Difference: 20151129_MSciSpectrocopyLab (1 vs. 11)

Revision 1112 Sep 2016 - AshleaKemp

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Line: 44 to 44
 
  • Finally a quadratic term was fitted for the background of the image, which has the equation:
\begin{equation} f(x) = b_{0} + b_{1} x + b_{2} x^2 \end{equation}
  • These are plotted below
Changed:
<
<		3Fits.png
>
>		3Fits.png
 
  • The quadratic can be seen to improve the fit to the background of the data as shown below:
Changed:
<
<		3Fit_Back.png
>
>		3Fit_Back.png
 
  • The three different fits produced parameter values of:
Parameters Gaussian + circle Skewed Gaussian + Circle Skewed Gaussian + circle + Quadratic background
Line: 76 to 76
 
\begin{equation} L(x;\gamma, x_{0}) = \frac{A}{\pi} \frac{\gamma/2}{(x-x_{0})^2 + (\gamma/2)^2} \end{equation}
  • Both of these fits are shown with the data in the plot below:
Changed:
<
<		VegaFit.png
>
>		VegaFit.png
 
Paramater Skewed Gaussian + Circle + Quadratic Background Voigt + Circle + Quadratic Background
Gauss Amp 1.077 -1.48±(1.39e05)
Line: 122 to 122
 
$\chi^2$ per dof 1587 968 969

  • Some of the grating setting are shown below
Changed:
<
<		0.5mm.png
2.0mm.png
5mm.png
7mm.png
8mm.png
>
>		0.5mm.png
2.0mm.png
5mm.png
7mm.png
8mm.png
 

Halogen Lamp

  • For the halogen lamp the above fit parameters were used to set the wavelength of each frame, these were then plotted as shown below:
  • The below plot shows the linear and squared plots and it can clearly be seen to improve at larger and smaller wavelengths, however not much change in the center.
Changed:
<
<		LinearSquare.png
>
>		LinearSquare.png
 
  • When the cubed parameters were used, the plot did no seem to improve, as the image shows
Changed:
<
<		Cubed.png
>
>		Cubed.png
 
  • This may be due to an incorrect point which the cubed plot fits better to however is further from the true value
-- AshleaKemp - 27 Nov 2015

Revision 1020 Feb 2016 - AshleaKemp

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Revision 909 Feb 2016 - AshleaKemp

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Line: 44 to 44
 
  • Finally a quadratic term was fitted for the background of the image, which has the equation:
\begin{equation} f(x) = b_{0} + b_{1} x + b_{2} x^2 \end{equation}
  • These are plotted below
Changed:
<
<		3Fits.png
>
>		3Fits.png
 
  • The quadratic can be seen to improve the fit to the background of the data as shown below:
Changed:
<
<		3Fit_Back.png
>
>		3Fit_Back.png
 
  • The three different fits produced parameter values of:
Parameters Gaussian + circle Skewed Gaussian + Circle Skewed Gaussian + circle + Quadratic background
Line: 76 to 76
 
\begin{equation} L(x;\gamma, x_{0}) = \frac{A}{\pi} \frac{\gamma/2}{(x-x_{0})^2 + (\gamma/2)^2} \end{equation}
  • Both of these fits are shown with the data in the plot below:
Changed:
<
<		VegaFit.png
>
>		VegaFit.png
 
Paramater Skewed Gaussian + Circle + Quadratic Background Voigt + Circle + Quadratic Background
Gauss Amp 1.077 -1.48±(1.39e05)
Line: 122 to 122
 
$\chi^2$ per dof 1587 968 969

  • Some of the grating setting are shown below
Changed:
<
<		0.5mm.png
2.0mm.png
5mm.png
7mm.png
8mm.png
>
>		0.5mm.png
2.0mm.png
5mm.png
7mm.png
8mm.png
 

