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Updates in the He-Ne beam profiling experiment.
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New and improved plots for the He-Ne profiling experiment
Font size has been increased to 30.
The plots are maximum size (Following Rana's advice, I saved the plots as eps files(maximized) and converted them to pdf later).
There is a shaded region around the trendline that represents the parameter error.
Function that I fit my data to (should have mentioned this in my earlier elog entries)
![P = \dfrac{P_0}{2}\Bigg[1+erf\Big(\dfrac{\sqrt2(X-X_0)}{w}\Big) \Bigg]](https://latex.codecogs.com/gif.latex?P%20%3D%20%5Cdfrac%7BP_0%7D%7B2%7D%5CBigg%5B1+erf%5CBig%28%5Cdfrac%7B%5Csqrt2%28X-X_0%29%7D%7Bw%7D%5CBig%29%20%5CBigg%5D)
Description of my error analysis -
1. I have assumed a 20% deviation from markings in the micrometer error.
2. Using the error in the micrometer, I have calculated the propogated error in the beam power :

I added this error to the stastistical error due to the fluctuation of the oscilloscope reading to obtain the total error in power.
3. I found the Fisher Matrix by numerically differentiating the function at different data points with respect to the parameters and .
 
I then found the covariance matrix by inverting the Fisher Matrix and found the error in spot size estimation.
EDIT : Residuals added to plots and all axes made equal |