LB Thesis SNR - Revision history

Brenleyt: /* Background Analysis */

2018-06-27T19:41:38Z

Background Analysis

Brenleyt: /* Background Analysis */

2018-06-24T23:48:07Z

Background Analysis

Brenleyt: /* Background Analysis */

2018-06-24T23:43:25Z

Background Analysis

Brenleyt: /* Background Analysis */

2018-06-24T23:27:43Z

Background Analysis

Brenleyt: /* Background Analysis */

2018-06-24T23:23:18Z

Background Analysis

Brenleyt: /* Background Analysis */

2018-06-24T21:50:37Z

Background Analysis

Brenleyt: /* Background Analysis */

2018-06-24T21:40:27Z

Background Analysis

Brenleyt at 21:35, 24 June 2018

2018-06-24T21:35:31Z

Brenleyt: /* Background Analysis */

2018-06-24T21:34:20Z

Background Analysis

Brenleyt: Created page with "=Background Analysis= In order to find the SNR at $t_{Beam Off}$ , the background was analyzed to check if it remained constant from $t_{Beam Off}$ un..."

2018-06-24T20:48:21Z

Created page with "=Background Analysis= In order to find the SNR at <math> t_{Beam Off} </math>, the background was analyzed to check if it remained constant from <math> t_{Beam Off} </math> un..."

New page

=Background Analysis=
In order to find the SNR at <math> t_{Beam Off} </math>, the background was analyzed to check if it remained constant from <math> t_{Beam Off} </math> until <math> 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.

@@ Line 29: / Line 29: @@
 [[File:LB Thesis SNR Se75 BeamOff.png|200px]]
-Se-81m Fit Parameters: b = -0.32 <math> \pm </math> 0.01, m = 0.39 <math> \pm </math> 0.01
+Se-81m Fit Parameters: b = -0.32 <math> \pm </math> 0.01, m = 0.39 <math> \pm </math> 0.01, p<0.01
-Se-75 Fit Parameters: b = -0.01 <math> \pm </math> 0.0004 , m = 0.01 <math> \pm </math> 0.0004
+Se-75 Fit Parameters: b = -0.01 <math> \pm </math> 0.0004 , m = 0.01 <math> \pm </math> 0.0004, p = 0.02
 The intersection with unity was found to be 3.38 <math> \pm </math> 0.07% for Se-81m and 101 <math> \pm </math> 4%. This makes physical sense because the signal to noise ratio for the first two measurements of Se-81m in the 1% sample had a signal to noise ratio of less than one, while the energy line for Se-75 was never visible in any of the initial spectra.

← Older revision		Revision as of 23:48, 24 June 2018
Line 28:		Line 28:
	[[File:LB Thesis SNR Se81m BeamOff.png\|200px]]		[[File:LB Thesis SNR Se81m BeamOff.png\|200px]]
	[[File:LB Thesis SNR Se75 BeamOff.png\|200px]]		[[File:LB Thesis SNR Se75 BeamOff.png\|200px]]
		+
		+	Se-81m Fit Parameters: b = -0.32 <math> \pm </math> 0.01, m = 0.39 <math> \pm </math> 0.01
		+
		+	Se-75 Fit Parameters: b = -0.01 <math> \pm </math> 0.0004 , m = 0.01 <math> \pm </math> 0.0004
		+
		+	The intersection with unity was found to be 3.38 <math> \pm </math> 0.07% for Se-81m and 101 <math> \pm </math> 4%. This makes physical sense because the signal to noise ratio for the first two measurements of Se-81m in the 1% sample had a signal to noise ratio of less than one, while the energy line for Se-75 was never visible in any of the initial spectra.
		+
		+	The error in the signal to noise ratio was calculated with
		+
		+	<math> \sigma_{SNR} = \sqrt{(\frac{1}{m^2})^2 \sigma_{m}^2 + \sigma_b^2}

← Older revision		Revision as of 23:43, 24 June 2018
Line 19:		Line 19:
	1% Fit Parameters:		1% Fit Parameters:
	1% Fit Parameters 4.685 <math> \pm </math> 0.004, 4.30 <math> \pm </math> 0.001 <math> \times 10^{-4} </math>		1% Fit Parameters 4.685 <math> \pm </math> 0.004, 4.30 <math> \pm </math> 0.001 <math> \times 10^{-4} </math>
		+
		+	The exponentiated constant was used as an "initial activity" of the background. This "initial activity" was then efficiency corrected and divided by the initial activity of the selenium line of interest's activity (103 for Se-81m and 265 for Se-75). The signal to noise ratio was calculated with
		+
		+	<math> \frac{Signal-Background}{Background} </math> and the relative error was taken.
		+
		+	Once the points had been found, a linear fit was used to determine where the signal to noise ratio would intersect with unity.
		+
		+	[[File:LB Thesis SNR Se81m BeamOff.png\|200px]]
		+	[[File:LB Thesis SNR Se75 BeamOff.png\|200px]]