Halogen Lamp

  • For the halogen lamp the above fit parameters were used to set the wavelength of each frame, these were then plotted as shown below:
  • The below plot shows the linear and squared plots and it can clearly be seen to improve at larger and smaller wavelengths, however not much change in the center.
Changed:
<
<		LinearSquare.png
>
>		LinearSquare.png
 
  • When the cubed parameters were used, the plot did no seem to improve, as the image shows
Changed:
<
<		Cubed.png
>
>		Cubed.png
 
  • This may be due to an incorrect point which the cubed plot fits better to however is further from the true value
-- AshleaKemp - 27 Nov 2015

Revision 808 Dec 2015 - JosephBayley

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Revision 701 Dec 2015 - JosephBayley

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Line: 44 to 44
 
  • Finally a quadratic term was fitted for the background of the image, which has the equation:
\begin{equation} f(x) = b_{0} + b_{1} x + b_{2} x^2 \end{equation}
  • These are plotted below
Changed:
<
<		3Fits.png
>
>		3Fits.png
 
  • The quadratic can be seen to improve the fit to the background of the data as shown below:
Changed:
<
<		3Fit_Back.png
>
>		3Fit_Back.png
 
  • The three different fits produced parameter values of:
Parameters Gaussian + circle Skewed Gaussian + Circle Skewed Gaussian + circle + Quadratic background
Line: 76 to 76
 
\begin{equation} L(x;\gamma, x_{0}) = \frac{A}{\pi} \frac{\gamma/2}{(x-x_{0})^2 + (\gamma/2)^2} \end{equation}
  • Both of these fits are shown with the data in the plot below:
Changed:
<
<		VegaFit.png
>
>		VegaFit.png
 
Paramater Skewed Gaussian + Circle + Quadratic Background Voigt + Circle + Quadratic Background
Gauss Amp 1.077 -1.48±(1.39e05)
Line: 98 to 98
 
$N_{\mathrm{dof}}$ 288 285
$\chi^2$ per dof 4.75 3.91
Added:
>
>

Mapping Wavelength

  • The three different equations that were fitted were:
\begin{equation} f(\mu,m) = \lambda_{0} + a_{1} \mu + b_{1} m \end{equation} \begin{equation} f(\mu,m) = \lambda_{0} + a_{1} \mu + b_{1} m + a_{2} \mu^{2} + b_{2} m^{2} + c_{2} \mu m \end{equation} \begin{equation} f(\mu,m) = \lambda_{0} + a_{1} \mu + b_{1} m + a_{2} \mu^{2} + b_{2} m^{2} + c_{2} \mu m + a_{3}\mu^{3} + b_{3} m^{3} + c_{3} \mu^{2} m + d_{3} \mu m^{2}\end{equation}
  • These were then plotted for each micrometer setting with the data.
  • Ask about what errors to put in??
  • The parameters were found to be:

Parameter Linear Squared Cubed
$\lambda_{0}$ 278±2 265±2.8 275±7
$a_{1}$ 0.105±0.002 0.122±0.008 0.074±0.028
$b_{1}$ 55.64±0.26 62.07±1.08 56.75±4.45
$a_{2}$   (-1.19±0.89)e-05 (6.73±6.16)e-05
$b_{2}$   -0.689±0.104 0.08±0.94
$c_{2}$   (-1.61±0.98)e-03 0.011±0.007
$a_{3}$     (-4.62±4.81)e-08
$b_{3}$     (-3.35±6.44)e-02
$c_{3}$     (-7.59±6.11)e-06
$d_{3}$     (-7.63±5.07)e-04
$\chi^2$ 109524 63944 60107
$N_{dof}$ 69 66 62
$\chi^2$ per dof 1587 968 969

  • Some of the grating setting are shown below
0.5mm.png
2.0mm.png
5mm.png
7mm.png
8mm.png

