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.
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.