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:

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.