Difference: 20151129_MSciSpectrocopyLab (8 vs. 9)

Revision 909 Feb 2016 - AshleaKemp

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META TOPICPARENT	name="StewartBoogertSpectroscopy2015"

Fixing errors

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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

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

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The three different fits produced parameter values of:

Parameters

Gaussian + circle

Skewed Gaussian + Circle

Skewed Gaussian + circle + Quadratic background

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$\begin{equation} L(x;\gamma, x_{0}) = \frac{A}{\pi} \frac{\gamma/2}{(x-x_{0})^2 + (\gamma/2)^2} \end{equation}$

Both of these fits are shown with the data in the plot below:

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Paramater	Skewed Gaussian + Circle + Quadratic Background	Voigt + Circle + Quadratic Background
Gauss Amp	1.077	-1.48±(1.39e05)

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$\chi^2$ per dof

1587

968

969

Some of the grating setting are shown below

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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.

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When the cubed parameters were used, the plot did no seem to improve, as the image shows

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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

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