Slope = 3.67 [math]\displaystyle{ \pm }[/math] 0.003 [math]\displaystyle{ \times 10^{-4} }[/math]

1% Fit Parameters: 1% Fit Parameters 4.685 [math]\displaystyle{ \pm }[/math] 0.004, 4.30 [math]\displaystyle{ \pm }[/math] 0.001 [math]\displaystyle{ \times 10^{-4} }[/math]