Project Overview

__General__

The observation of
charged particles is of great importance to molecular physics. We are allowed
to accomplish this using the technology of microchannel plates (MCP) which
amplify the signal from one charged particle into an electric current. This
current is in turn transmitted onto a delay line detector (DLD) which gathers
time and position of impact data. This research was focused on calibrating the
detector and finding the resolution given different settings. Having the
calibration of the detector is crucial for when experiments are run so that
digital data can be converted into physical measurements. The resolution of the
detector is important to know the precision of measurements taken.

__Detector Calibration__

The first step in deciphering the data collected by a detector is
converting data given in pixels into a real measurement. The way that this is
achieved is by placing a ruler of sorts in front of the detector while hitting
it with charged particles. This ruler is in the form of a mask that covers the
detector. This mask has holes in it placed exactly 5mm apart center to center
in a square grid arrangement. The general concept here is to figure out how
many pixels are between the holes and use that information to figure the
conversion from pixels to millimeters.

The software used (SpecTcl) displays the data taken from the detector as a
400x400 pixel matrix. Each pixel is given a number corresponding to the number
of hit counts accumulated in the area of the detector represented by the pixel.
Normally the recorded data must be rotated via a matrix transformation so that
the x and y axes of the mask align with those of the software. This rotated
data is displayed in SpecTcl where projections are
made of each row and column on the mask. These projections take a given set of
pixels within a set of y limits and sum their values for each value of x to get
a projection of the rows – this discussion will concern calibrating rows; swap
the variables to project the columns.

Once a two
dimensional spectrum is made of counts per x position, the data is analyzed in
a graphing program – Origin 7.5 was used for this research. The peaks of the
spectrum correspond to the holes in the mask so the x position of each peak is
noted. On a graph, these peaks are plotted on the y axis against the x axis
that is in 5mm increments representing the known position of the holes on the
mask. Next a linear regression is taken to find the line of best fit through
the data. The slope of this line is the desired conversion factor as its units
are in pixels/mm.

__Detector Resolution__

To find the
resolution of the detector, another feature of the mask is utilized. There are
slots cut between some of the rows and columns for this purpose. Another
projection needs to be made, but this time the limits should be made to exclude
the holes. Find the resolution in the x direction by setting y limits and
projecting in x to intercept a slot cut between columns. The y limits should be
set so that the projection goes through the middle of the slot rather than the
top or bottom.

Again, SpecTcl is used to make the spectrum and Origin to analyze.
A derivative of the data points corresponding to the slot – and a few adjacent
pixels – is taken. This plot has a positive peak where the slot begins and a
negative peak where the slot ends. An ideal case would have a spectrum going
from a background of zero counts, to the slot where the counts would jump up to
some constant level, to the end of the slot where the counts would instantly
drop back to zero. The derivative of this spectrum would be delta functions
without a discernable width from the two peaks. No width of the derivative peaks
translates to perfect resolution.

Actual experiments
do not have ideal resolution, so when the derivative of the slot projection is
taken there is a width to the peaks. This width is determined by first fitting
a Gaussian curve to the data. The value of σ is used to find
the full width at half maximum (FWHM) by the relation:

FWHM = 2√(2*LN(2))*σ.

This width was then converted from pixels to millimeters to
find the resolution of the detector.