Halogen Lamp

  • For the halogen lamp the above fit parameters were used to set the wavelength of each frame, these were then plotted as shown below:
  • The below plot shows the linear and squared plots and it can clearly be seen to improve at larger and smaller wavelengths, however not much change in the center.
LinearSquare.png
  • When the cubed parameters were used, the plot did no seem to improve, as the image shows
Cubed.png
  • This may be due to an incorrect point which the cubed plot fits better to however is further from the true value
 -- AshleaKemp - 27 Nov 2015

META FILEATTACHMENT attachment="Helium.png" attr="" comment="" date="1448646981" name="Helium.png" path="Helium.png" size="20496" user="zxap013" version="2"
Line: 135 to 168
 
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Added:
>
>
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Revision 601 Dec 2015 - AshleaKemp

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Line: 21 to 21
 
255 (peak) 4016.91 31.86 3.97 8.03
655 (peak) 3964.86 28.23 3.94 7.16
Added:
>
>

Assigning error bars?

  • Found that for calibration lamps, standard deviation $\sigma$ not equivalent to $\sigma_{\mathrm{Poisson}}$. Wanted to find a way to assign error bars
  • Using Helium lamp, micrometer position at 4.0mm, took 10 frames at each exposure time, starting at 0.05s up to 1s in 0.05s increments. For each of the 10 frames of each exposure time, chose 5 points close together that were all in background (pixel numbers: 170,180,190,200,210) and 5 points close together in the peak (pixel numbers: 185,190,195,200,205). Found the $\sigma$ of the 10 frames for each of these points, then found $&amp;lt;\sigma&amp;gt;$ for that exposure time
  • Plotted $&amp;lt;\sigma&amp;gt;$ as a function of exposure time. Expected to be able to fit a function to these points, such that for a specific exposure time, can find the appropriate error.
  • However, the plot was not what we expected - the points are random, a function cannot be fitted.
  • Unsure what is the best method in assigning error bars?
sigma.png

sigmapeak.png

 

Skewed Gaussian Fit

  • Firstly a Gaussian convoluted with a circular function was fitted to a spectral line
Line: 33 to 44
 
  • Finally a quadratic term was fitted for the background of the image, which has the equation:
\begin{equation} f(x) = b_{0} + b_{1} x + b_{2} x^2 \end{equation}
  • These are plotted below
Changed:
<
<		3Fits.png
>
>		3Fits.png
 
  • The quadratic can be seen to improve the fit to the background of the data as shown below:
Changed:
<
<		3Fit_Back.png
>
>		3Fit_Back.png
 
  • The three different fits produced parameter values of:
Parameters Gaussian + circle Skewed Gaussian + Circle Skewed Gaussian + circle + Quadratic background
Line: 65 to 76
 
\begin{equation} L(x;\gamma, x_{0}) = \frac{A}{\pi} \frac{\gamma/2}{(x-x_{0})^2 + (\gamma/2)^2} \end{equation}
  • Both of these fits are shown with the data in the plot below:
Changed:
<
<		VegaFit.png
>
>		VegaFit.png
 
Paramater Skewed Gaussian + Circle + Quadratic Background Voigt + Circle + Quadratic Background
Gauss Amp 1.077 -1.48±(1.39e05)
Line: 122 to 132
 
META FILEATTACHMENT attachment="latex8660b278054f33e34cb09160ea2c9919.png" attr="h" comment="" date="1448920081" name="latex8660b278054f33e34cb09160ea2c9919.png" user="zxap044" version="1"
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Added:
>
>
META FILEATTACHMENT attachment="sigma.png" attr="" comment="" date="1448969027" name="sigma.png" path="sigma.png" size="15997" user="zxap013" version="1"
META FILEATTACHMENT attachment="latexd53d1ffd17fe7e60218364bb02277065.png" attr="h" comment="" date="1448969060" name="latexd53d1ffd17fe7e60218364bb02277065.png" user="zxap013" version="1"
META FILEATTACHMENT attachment="sigmapeak.png" attr="" comment="" date="1448971046" name="sigmapeak.png" path="sigmapeak.png" size="18089" user="zxap013" version="1"

