Difference: 20170308_MSciSpectroscopyMeeting (1 vs. 5)

Revision 508 Mar 2017 - JamesAngthopo

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
$\sigma_0$ Error
  • $\chi^2$ equation used
Line: 84 to 84
 
META FILEATTACHMENT attachment="chivals.pdf" attr="" comment="shows values for all cadmium and helium data" date="1488959177" name="chivals.pdf" path="chivals.pdf" size="30690" user="zyvb137" version="1"
META FILEATTACHMENT attachment="Part_spec.pdf" attr="" comment="sigam0 for 60000 instead of 5000" date="1488959358" name="Part_spec.pdf" path="Part_spec.pdf" size="286063" user="zyvb137" version="1"
META FILEATTACHMENT attachment="Postage_y_f.pdf" attr="" comment="'Postage stamp' plot of all y-fit differences" date="1488969037" name="Postage_y_f.pdf" path="Postage_y_f.pdf" size="54083" user="zyvb951" version="2"
Added:
>
>
META FILEATTACHMENT attachment="allparams.txt" attr="" comment="Parameters for all spectral lines used to calibrate" date="1488970015" name="allparams.txt" path="allparams.txt" size="5176" user="zyvb137" version="1"

Revision 408 Mar 2017 - WilliamBurrows

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
$\sigma_0$ Error
  • $\chi^2$ equation used
Line: 8 to 8
 
  • Returned plot of gaussian fit with error bars:

Calib_Cd_0300.png

Calib_He_0400.png
  • Cadmim at micrometer setting of 03.00mm had $\chi^2$ value of 8541.6015 abd Helium at micrometer setting of 4.00 had a $\chi^2$ value of 88793.4233.
Deleted:
<
<

RMS Error

  • Fit-data difference as a function of intensity for G*C fits to lamp lines:
    Inensity_diff.png

  • RMS equation used:
 \begin{equation} x_{\rm{rms}} = \sqrt{ \bigg( \frac{1}{N} \sum_{i = i}^{N} x_i^2 \bigg) } \end{equation}

  • RMS values of data in 20 bins of width 1003796 PE:
    RMS_diff.png

  • Form of the fit:
 \begin{equation} f(x; C_1, C_0) = C_1x + C_0 \end{equation}

  • Fitted parameter values:
Parameter Value
$C_1$ 6.27E-03 $\pm$ 2.14E-03
$C_0$ 1.72E05 $\pm$ 2.48E04
 Convolutions

  • Gaussian equation:
Line: 57 to 36
 
$N_{\rm{DOF}}$ 115 114
$\chi^2 /$ $N_{\rm{DOF}}$ 1.18E04 3.98E03
Added:
>
>
RMS Error

  • Fit-data difference as a function of intensity for G*C fits to lamp lines:
    Inensity_diff.png

  • RMS equation used:
 \begin{equation} x_{\rm{rms}} = \sqrt{ \bigg( \frac{1}{N} \sum_{i = i}^{N} x_i^2 \bigg) } \end{equation}

  • RMS values of data in 20 bins of width 1003796 PE:
    RMS_diff.png

  • Form of the fit:
 \begin{equation} f(x; C_1, C_0) = C_1x + C_0 \end{equation}

  • Fitted parameter values:
Parameter Value
$C_1$ 6.27E-03 $\pm$ 2.14E-03
$C_0$ 1.72E05 $\pm$ 2.48E04

 -- WillBurrows - 07 Mar 2017
Added:
>
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META FILEATTACHMENT attachment="chivals.pdf" attr="" comment="shows values for all cadmium and helium data" date="1488959177" name="chivals.pdf" path="chivals.pdf" size="30690" user="zyvb137" version="1"
META FILEATTACHMENT attachment="Part_spec.pdf" attr="" comment="sigam0 for 60000 instead of 5000" date="1488959358" name="Part_spec.pdf" path="Part_spec.pdf" size="286063" user="zyvb137" version="1"
Added:
>
>
META FILEATTACHMENT attachment="Postage_y_f.pdf" attr="" comment="'Postage stamp' plot of all y-fit differences" date="1488969037" name="Postage_y_f.pdf" path="Postage_y_f.pdf" size="54083" user="zyvb951" version="2"

Revision 308 Mar 2017 - JamesAngthopo

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
Added:
>
>
$\sigma_0$ Error
  • $\chi^2$ equation used
 \begin{equation} \chi^2=\sum_{i=1}^{N}\frac{y_i-f(x_i;\vec{\theta})}{\sigma_i^2+\sigma_0^2} \end{equation}
  • $\sigma_0$ chosen to be a constant at 5E3.
  • Returned plot of gaussian fit with error bars:

Calib_Cd_0300.png

Calib_He_0400.png
  • Cadmim at micrometer setting of 03.00mm had $\chi^2$ value of 8541.6015 abd Helium at micrometer setting of 4.00 had a $\chi^2$ value of 88793.4233.

