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TMIT and the integral of the raw waveform are used to calculate the bunch length. The parameters that need to be input in the system are the integration windows, plus a linear adjustment function [f(x)=a.x+b] for the sum of the signal, plus the coefficients of this equation:

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Each group of elements will be broken into sections for better comprehension:

Adjustment of the integration windows

The system provides a way to adjust 3 regions for the signal. The leftmost region, shown as "Duration pre edge (ns)" on the picture below, integrates the background noise to be subtracted from the signal region. The rightmost region, shown as "Duration pos edge (ns)" on the picture below, integrates the signal. An optional "Duration inter edges (ns)" defines a region between the background noise and the signal where the integration is ignored. It is useful for removing the slope from the calculation. This middle region is not shown in the chart below.

Image Added

Both pre-edge and inter-edge regions have its zero nanosecond reference in the same place: the starting point of a trigger (corresponds to the beginning of the chart). That's why selecting an inter-edge with a value less than the pre-edge makes the middle region disappear. Check the diagram below to have things more clear. The post-edge zero reference starts at the end of the pre-edge or the inter-edge, which one is greater.

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Coefficients of the equation

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The firmware doesn't work in terms of nanoseconds, but it uses clock ticks. A transformation must be done from clock ticks to nanoseconds and vice-versa. Also, the firmware doesn't accept odd values for tick counts. The first 28 bytes of the raw waveform sent by the firmware contains diagnostics data and not sampled data and have to be removed. All of these operations are described in the section "Waveform and integration windows".

Linear adjustment function for the sum of the signal

Coefficients of the equation

Algorithm description

Waveform and integration windows