Time of flight measurement uncertainty

In summary, the conversation discusses creating electrons from a 3D gaussian source in between 2 plates acting as a capacitor and a time of flight detector. The uncertainty on the position is given by the tof uncertainty, which can be improved with enough events. The tof distribution is a gaussian with a mean that can be accurately measured below the resolution of the detector. The uncertainty is expected to decrease with the number of events and is affected by both the detector resolution and the uncertainty in the position of creation of individual electrons.
  • #1
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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  • #2
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?
 
  • #3
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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  • #4
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.
 

What is time of flight measurement uncertainty?

Time of flight measurement uncertainty is the amount of error or variation in the measured time of flight of a signal or particle. It is a measure of the accuracy and precision of the measurement.

What factors contribute to time of flight measurement uncertainty?

There are several factors that can contribute to time of flight measurement uncertainty, including the accuracy of the timing equipment, the stability of the signal source, and external factors such as temperature and pressure.

How is time of flight measurement uncertainty calculated?

Time of flight measurement uncertainty is typically calculated using statistical methods, such as standard deviation or confidence intervals. It takes into account the variability in the measured time of flight and the precision of the measurement equipment.

Why is time of flight measurement uncertainty important in scientific research?

Time of flight measurement uncertainty is important because it can affect the accuracy and reliability of scientific research. If the uncertainty is too high, it can lead to incorrect conclusions and potentially invalidate the results of a study.

How can time of flight measurement uncertainty be minimized?

There are several ways to minimize time of flight measurement uncertainty, such as using high-quality and stable measurement equipment, controlling external factors that can affect the measurement, and performing multiple measurements to reduce the effects of random errors.

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