There are two different types of relative timing offsets. The first set controls the relative timing between the cells in each of the neutron planes. The other set controls the relative timing between the planes.
The relative timing between the cells in a plane is calibrated by measuring the time difference between hits in those cells relative to the first cell. The time of a hit in the first cell (i.e. NA00) is used as a reference and then, given the calculated path of the cosmic ray, the separation between the cells, and the assumption that the cosmic ray is travelling at the speed of light, the time that hits should take place in the other cells is determined. This calculated relative time difference is then compared to the actual arrival time of the signals from those cells, and then software offsets are adjusted to compensate for discrepancies. A sample of the relative TOF signals from one plane are shown in figure
Figure: Time difference spectrum between the calculated and actual times of a COSMIC event in a cell relative to the first cell (i.e. NA00). Note: The first cell gives a delta function because the estimated time of a signal is taken with respect to the hit in the first plane. Narrow distributions around ns indicate the offsets are set correctly.
The relative timing between the planes is essentially calibrated in the same manner as between the cells. The difference is that the PP events (mostly cosmic rays which traverse all six planes) are used. Again the assumption is made that the cosmic ray is travelling at the speed of light and, because the separation between the planes is known, the expected timing (in this case relative to first plane, NA0) can be compared to the timing actually observed. Software offset are then adjusted to bring these two quantities into agreement. Figure shows the time difference spectra for a representative run.
Figure: Time difference spectrum between the calculated and actual time for a PP event in the four different neutron planes relative to the first plane. Note: The first plane gives a delta function because the estimated time of a signal is taken with respect to the hit in the first plane.
The timing between the planes can also be checked by comparing the gamma peaks in the time-of-flight spectra of each plane. The gamma peak seen in the TOF spectrum is the result of detection of gamma rays produced by pion production and decay in the target at the same time as the interaction which produces the neutrons. Since they are produced at the same time there should be a difference in the total flight time to each plane. This is shown in figure , and when calibrated the timing differences between planes agree with the offsets calculated from the PP events.
Figure: Overlay of the time-of-flight spectra of the gamma rays to each neutron detector plane. TOF determined relative to the corrected RF signal.