Difference: 20161104_MSciSpectroscopyMeeting (1 vs. 5)

Revision 504 Nov 2016 - WilliamBurrows

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
Peak Algorithm
Line: 16 to 16
 
  • First attempt at error bars, setting y error as the square root of the count:
    Improved_Cd_0650_Gaussians_lowest_errorbar.png
  • Error bars are tiny due to incorrect assumption that data follows a poison distribution.
Added:
>
>
  • Gaussian function used:
 \begin{equation} f(x) = a e^{- \frac{(x - \mu )^2}{2 \sigma ^2}} + b \end{equation}
 
  • Chi squared function used:
 \begin{equation} \chi2 = \sum \frac{(x_i - \mu)^2}{\sigma^2} \, . \end{equation}
  • Cd spectrum at 06.50mm with Gaussian fits, error bars and Chi squared values:
    Cd_0650_gaussian_errors_chi.png
Added:
>
>
  • Array of test parameters passed to fucntion : test_array_Cd650 = [[8E6, 150, 30, 3E5], [1.6E7, 270, 30, 3E5], [1.6E7, 520, 30, 3E5]]
 
  • Chi squared values are huge as expected due to poor fit. Once errors and fit equation are correct, Chi squared should reduce.
Added:
>
>
 -- JamesAngthopo - 03 Nov 2016

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Added:
>
>
META FILEATTACHMENT attachment="gaussian_fit.py.txt" attr="" comment="Gaussian, erro, chi squared pyhton code" date="1478267403" name="gaussian_fit.py.txt" path="gaussian_fit.py.txt" size="6243" user="zyvb951" version="1"
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Revision 404 Nov 2016 - AnishaVadher

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
Peak Algorithm
Line: 32 to 32
 
META FILEATTACHMENT attachment="Improved_Cd_0650_Gaussians_lowest.png" attr="" comment="Zoomed in look at the lowest Cd peak at 06.50mm" date="1478254637" name="Improved_Cd_0650_Gaussians_lowest.png" path="Improved_Cd_0650_Gaussians_lowest.png" size="20094" user="zyvb951" version="1"
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Deleted:
<
<
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Revision 304 Nov 2016 - WilliamBurrows

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
Peak Algorithm
Line: 11 to 11
 
  • FWHM can be obtained by $2\sqrt{ln2}\sigma$.

  • Peak locator algorithm used for camera angle at 1.50mm:
    PeakAt1.50mm.png
Changed:
<
<
Error Bars
>
>
Error Bars and Chi Squared
 
Changed:
<
<
  • Zoomed in look at the lowest Cd peak at 06.50mm:
    Improved_Cd_0650_Gaussians_lowest.png

  • First attempt at error bars, setting y error as sqrt of count:
    Improved_Cd_0650_Gaussians_lowest_errorbar.png
>
>
  • First attempt at error bars, setting y error as the square root of the count:
    Improved_Cd_0650_Gaussians_lowest_errorbar.png
  • Error bars are tiny due to incorrect assumption that data follows a poison distribution.
 
Added:
>
>
  • Chi squared function used:
 \begin{equation} \chi2 = \sum \frac{(x_i - \mu)^2}{\sigma^2} \, . \end{equation}
  • Cd spectrum at 06.50mm with Gaussian fits, error bars and Chi squared values:
    Cd_0650_gaussian_errors_chi.png
  • Chi squared values are huge as expected due to poor fit. Once errors and fit equation are correct, Chi squared should reduce.
 -- JamesAngthopo - 03 Nov 2016

META FILEATTACHMENT attachment="latex571589bb63149f4a0fe5f7816db4a267.png" attr="h" comment="" date="1478204640" name="latex571589bb63149f4a0fe5f7816db4a267.png" user="zyvb137" version="1"
Line: 27 to 31
 