← Older revision		Revision as of 23:27, 24 June 2018
Line 12:		Line 12:
	[[File:LB 170048 Background HLPlot Expo.png\|200px]]		[[File:LB 170048 Background HLPlot Expo.png\|200px]]
	[[File:LB 170049 Background HLPlot Expo.png\|200px]]		[[File:LB 170049 Background HLPlot Expo.png\|200px]]
		+
		+	50% Fit Parameters: Constant = 2.11 <math> \pm </math> 0.004 , Slope = 1.99 <math> \pm </math> 0.002 <math> \times 10^{-4} </math>
		+
		+	10% Fit Parameters: 3.22 <math> \pm </math> 0.008, Slope = 3.67 <math> \pm </math> 0.003 <math> \times 10^{-4} </math>
		+
		+	1% Fit Parameters:
		+	1% Fit Parameters 4.685 <math> \pm </math> 0.004, 4.30 <math> \pm </math> 0.001 <math> \times 10^{-4} </math>

← Older revision		Revision as of 23:23, 24 June 2018
Line 8:		Line 8:
	The clearest exponential behavior is seen in the 1% sample. The background rate dropped by 62% between the first and second measurements (<math> \Delta t </math> = 7.5 minutes). This indicated that considering the background to be constant from <math> t_{Beam Off} </math> until <math> t_{Measure} </math>, which was an average of 23.3 <math> \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).		The clearest exponential behavior is seen in the 1% sample. The background rate dropped by 62% between the first and second measurements (<math> \Delta t </math> = 7.5 minutes). This indicated that considering the background to be constant from <math> t_{Beam Off} </math> until <math> t_{Measure} </math>, which was an average of 23.3 <math> \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).

		+
		+	[[File:LB 170047 Background HLPlot Expo.png\|200px]]
		+	[[File:LB 170048 Background HLPlot Expo.png\|200px]]
	[[File:LB 170049 Background HLPlot Expo.png\|200px]]		[[File:LB 170049 Background HLPlot Expo.png\|200px]]

← Older revision		Revision as of 21:50, 24 June 2018
Line 6:		Line 6:
	[[File:LB 170049 Background Overlay xmgrace.png\|200px]]		[[File:LB 170049 Background Overlay xmgrace.png\|200px]]

−	The clearest exponential behavior is seen in the 1% sample. The background rate dropped by 62% between the first and second measurements (<math> \~~delta~~ t </math> = 7.5 minutes). This indicated that considering the background to be constant from <math> t_{Beam Off} </math> until <math> t_{Measure} </math>, which was an average of	+	The clearest exponential behavior is seen in the 1% sample. The background rate dropped by 62% between the first and second measurements (<math> \Delta t </math> = 7.5 minutes). This indicated that considering the background to be constant from <math> t_{Beam Off} </math> until <math> t_{Measure} </math>, which was an average of 23.3 <math> \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).
		+
		+	[[File:LB 170049 Background HLPlot Expo.png\|200px]]

← Older revision		Revision as of 21:40, 24 June 2018
Line 5:		Line 5:
	[[File:LB 170048 Background Overlay xmgrace.png\|200px]]		[[File:LB 170048 Background Overlay xmgrace.png\|200px]]
	[[File:LB 170049 Background Overlay xmgrace.png\|200px]]		[[File:LB 170049 Background Overlay xmgrace.png\|200px]]
		+
		+	The clearest exponential behavior is seen in the 1% sample. The background rate dropped by 62% between the first and second measurements (<math> \delta t </math> = 7.5 minutes). This indicated that considering the background to be constant from <math> t_{Beam Off} </math> until <math> t_{Measure} </math>, which was an average of

← Older revision		Revision as of 21:35, 24 June 2018
Line 3:		Line 3:

	[[File:LB 170047 Background Overlay xmgrace.png\|200px]]		[[File:LB 170047 Background Overlay xmgrace.png\|200px]]
		+	[[File:LB 170048 Background Overlay xmgrace.png\|200px]]
		+	[[File:LB 170049 Background Overlay xmgrace.png\|200px]]

← Older revision		Revision as of 21:34, 24 June 2018
Line 1:		Line 1:
	=Background Analysis=		=Background Analysis=
	In order to find the SNR at <math> t_{Beam Off} </math>, the background was analyzed to check if it remained constant from <math> t_{Beam Off} </math> until <math> 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.		In order to find the SNR at <math> t_{Beam Off} </math>, the background was analyzed to check if it remained constant from <math> t_{Beam Off} </math> until <math> 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.
		+
		+	[[File:LB 170047 Background Overlay xmgrace.png\|200px]]

LB Thesis SNR - Revision history

Brenleyt: /* Background Analysis */

Brenleyt: /* Background Analysis */

Brenleyt: /* Background Analysis */

Brenleyt: /* Background Analysis */

Brenleyt: /* Background Analysis */

Brenleyt: /* Background Analysis */

Brenleyt: /* Background Analysis */

Brenleyt at 21:35, 24 June 2018

Brenleyt: /* Background Analysis */

Brenleyt: Created page with "=Background Analysis= In order to find the SNR at t_{Beam Off} , the background was analyzed to check if it remained constant from t_{Beam Off} un..."

Brenleyt: Created page with "=Background Analysis= In order to find the SNR at $t_{Beam Off}$ , the background was analyzed to check if it remained constant from $t_{Beam Off}$ un..."