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Amplitude Walk in Fast Timing: The Role of Dual Thresholds

Sebastian White, Alessio Boletti

TL;DR

The paper tackles calibrating large MIP timing detector arrays under HL-LHC conditions by exploiting a dual-threshold slope measurement to model and correct amplitude walk with a per-channel Amplitude Walk Coefficient (AWC). Using CMS BTL/TOFHIR data, it shows that time walk correlates linearly with the inverse of the pulse slope, enabling a stand-alone Day-1 calibration without outside $t_0$ references. AWCs exhibit channel-to-channel spread (~22%), which can be reduced to ~13% by leveraging the slope–to–charge relation (Slope = a + bQ) to trim each channel’s coefficient. The approach offers a practical, scalable calibration pathway for large timing systems in high-rate environments, potentially reducing reliance on full event reconstruction during initial operation. The work lays the groundwork for later beam-based validation and refinement of channel-wise AWC trimming.

Abstract

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.

Amplitude Walk in Fast Timing: The Role of Dual Thresholds

TL;DR

The paper tackles calibrating large MIP timing detector arrays under HL-LHC conditions by exploiting a dual-threshold slope measurement to model and correct amplitude walk with a per-channel Amplitude Walk Coefficient (AWC). Using CMS BTL/TOFHIR data, it shows that time walk correlates linearly with the inverse of the pulse slope, enabling a stand-alone Day-1 calibration without outside references. AWCs exhibit channel-to-channel spread (~22%), which can be reduced to ~13% by leveraging the slope–to–charge relation (Slope = a + bQ) to trim each channel’s coefficient. The approach offers a practical, scalable calibration pathway for large timing systems in high-rate environments, potentially reducing reliance on full event reconstruction during initial operation. The work lays the groundwork for later beam-based validation and refinement of channel-wise AWC trimming.

Abstract

We apply lessons from fast timing detector RD to strategies for initial calibration of large timing arrays at future colliders. Detector RD 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.

Paper Structure

This paper contains 14 sections, 7 equations, 9 figures.

Table of Contents

  1. Introduction
  2. Outline
  3. Slope Measurement with dual thresholds
  4. Naive case
  5. Lessons from Naive Case
  6. Departure from the Naive Case
  7. Data Sets Used for this Paper
  8. Laser Data
  9. Determining individual Amplitude Walk Coefficients
  10. Discussion
  11. Conclusion
  12. Acknowledgement
  13. Appendix: Future CMS-specific Development
  14. Appendix: Use of Slope Measurement to Mitigate Effects of Dark Count Noise on Time Jitter

Figures (9)

  • Figure 1: Obtaining "pulse slope at threshold" from dual thresholds as used throughout this paper (left). A simple example (right) illustrating the direct relation between "pulse slope at threshold" and walk for two different signals with slopes Sl1 and Sl2 and amplitudes Q1 and Q2.
  • Figure 2: The resulting walk corrected data (right) after application of an analytic expression in pulse slope for a system with linear response- taken from ref. 7.
  • Figure 3: A single LYSO/SiPM array (Left). The light reflector wrapping has been removed in a single strip (Right) so that a pulsed UV laser beam can illuminate individual bars.
  • Figure 4: A typical data set for one channel (SiPM17) , where each point is an average of $\sim200$ laser shots (left) and the resulting curves represent the pulse shape at the input of the timing discriminator for each laser intensity. Since we present results for a range of thresholds, we capture times (i.e. walk relative to t$_{corrected}$) and slopes in a quadratic fit (right) for this analysis.
  • Figure 5: The time at threshold ( i.e. $t_i$ in eqn 2.4) vs. inverse slope are well fitted to a linear relation in this and all other channels. Measurements are repeated for 4 different "thr2" settings.
  • ...and 4 more figures