META FILEATTACHMENT attachment="PeakAt1.50mm.png" attr="" comment="Peak locator algorithm used for camera angle at 1.50mm" date="1478205562" name="PeakAt1.50mm.png" path="PeakAt1.50mm.png" size="97377" user="zyvb137" version="1"
META FILEATTACHMENT attachment="Improved_Cd_0650_Gaussians_lowest.png" attr="" comment="Zoomed in look at the lowest Cd peak at 06.50mm" date="1478254637" name="Improved_Cd_0650_Gaussians_lowest.png" path="Improved_Cd_0650_Gaussians_lowest.png" size="20094" user="zyvb951" version="1"
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Added:
>
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META FILEATTACHMENT attachment="Cd_0650_gaussian_errors_chi.png" attr="" comment="Cd spectrum at 06.50mm with Gaussian fits, error bars and Chi squared values" date="1478262095" name="Cd_0650_gaussian_errors_chi.png" path="Cd_0650_gaussian_errors_chi.png" size="50103" user="zyvb951" version="1"
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Revision 204 Nov 2016 - WilliamBurrows

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
Peak Algorithm
Line: 11 to 11
 
  • FWHM can be obtained by $2\sqrt{ln2}\sigma$.

  • Peak locator algorithm used for camera angle at 1.50mm:
    PeakAt1.50mm.png
Added:
>
>
Error Bars
 
Changed:
<
<
-- JamesAngthopo - 03 Nov 2016
>
>
  • Zoomed in look at the lowest Cd peak at 06.50mm:
    Improved_Cd_0650_Gaussians_lowest.png
 
Added:
>
>
  • First attempt at error bars, setting y error as sqrt of count:
    Improved_Cd_0650_Gaussians_lowest_errorbar.png
 
Added:
>
>
-- JamesAngthopo - 03 Nov 2016
 
META FILEATTACHMENT attachment="latex571589bb63149f4a0fe5f7816db4a267.png" attr="h" comment="" date="1478204640" name="latex571589bb63149f4a0fe5f7816db4a267.png" user="zyvb137" version="1"
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META FILEATTACHMENT attachment="PeakAt1.50mm.png" attr="" comment="Peak locator algorithm used for camera angle at 1.50mm" date="1478205562" name="PeakAt1.50mm.png" path="PeakAt1.50mm.png" size="97377" user="zyvb137" version="1"
Added:
>
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META FILEATTACHMENT attachment="Improved_Cd_0650_Gaussians_lowest.png" attr="" comment="Zoomed in look at the lowest Cd peak at 06.50mm" date="1478254637" name="Improved_Cd_0650_Gaussians_lowest.png" path="Improved_Cd_0650_Gaussians_lowest.png" size="20094" user="zyvb951" version="1"
META FILEATTACHMENT attachment="Improved_Cd_0650_Gaussians_lowest_errorbar.png" attr="" comment="First attempt at error bars, setting y error as sqrt of count" date="1478254666" name="Improved_Cd_0650_Gaussians_lowest_errorbar.png" path="Improved_Cd_0650_Gaussians_lowest_errorbar.png" size="22613" user="zyvb951" version="1"

Revision 103 Nov 2016 - JamesAngthopo

Line: 1 to 1
Added:
>
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META TOPICPARENT name="StewartBoogertSpectroscopy2016"
Peak Algorithm

  • Found peak using second derivative of data. Double differential used as it enables us to find some hidden peaks.
  • Picked a cut off point for second derivative of data to give a range, $x_1$ and $x_2$, where the values inside the range would be considered a peak
  • Used equation,
 \begin{equation} W.A.= \frac{\sum x_iy_i}{\sum y_i} \end{equation}
to find the weighted average, peak, of the for each spectrum.
  • RMS was obtained by the equation,
 \begin{equation} \sigma= \frac{\sum (x_i-\bar{x_i})^2y_i}{\sum y_i} \end{equation}
  • FWHM can be obtained by $2\sqrt{ln2}\sigma$.

  • Peak locator algorithm used for camera angle at 1.50mm:
    PeakAt1.50mm.png

-- JamesAngthopo - 03 Nov 2016

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