Time of flight measurement uncertainty

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Discussion Overview

The discussion centers on the measurement of time of flight (tof) for electrons generated from a 3D Gaussian source, specifically focusing on the uncertainty in determining the mean of the tof distribution. Participants explore the relationship between the number of events and the uncertainty in the measurement, considering both the resolution of the tof detector and the inherent uncertainty from the source.

Discussion Character

  • Technical explanation, Mathematical reasoning

Main Points Raised

  • One participant describes a setup involving electrons emitted isotropically from a Gaussian source and seeks to understand the uncertainty in measuring the mean tof based on the detector's resolution.
  • Another participant asserts that with sufficient statistical events, it is possible to measure the mean tof with an uncertainty that is lower than the detector's resolution.
  • A follow-up question clarifies whether the uncertainty in the mean measurement would scale as ##\sigma/\sqrt{N}##, where N is the number of events and ##\sigma## represents the combined uncertainty from both the detector resolution and the source uncertainty.
  • A later reply confirms the scaling relationship and likens the statistical reasoning to that of a biased coin flip, relating it to the distribution of time bins in the detector.

Areas of Agreement / Disagreement

Participants generally agree that it is possible to achieve a mean measurement uncertainty below the detector's resolution with enough events. However, the specifics of how the uncertainties combine and the implications of the statistical model remain open to further discussion.

Contextual Notes

The discussion does not resolve the exact contributions of the source uncertainty versus the detector resolution to the overall uncertainty in the mean measurement, nor does it clarify the assumptions underlying the statistical model used.

Malamala
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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!
 
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Malamala said:
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?
 
Twigg said:
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)?
 
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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.
 

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