 RMS Error

  • Fit-data difference as a function of intensity for G*C fits to lamp lines:
    Inensity_diff.png
Line: 65 to 75
 
META FILEATTACHMENT attachment="latex5081678e994636ab4b8922cf136e0409.png" attr="h" comment="" date="1488934101" name="latex5081678e994636ab4b8922cf136e0409.png" user="zyvb137" version="1"
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Added:
>
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META FILEATTACHMENT attachment="Calib_Cd_0300.png" attr="" comment="Cadmium data at micrometer setting of 3mm" date="1488957198" name="Calib_Cd_0300.png" path="Calib_Cd_0300.png" size="114797" user="zyvb137" version="1"
META FILEATTACHMENT attachment="Calib_He_0400.png" attr="" comment="Helium data mircometer setting of 4.00mm" date="1488957230" name="Calib_He_0400.png" path="Calib_He_0400.png" size="88333" user="zyvb137" version="1"
META FILEATTACHMENT attachment="latex813baac07644eb59ab88819cdc08e64d.png" attr="h" comment="" date="1488957502" name="latex813baac07644eb59ab88819cdc08e64d.png" user="zyvb137" version="1"
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META FILEATTACHMENT attachment="chivals.pdf" attr="" comment="shows values for all cadmium and helium data" date="1488959177" name="chivals.pdf" path="chivals.pdf" size="30690" user="zyvb137" version="1"
META FILEATTACHMENT attachment="Part_spec.pdf" attr="" comment="sigam0 for 60000 instead of 5000" date="1488959358" name="Part_spec.pdf" path="Part_spec.pdf" size="286063" user="zyvb137" version="1"

Revision 208 Mar 2017 - JamesAngthopo

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
RMS Error
Changed:
<
<
  • Fit-data difference as a function of intensity for G*C fits to lamp lines:
    Inensity_diff.png
>
>
  • Fit-data difference as a function of intensity for G*C fits to lamp lines:
    Inensity_diff.png
 
  • RMS equation used:
 \begin{equation} x_{\rm{rms}} = \sqrt{ \bigg( \frac{1}{N} \sum_{i = i}^{N} x_i^2 \bigg) } \end{equation}
Changed:
<
<
  • RMS values of data in 20 bins of width 1003796 PE:
    RMS_diff.png
>
>
  • RMS values of data in 20 bins of width 1003796 PE:
    RMS_diff.png
 
  • Form of the fit:
%BEGINLATEX% \begin{equation} f(x; C_1, C_0) = C_1x + C_0 \end{equation}
Line: 33 to 33
 
 \begin{equation} (G * C)(x) = \sum_{i} G(x - i;a, x_0, \sigma, C_0, C_1)C(i;r) \end{equation}
Changed:
<
<
  • G*C and Gaussian fits to the He line at 4.00mm:
    Conv_Gauss_He0400.png
>
>
  • G*C and Gaussian fits to the He line at 4.00mm:
    Conv_Gauss_He0400.png
 
  • Fitted parameter values:
Parameter Gaussian G*C
Line: 45 to 45
 
$C_0$ 1.15E05 $\pm$ 1.09E05 1.31E05 $\pm$ 2.78E04
$\chi^2$ 1.35E06 4.53E05
$N_{\rm{DOF}}$ 115 114
Changed:
<
<
| $\chi^2 / $N_{\rm{DOF}}$ | 1.18E04 | 3.98E03 |
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>
>
$\chi^2 /$ $N_{\rm{DOF}}$ 1.18E04 3.98E03
 -- WillBurrows - 07 Mar 2017

META FILEATTACHMENT attachment="latex9e04011600637bf22774650d76472879.png" attr="h" comment="" date="1488930139" name="latex9e04011600637bf22774650d76472879.png" user="zyvb951" version="1"
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Revision 108 Mar 2017 - WilliamBurrows

Line: 1 to 1
Added:
>
>
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
RMS Error

  • Fit-data difference as a function of intensity for G*C fits to lamp lines:
    Inensity_diff.png

  • RMS equation used:
 \begin{equation} x_{\rm{rms}} = \sqrt{ \bigg( \frac{1}{N} \sum_{i = i}^{N} x_i^2 \bigg) } \end{equation}

  • RMS values of data in 20 bins of width 1003796 PE:
    RMS_diff.png

  • Form of the fit:
 \begin{equation} f(x; C_1, C_0) = C_1x + C_0 \end{equation}

  • Fitted parameter values:
Parameter Value
$C_1$ 6.27E-03 $\pm$ 2.14E-03
$C_0$ 1.72E05 $\pm$ 2.48E04

Convolutions

  • Gaussian equation:
 \begin{equation} G(x; a, x_0, \sigma, C_0, C_1) = \frac{1}{\sqrt{2\pi\sigma^2}} \rm{exp} \bigg[ {\frac{-(x - x_0)^2}{2\sigma^2}} \bigg] + C_1x + C_0 \end{equation}

  • Circle equation:
 \begin{equation} C(x;r) = \frac{2}{\pi r^2}\sqrt{(r^2 - x^2)} \end{equation}

  • Convolution:
 \begin{equation} (G * C)(x) = \sum_{i} G(x - i;a, x_0, \sigma, C_0, C_1)C(i;r) \end{equation}

  • G*C and Gaussian fits to the He line at 4.00mm:
    Conv_Gauss_He0400.png

  • Fitted parameter values:
Parameter Gaussian G*C
a 2.41E08 $\pm$ 3.48E06 1.10E07 $\pm$ 2.35E04
$x_0$ 2.68E02 $\pm$ 2.39E-02 2.68E02 $\pm$ 5.85E-03
$\sigma$ 8.27 $\pm$ 1.39E-01 2.08 $\pm$ 6.45E-02
r   4.51 $\pm$ 3.80E-03
$C_1$ 6.49E01 $\pm$ 4.04E02 8.19E01 $\pm$ 1.03E02
$C_0$ 1.15E05 $\pm$ 1.09E05 1.31E05 $\pm$ 2.78E04
$\chi^2$ 1.35E06 4.53E05
$N_{\rm{DOF}}$ 115 114
$\chi^2 / $N_{\rm{DOF}}$ 1.18E04 3.98E03
-- WillBurrows - 07 Mar 2017

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