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NMR Background Curve Fitting
Caitlyn Meditz, on behalf of the Nuclear and Particle Physics Group. Advisor K. Slifer, E. Long
Overview
NMR Curve
My Contribution
Dynamic Nuclear Polarization (DNP) is a
technique used in experiments where the
scattering of electrons from a polarized target
is used to probe the internal structure of the
target. DNP uses low temperature and a high
magnetic field to polarize a target and orient
spins. Our target is oriented using a 5T
magnetic field and is submerged in a vessel of
liquid helium held at 1K. This polarizes the
electrons to a high degree. Millimeter waves
tuned to the Lamour frequency are used to
induce spin flips on the electrons and a nearby
proton.
The NMR curve is composed of two signals. The x values of
the graph are given by an input triangle wave which shows a
reference frequency vs time. The y values are the output of
a modulator from which we use the amplitude over time.
It has been my task to eliminate the wings on
either side of the NMR curve by assuming they
can be described by a polynomial, and finding
and subtracting their polynomial equation of fit.
In addition to displaying the NMR curve, the
program also displays temperature data from
various points in the fridge using the current
through resistors whose resistance changes
depending on the temperature. It also shows a
graph of the temperature of the Q Meter over
time, and the integral of the calibrated
modulator signal over time. These other
outputs can be seen in the upper left, lower left,
and lower right graphs, respectively.
NMR Background Removal
The above diagram shows the layout of
the four subsystems of our DNP setup
The polarization is measured using Nuclear
Magnetic Resonance (NMR). Our data is
viewed using the visual programming language
LabVIEW. NMR can be observed with a small
pickup coil positioned near our target sample,
and is observed as a sharp resonant signal.
The integral of this curve is proportional to the
polarization of the target. On either side of the
spike are "wings" that result from background
contributions that are artifacts of the circuit
response and are not related to the resonance.
These wings must be subtracted in order to
isolate the NMR signal.
Before the magnetic field is applied, the NMR graph shows
a curved background wave which peaks or reaches a
minimum at the value in MHz where we would expect to find
the proton. When the magnetic field is applied, we see the
NMR curve, which is displayed below in the graph in the
upper right hand corner. This graphic is a screenshot of our
program's output. The curve points upwards or downwards
depending on the direction of the polarization, and the
higher the spike the greater the polarization. On either side
of the spike we can see the “wings” of background
information.
Graphs to the right from:
Maxwell, James D. Probing Proton Spin Structure: A
Measurement of G 2 at Four-momentum Transfer of 2 to 6
GeV. Thesis. University of Virginia, 2011. N.p.:. n.d. Print.
My code works by first accepting user defined
input values for the cutoff points of the left and
right wings: the x value at which the left wing
ends, and by comparing the arrays of the input
triangle wave (x values) and the modulator (y
values), creates new arrays with only the
values on the wings. A function within
LabVIEW then accepts the new arrays as
inputs and outputs an equation of fit, which is
subtracted. A simplified version of the
outcome of this procedure can be seen below
in a set of curves taken from James Maxwell's
thesis.