SPAD Dead Time
Dead time effects on measured count rates, pile-up loss, and correction for SPAD detectors.
Results
Measured Rate (nonparalyzable)
8.000 Mcps
Count Loss = dead fraction of the time
20.00%
Correction Factor R/m
1.2500
True Rate at 10 % Loss
4.44 Mcps
Pile-up Correction Table (τ = 25 ns)
| True rate (Mcps) | Measured NP | Measured P | Loss NP | Loss P |
|---|---|---|---|---|
| 1 | 0.976 | 0.975 | 2.4% | 2.5% |
| 5 | 4.444 | 4.412 | 11.1% | 11.8% |
| 10 | 8.000 | 7.788 | 20.0% | 22.1% |
| 20 | 13.333 | 12.131 | 33.3% | 39.3% |
| 50 | 22.222 | 14.325 | 55.6% | 71.3% |
| 100 | 28.571 | 8.208 | 71.4% | 91.8% |
Measured vs True Rate
Count Loss vs Dead Time
Formulas
Non-paralyzable: m = R / (1 + R·τ); correction R = m / (1 − m·τ)
Paralyzable: m = R·exp(−R·τ); peak m = 1/(e·τ) at R = 1/τ
Loss 1 − m/R equals the fraction of time the counter is dead
Model and references
Textbook approximation. A standard approximation from the literature (for example paraxial, plane-wave or Gaussian-beam), valid within the range the page states. About the tiers
The two limiting dead-time models for Poisson arrivals. Real SPADs with active quenching sit near the non-paralyzable case, passively quenched ones between the two, and the dead time itself may vary.
- Knoll G. F. (2010). Radiation Detection and Measurement, 4th ed. Wiley. Ch. 4, section VII: non-paralyzable m = n/(1 + nτ) and paralyzable m = n·e^(−nτ) dead-time models.
- Müller J. W. (1973). Dead-time problems. Nucl. Instrum. Methods 112, 47–57. Dead-time models and the statistics of the recorded counts. doi:10.1016/0029-554X(73)90773-8