Evaluation of an experiment: PET scans of a small source along the x-axis

[Lambda96]

Homework Statement

Evaluation of an experiment

Relevant Equations

none

Hi,


I did a PET scan and positioned a sample almost in the center of a moving carriage, taking measurements along the x-axis and measuring the counts. Each measurement took 60 seconds, and I took a total of 27 measurements. Here are my results

As the display was in mm, I always assumed an error of 1 mm. For the error calculation of the counts, I used Poisson, i.e. $\Delta count= \sqrt{n}$ and for the errors of the counts per seconds I calculated as follows: $\Delta$ counts per second = $\frac{\Delta count}{t}$


Now I have to do the following

Plot the position of the trolley (error discussion!) against the measured coincidence count rate graphically (with x-y errors). Fit the peak with a Gaussian curve (with x-y errors) and determine the FWHM. How does this result serve as an error for further measurements?

For the plots I used Origin and for the plot of the counts per second plus the error in x and y I had no problem and got the following:

Unfortunately, I'm not sure if I did the plot regarding the peak with the Gauss curve correctly and that I calculated the FWHM correctly, for FWHM I have used the formula $FWHM=2 \sqrt{2 \ln{2}} \sigma$, where $\sigma=1.4215$ which means that $FWHM=3.35$. But how do I calculate the error of the FWHM?

Here is the plot

 

[gleem]

Let me begin by saying that I believe this experiment was meant to determine a point response function and thus the spatial resolution of your scanner assuming you used a point source. It would also seem that there were a substantial number of accidental counts meaning that the distribution was not a pure Gaussian but a Gaussian sitting on a background of some sort. I think the FWHM is significantly correlated with the accidental count background. I would try to estimate the form of the background and include it in the fit at least to see its effect on the value of σ. If you used a nonlinear fitting routine it should estimate the uncertainty in σ of the Gaussian from which you can determine the FWHM uncertainly.

 

[Lambda96]

Thank you very much for your help

How exactly can I estimate the background with the help of the measured data?

 

[gleem]

My approach is to start with the simplest functional form that makes sense Usually a straight line. bg = ax +b and see if that gives a reasonable χ². If the χ² is still unreasonable add a cx² term and repeat. Don't try to overfit it. Backgrounds usually are structureless, with no peaks or fissures that might have too much effect unless you have a valid reason to use a more complex form. You can look at residuals to see where your model is failing. It might provide some guidance as to what to use.