Position Resolution Study

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Before we made any corrections to it, a count of the difference between measured path and predicted path using the other 2 gems

X diff 722.png Y diff 722.png

Using a slope vs difference plot, we noticed a correlation that should not have been there.

X diff slope 722.png Y diff slope 722.png

We decided that our Z distance (distance between gems) was off. This could have been due to human error or not know where exactly a partical interacts with the gas. Using RMS VS %Z distance we got the following.

X Sigma z2.png X Sigma z3.png Y Sigma z2.png Y Sigma z3.png

Using the parameters, we can concluded what the lowest Sigma was and adjusted the the Z distance. Our final difference looked like this.

X diff 722 corrected.png Y diff 722 corrected.png

The goal is to figure out what the error on the gems is. 75um is the assumed error, but we wanted to calculate it using our data. With a Gaussian error distribution we must use <math>\Delta x_d^2 = \Delta x_1^2 + \Delta x_2^2</math>. using this we can calculate the error. The final equations for the error come out to be: <math>\Delta x_1 = \Delta x1_D/3.23</math>, <math>\Delta x_2 = \Delta x2_D/1.57</math>, <math>\Delta x_3 = \Delta x3_D/3.23</math>.


X: 153.99μm

Y: 203.90μm


X: 198.22μm

Y: 216.88μm


X: 141.33μm

Y: 186.35μm