Difference: 20170208_MsciSpectroscopyMeeting (10 vs. 11)

Revision 1108 Feb 2017 - JamesAngthopo

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2016"
Error propagation
  • Assumed the photoelectrons distribution is a p.d.f therefore assumed error on the number of photoelectrons to be
Changed:
<
<		%BEGINLATEX% \begin{equation} \sigma^2=\sqrt{N_{PE}} \end{equation}
>
>		%BEGINLATEX% \begin{equation} \sigma=\sqrt{N_{PE}} \end{equation}
 %ENDLATEX%
  • Plot showing the data and the gaussian fit for micrometer setting of 4.00mm and 6.00mm:
    plotgaussfit.png
  • Plot showing the error for Helium lamp at 6.0mm:
    enchancedgaussplot.png

  • The table shows the $\chi ^2$ value, $N_{DOF}$ and the error on the location of the peak.
Changed:
<
<
micrometer setting (mm) $\chi ^2$ $ N_{DOF} $ PeakError
>
>
micrometer setting (mm) $\chi ^2$ $ N_{DOF} $ width on guassian
 
$4.00 \pm 1e-4$ 1310296.532 764 2.44
$6.00 \pm 1e-4$ 847762.900 764 2.79
  • Equation used for $\chi ^2$:
%BEGINLATEX% \begin{equation}
Changed:
<
<		\chi ^2=\sum_{n=1}^{N}\frac{(x_i-\mu)^2}{\sigma_i^2}
>
>		\chi ^2=\sum_{n=1}^{N}\frac{(y_i-f(y_i;a,b,c))^2}{\sigma_i^2}
  \end{equation} %ENDLATEX%
Changed:
<
<
  • Since the poisson distribution is assumed $\sigma ^2 = N_{PE} = \mu$.
>
>
  • $y_i$ is the observed value, $f(y_i,a,b,c)$ is the expected values, $\sigma$ is the error.
  • Since the poisson distribution is assumed $\sigma ^2 = N_{PE} = \mu$ where $\mu$ is the gaussian mean.
 
  • Therefore if it is a poisson distribution, the equation below is true.
\begin{equation} \sigma=\sqrt{\mu} \end{equation}
Line: 112 to 111
 
META FILEATTACHMENT attachment="Vega_0290_LB.png" attr="" comment="Lorentzian + background fit to the peak in Vega, centered at 2.90mm" date="1486504541" name="Vega_0290_LB.png" path="Vega_0290_LB.png" size="67753" user="zyvb951" version="1"
META FILEATTACHMENT attachment="Vega_0290_LB_zoomed.png" attr="" comment="Lorentzian + background fit to the peak in Vega, centered at 2.90mm" date="1486504573" name="Vega_0290_LB_zoomed.png" path="Vega_0290_LB_zoomed.png" size="64577" user="zyvb951" version="1"
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Deleted:
<
<
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META FILEATTACHMENT attachment="plotgaussfit.png" attr="" comment="Plot showing the data and the gaussian fit for micrometer setting of 4.00mm and 6.00mm" date="1486507185" name="plotgaussfit.png" path="plotgaussfit.png" size="67609" user="zyvb137" version="1"
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Line: 120 to 118
 
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Deleted:
<
<
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META FILEATTACHMENT attachment="enchancedgaussplot.png" attr="" comment="Plot showing the error for Helium lamp at 6.0mm" date="1486508547" name="enchancedgaussplot.png" path="enchancedgaussplot.png" size="82931" user="zyvb137" version="1"
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Line: 144 to 141
 
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META FILEATTACHMENT attachment="quad0700.png" attr="" comment="plot for 7.00mm with cadmium data" date="1486551210" name="quad0700.png" path="quad0700.png" size="65474" user="zyvb137" version="3"
Added:
>
>
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