Revision 501 Dec 2015 - JosephBayley

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Line: 69 to 67
 
  • Both of these fits are shown with the data in the plot below:
VegaFit.png
Added:
>
>
 
Paramater Skewed Gaussian + Circle + Quadratic Background Voigt + Circle + Quadratic Background
Changed:
<
<
Gauss Amp 1.077 1.39±(1.39e05)
Gauss mean, $\mu$ 130 173±(4.2e06)
Gauss $\sigma$ 9.33 16.4±(3.1e05)
$a_{0}$ 4.3 -41.4±(1.6e06)
$a_{1}$ 0.26 -2.04±(3.93e04)
$a_{2}$ 0.088 0.0636±1226
Lorentz Amp, $A$   6.97±(6.8e05)
>
>
Gauss Amp 1.077 -1.48±(1.39e05)
Gauss mean, $\mu$ 130 138±(4.2e06)
Gauss $\sigma$ 9.33 19.7±(3.1e05)
$a_{0}$ 4.3 -15.6±(1.6e06)
$a_{1}$ 0.26 -5.44±(3.93e04)
$a_{2}$ 0.088 0.0982±1226
Lorentz Amp, $A$   -7.43±(6.8e05)
 
Lorentz width, $\gamma$   18.69±0.29
Lorentz center, $x_{0}$   204±1.86
Changed:
<
<
Circle radius 5.98 2.49±286
>
>
Circle radius 5.98 2.39±286
 
Circle mean 130 128±231
Changed:
<
<
Circle Amplitude -21.7 -28.8±(7.1e05)
>
>
Circle Amplitude -21.7 -30.2±(7.1e05)
 
$b_{1}$ 3.64 3.68±0.19
$b_{2}$ 0.00088 (8.42±14.7)e-04
$b_{3}$ -8.49e-07 (-3.18±0.07)e-06

Revision 430 Nov 2015 - JosephBayley

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

Line: 25 to 25
 
  • Firstly a Gaussian convoluted with a circular function was fitted to a spectral line
  • Then as towards the edges of the frame the line appeared to become skewed therefore a skewed Gaussian was convoluted with the circular function and fitted
Changed:
<
<
  • Finally a quadratic term was fitted for the background of the image
>
>		The skewed Gaussian has the equation:

\begin{equation} f(y;\mu,\sigma) = \frac{1}{\sqrt{2\pi} \sigma^2} e^{\frac{-(y-\mu)^2}{2 \sigma^2}} \end{equation}

where $ y = a_{0} + a_{1} x + a_{2} x^2 $

  • Finally a quadratic term was fitted for the background of the image, which has the equation:

\begin{equation} f(x) = b_{0} + b_{1} x + b_{2} x^2 \end{equation}
 
  • These are plotted below
Changed:
<
<		3Fits.png
>
>		3Fits.png
 
  • The quadratic can be seen to improve the fit to the background of the data as shown below:
Changed:
<
<		3Fit_Back.png
>
>		 3Fit_Back.png
 
  • The three different fits produced parameter values of:
Changed:
<
<
Parameters Gaussian and circle Skewed Gaussian and circle Skewed Gaussian and circle and Quadratic background
>
>
Parameters Gaussian + circle Skewed Gaussian + Circle Skewed Gaussian + circle + Quadratic background
 
Gaussian amplitude 369 ±(7.8e6) 417±(7.7e05) 447±(4.7e06)
Gaussian mean 33.34±0.001 14.2±(5e04) 13.3±(1e04)
Gaussian Sigma 1.99±0.001 2.19±(2e04) 3.14±(2.06e04)
Line: 41 to 49
 
