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# 20130212 Function for Vertical Alignment

Currently there is not fitting function for the vertical alignment scans using the OTR screen. This could be calculated using an overlap integral if a function was made to describe the screen. This would only be an approximation though as the notch in the screen does not have a well defined shape due to its origins. An easier solution is to use a generic function - as long as it is repeatable and consistent. This should be better than judging by eye. Below is a typical vertical chamber scan with the OTR screen set to the laser focus position - laser off during this. Wire-scanner detector used as much more scattering when a solid target is used - would saturate the laser-wire detector.

For this, a generalised logistic function was used. It is described by (taken from wikipedia):

with the following definitions:

• A: the lower asymptote
• K: the upper asymptote. If A=0 then K is called the carrying capacity
• B: the growth rate
• v;>0 : affects near which asymptote maximum growth occurs.
• Q: depends on the value Y(0)
• M: the time of maximum growth if Q=ν

This function was simulated to ascertain the best values to use and which parameters should be fixed - with a 6 parameter fit you can get anything so with the general shape know, it should be possible to limit this down a bit. In each case the other parameters were fixed at the values found from a free 6 parameter fit. The apparent uncertainty in the fit details is just the initial set size supplied to minuit for that parameter.

v Dependence Q Dependence
Q Dependence Zoomed B Dependence

In the end, the following set of parameters was chosen:

Wiki Name Fixed Value Lower Limit Upper Limit
A No NA -0.5 16000
K No NA 0 16000
B No NA 0.00001 0.5
v No NA 0 40
Q Yes 20.0 NA NA
M No NA NA NA

Here A is the offset, K is the ceiling and M is the approximate middle. It still has to be determined how stable this is and what the fudge factor is between the fitted M and the point were laser-wire collisions are found.

Topic attachments
I Attachment History Action Size Date Who Comment
png 20130208_0149_lws_xy_errbar_plot7.png r1 manage 30.7 K 14 Feb 2013 - 09:35 LaurieNevay typical scan
png 20130208_0149_lws_xy_fit_plot6.png r1 manage 49.5 K 14 Feb 2013 - 09:37 LaurieNevay fitted
png 6f2f898447173ea8f33d0cc427d1ea97.png r1 manage 1.4 K 14 Feb 2013 - 09:34 LaurieNevay equation
png b_dependence.png r1 manage 93.8 K 14 Feb 2013 - 09:37 LaurieNevay b dependance
png q_dependence.png r1 manage 69.8 K 14 Feb 2013 - 09:36 LaurieNevay q dependance
png q_dependence_zoomed.png r1 manage 90.1 K 14 Feb 2013 - 09:36 LaurieNevay q dependance zoomed
png v_dependence.png r1 manage 103.6 K 14 Feb 2013 - 09:36 LaurieNevay v dependance

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Topic revision: r1 - 14 Feb 2013 - LaurieNevay

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