Choosing an Appropriate Bin Width for Histograms

With our Time Tagger you can choose any binwidth in the range from 1 ps to more than a day. The entire range is adjustable with one picosedond resolution. In addition to the number of bins, this setting determines the maximum time difference that you measure. This flexibility allows you to choose a proper binwidth purely based on the requirements of your experiment.

The following questions may help you identify and decide on the optimal bin width value for your measurement:

1. What is the maximum time difference you want to measure?

histogram_span = bindwidth × n_bins

Large values of n_bins require more memory, and you may want to trade off bin width for fewer bins if you are measuring very long time differences. As a general guideline, n_bins < 1e7 is usually acceptable for measurements created in Time Tagger Lab/Python/Matlab/LabView/C++/C# etc. With the Time Tagger Web App, values of n_bins greater than 10,000 may cause higher CPU load due to the increased data transmission and frequent plot refreshes.

2. What time resolution do you expect from your measurement?

Smaller binwidths will give you finer digital resolution of a histogram, however, the actual resolution is limited by the inherent time measurement uncertainty (timing jitter). The minimum timing jitter values are:

  • 34 ps RMS for Time Tagger 20
  • 3-8 ps RMS for Time Tagger Ultra
  • 1.5-2 ps RMS for Time Tagger X

Additionally, the timing jitter of your detectors introduces further uncertainty into your measurement. To account for this, you may choose a bin width slightly smaller than the total timing uncertainty in your experiment. For example, with the Time Tagger 20, a bin width of ≥ 10 ps is a good choice.

3. What signal-to-noise ratio (SNR) do you want to achieve, and in what time?

Smaller bin widths require more time to accumulate enough counts to achieve the desired noise level compared to larger bin widths. This is due to shot noise, which is proportional to 1/√N, where N is the number of counts in a single bin. This concept is similar to how SNR improves through averaging. Larger bin widths naturally result in higher counts per bin larger counts per bin in a shorter time for the same signal rate.

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