Circle mean 33.34±0.001 58.6±0.02 58.4±0.01
Circle amplitude 365±(7.7e6) 422±(4.2e06) 532±(5e06)
Background 624.7±0.2 618±0.2  
Changed:
<
<
$b_{0}$   8.18±(5e04) 4.23±(3e04)
$b_{1}$   0.034±308 0.264±1742
$b_{2}$   0.077±705 0.008±581
$a_{0}$     612±0.3
$a_{1}$     -3.54±0.003
$a_{2}$     -0.069±0.001
>
>
$a_{0}$   8.18±(5e04) 4.23±(3e04)
$a_{1}$   0.034±308 0.264±1742
$a_{2}$   0.077±705 0.008±581
$b_{0}$     612±0.3
$b_{1}$     -3.54±0.003
$b_{2}$     -0.069±0.001
 
$\chi^{2}$ 191158 21259 14404
$N_{\mathrm{DOF}}$ 64 60 58
$\chi^{2}$ per DOF 2987 354 248
Added:
>
>

Fitting to Vega Line

  • The line chosen was at a micrometer setting of 3.5mm, the exposure was 120s,
  • Initially the convolution of the skewed Gaussian and circle plus the quadratic background was fitted to the Vega line, this had the equations same as above.
  • Then to get a better fit the skewed Gaussian was convoluted with a Lorentz distribution so that a Voigt profile could be fit. The Lorentz had the equation:
\begin{equation} L(x;\gamma, x_{0}) = \frac{A}{\pi} \frac{\gamma/2}{(x-x_{0})^2 + (\gamma/2)^2} \end{equation}
  • Both of these fits are shown with the data in the plot below:
VegaFit.png

Paramater Skewed Gaussian + Circle + Quadratic Background Voigt + Circle + Quadratic Background
Gauss Amp 1.077 1.39±(1.39e05)
Gauss mean, $\mu$ 130 173±(4.2e06)
Gauss $\sigma$ 9.33 16.4±(3.1e05)
$a_{0}$ 4.3 -41.4±(1.6e06)
$a_{1}$ 0.26 -2.04±(3.93e04)
$a_{2}$ 0.088 0.0636±1226
Lorentz Amp, $A$   6.97±(6.8e05)
Lorentz width, $\gamma$   18.69±0.29
Lorentz center, $x_{0}$   204±1.86
Circle radius 5.98 2.49±286
Circle mean 130 128±231
Circle Amplitude -21.7 -28.8±(7.1e05)
$b_{1}$ 3.64 3.68±0.19
$b_{2}$ 0.00088 (8.42±14.7)e-04
$b_{3}$ -8.49e-07 (-3.18±0.07)e-06
$\chi^2$ 1369 1115
$N_{\mathrm{dof}}$ 288 285
$\chi^2$ per dof 4.75 3.91
 -- AshleaKemp - 27 Nov 2015

META FILEATTACHMENT attachment="Helium.png" attr="" comment="" date="1448646981" name="Helium.png" path="Helium.png" size="20496" user="zxap013" version="2"
Line: 74 to 112
 
META FILEATTACHMENT attachment="errorback.png" attr="" comment="" date="1448819249" name="errorback.png" path="errorback.png" size="48449" user="zxap013" version="2"
META FILEATTACHMENT attachment="spectrum.png" attr="" comment="" date="1448820078" name="spectrum.png" path="spectrum.png" size="29770" user="zxap013" version="2"
META FILEATTACHMENT attachment="errorpeak.png" attr="" comment="" date="1448819188" name="errorpeak.png" path="errorpeak.png" size="41989" user="zxap013" version="1"
Added:
>
>
META FILEATTACHMENT attachment="VegaFit.png" attr="h" comment="" date="1448918069" name="VegaFit.png" path="VegaFit.png" size="88325" user="zxap044" version="1"
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Revision 329 Nov 2015 - AshleaKemp

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

  • Found previously that errors in background of frame are not poisson - wanted to investigate how points fluctuate in peaks as well as background.
  • Plotted the spectrum of Helium lamp at micrometer position 6.5mm, exposure time 0.5s, to find pixel positions of background and peaks
Changed:
<
<

