Amplitude Walk in Fast Timing: The Role of Dual Thresholds

We apply lessons from fast timing detector R$\&$D to strategies for initial calibration of large timing arrays at future colliders. Detector R$\&$D often benefits from detailed information about the sensor and front-end signal (waveform capture) as well as a quality time reference and tracking. On the other hand, the systems for charged particle (MIP) timing under construction for the CERN High Luminosity LHC log only limited information for each timing channel -- usually amplitude and the time of the leading edge. Furthermore the high event rates certainly present a challenge for \textit{in situ }calibration of the large (compared to intrinsic) time jitter of the leading edge with pulse amplitude -- amplitude walk. In the examples presented here we find a simple linear dependence of walk on the inverse of the pulse slope at threshold for the dynamic range (in amplitude) suitable to charged particle timing. We present a straightforward calibration method for the small variation in the corresponding coefficient from channel-to-channel.