Undergrad Time of flight measurement uncertainty

[Malamala]

Hello! I am generating electrons from a 3D gaussian source. The electrons all have the same energy, but the direction is isotropic. The electron source is in between 2 plates that act as a capacitor, and one of them acts as a time of flight (tof) detector. I know the voltage on the plates very well, and I want to extract the center of the gaussian distribution (in one direction only), by measuring the tof of many electrons. So the uncertainty on the position is given by the tof uncertainty.

The distribution of tofs is a gaussian, with the mean being what I need for my measurement and a standard deviation which has contributions from both the standard deviation of the source and the resolution of the tof detector. Is it possible, if I have enough events, to extract the the mean of this tof distribution with an uncertainty better than the resolution of the detector, or that would always be the best I can do? Thank you!

 

[Twigg]

Is it possible, if I have enough events, to extract the the mean of this tof distribution with an uncertainty better than the resolution of the detector, or that would always be the best I can do? Thank you!

Yes. With enough statistics you can measure the mean accurately below the resolution of your detector. By resolution, I take it you mean the resolution on the time-of-flight?

 

[Malamala]

Yes. With enough statistics you can measure the mean accurately below the resolution of your detector. By resolution, I take it you mean the resolution on the time-of-flight?

Thank you! Yes, the tof resolution. So should I expect the uncertainty to go like $\sigma/\sqrt{N}$, where N is the number of events and $\sigma$ is the combined uncertainty (i.e. the detector resolution and the uncertainty in the position of creation of individual electrons)?

 

[Twigg]

Yep! If you want mathematical proof for it, it's just the same statistics as a biased coin flip, where "heads" and "tails" refer to adjacent time bins of your detector on either side of the true tof value.