Helium.png

>
>

spectrum.png

 
  • Chose 3 random pixel positions of background: 150, 350, 550
  • Chose 3 pixel positions where the two peaks is present: 245 (1st peak), 255 (1st peak), 655 (2nd peak)
  • Analysed the point at these pixel positions to see how they fluctuated in each of the 20 frames
Changed:
<
<

150.png

255.png

>
>

errorback.png

errorpeak.png

 
  • For each frame, calculated the mean of the 20 data points $\mu$, the calculated standard deviation of the data points $\sigma$, and the expected poisson error of the data points, $\sigma_{\mathrm{Poisson}} = \sqrt{\mu}$
Pixel Position $\mu$ $\sigma$ $\sigma_{\mathrm{Poisson}}$ $\sigma / \sigma_{\mathrm{Poisson}}$
Changed:
<
<
150 (back) 132845.0 596.14 364.48 1.64
350 (back) 137320.0 531.70 370.57 1.43
550 (back) 142843.0 617.57 377.95 1.63
245 (peak) 491678.0 4676.45 701.20 6.67
255 (peak) 1.02e+6 8125.23 1012.08 8.03
655 (peak) 1.01e+6 7199.49 1005.50 7.16
>
>
150 (back) 520.96 2.34 1.43 1.64
350 (back) 538.51 2.09 1.45 1.44
550 (back) 560.17 2.42 1.48 1.64
245 (peak) 1928.15 18.34 2.75 6.67
255 (peak) 4016.91 31.86 3.97 8.03
655 (peak) 3964.86 28.23 3.94 7.16
 

Skewed Gaussian Fit

Line: 27 to 27
 
  • Then as towards the edges of the frame the line appeared to become skewed therefore a skewed Gaussian was convoluted with the circular function and fitted
  • Finally a quadratic term was fitted for the background of the image
  • These are plotted below
Changed:
<
<
3Fits.png
>
>		3Fits.png
 
  • The quadratic can be seen to improve the fit to the background of the data as shown below:
Changed:
<
<
3Fit_Back.png
>
>		3Fit_Back.png
 
  • The three different fits produced parameter values of:
Parameters Gaussian and circle Skewed Gaussian and circle Skewed Gaussian and circle and Quadratic background
Line: 74 to 71
 
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META FILEATTACHMENT attachment="3Fit_Back.png" attr="h" comment="" date="1448732132" name="3Fit_Back.png" path="3Fit_Back.png" size="68032" user="zxap044" version="2"
META FILEATTACHMENT attachment="3Fits.png" attr="h" comment="" date="1448732132" name="3Fits.png" path="3Fits.png" size="76023" user="zxap044" version="2"
Added:
>
>
META FILEATTACHMENT attachment="errorback.png" attr="" comment="" date="1448819249" name="errorback.png" path="errorback.png" size="48449" user="zxap013" version="2"
META FILEATTACHMENT attachment="spectrum.png" attr="" comment="" date="1448820078" name="spectrum.png" path="spectrum.png" size="29770" user="zxap013" version="2"
META FILEATTACHMENT attachment="errorpeak.png" attr="" comment="" date="1448819188" name="errorpeak.png" path="errorpeak.png" size="41989" user="zxap013" version="1"

Revision 228 Nov 2015 - JosephBayley

Line: 1 to 1
 
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

  • Found previously that errors in background of frame are not poisson - wanted to investigate how points fluctuate in peaks as well as background.
  • Plotted the spectrum of Helium lamp at micrometer position 6.5mm, exposure time 0.5s, to find pixel positions of background and peaks
Changed:
<
<

Helium.png

>
>

Helium.png

 
  • Chose 3 random pixel positions of background: 150, 350, 550
  • Chose 3 pixel positions where the two peaks is present: 245 (1st peak), 255 (1st peak), 655 (2nd peak)
Line: 21 to 21
 
255 (peak) 1.02e+6 8125.23 1012.08 8.03
655 (peak) 1.01e+6 7199.49 1005.50 7.16
Added:
>
>

Skewed Gaussian Fit

  • Firstly a Gaussian convoluted with a circular function was fitted to a spectral line
  • Then as towards the edges of the frame the line appeared to become skewed therefore a skewed Gaussian was convoluted with the circular function and fitted
  • Finally a quadratic term was fitted for the background of the image
  • These are plotted below


3Fits.png

  • The quadratic can be seen to improve the fit to the background of the data as shown below:


3Fit_Back.png

  • The three different fits produced parameter values of:
Parameters Gaussian and circle Skewed Gaussian and circle Skewed Gaussian and circle and Quadratic background
Gaussian amplitude 369 ±(7.8e6) 417±(7.7e05) 447±(4.7e06)
Gaussian mean 33.34±0.001 14.2±(5e04) 13.3±(1e04)
Gaussian Sigma 1.99±0.001 2.19±(2e04) 3.14±(2.06e04)
Circle radius 4.16±0.01 4.46±0.01 4.43±0.00001
Circle mean 33.34±0.001 58.6±0.02 58.4±0.01
Circle amplitude 365±(7.7e6) 422±(4.2e06) 532±(5e06)
Background 624.7±0.2 618±0.2  
$b_{0}$   8.18±(5e04) 4.23±(3e04)
$b_{1}$   0.034±308 0.264±1742
$b_{2}$   0.077±705 0.008±581
$a_{0}$     612±0.3
$a_{1}$     -3.54±0.003
$a_{2}$     -0.069±0.001
$\chi^{2}$ 191158 21259 14404
$N_{\mathrm{DOF}}$ 64 60 58
$\chi^{2}$ per DOF 2987 354 248
 -- AshleaKemp - 27 Nov 2015
Added:
>
>
 
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META FILEATTACHMENT attachment="150.png" attr="" comment="Pixel position 150" date="1448647778" name="150.png" path="150.png" size="37183" user="zxap013" version="2"
META FILEATTACHMENT attachment="255.png" attr="" comment="Pixel position 255" date="1448647864" name="255.png" path="255.png" size="34226" user="zxap013" version="1"
Line: 31 to 64
 
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Added:
>
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META FILEATTACHMENT attachment="3Fits.png" attr="h" comment="" date="1448732132" name="3Fits.png" path="3Fits.png" size="76023" user="zxap044" version="2"

Revision 127 Nov 2015 - AshleaKemp

Line: 1 to 1
Added:
>
>
META TOPICPARENT name="StewartBoogertSpectroscopy2015"

Fixing errors

  • Found previously that errors in background of frame are not poisson - wanted to investigate how points fluctuate in peaks as well as background.
  • Plotted the spectrum of Helium lamp at micrometer position 6.5mm, exposure time 0.5s, to find pixel positions of background and peaks

Helium.png

  • Chose 3 random pixel positions of background: 150, 350, 550
  • Chose 3 pixel positions where the two peaks is present: 245 (1st peak), 255 (1st peak), 655 (2nd peak)
  • Analysed the point at these pixel positions to see how they fluctuated in each of the 20 frames

150.png

255.png

  • For each frame, calculated the mean of the 20 data points $\mu$, the calculated standard deviation of the data points $\sigma$, and the expected poisson error of the data points, $\sigma_{\mathrm{Poisson}} = \sqrt{\mu}$
Pixel Position $\mu$ $\sigma$ $\sigma_{\mathrm{Poisson}}$ $\sigma / \sigma_{\mathrm{Poisson}}$
150 (back) 132845.0 596.14 364.48 1.64
350 (back) 137320.0 531.70 370.57 1.43
550 (back) 142843.0 617.57 377.95 1.63
245 (peak) 491678.0 4676.45 701.20 6.67
255 (peak) 1.02e+6 8125.23 1012.08 8.03
655 (peak) 1.01e+6 7199.49 1005.50 7.16

-- AshleaKemp - 27 Nov 2015

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