spad op• Data kinds: countrate → countrate
• Call: import fullseye as fs; fs.ledger.spad_deadtime_apply(rate_hz, dead_time_ns=50.0, paralyzable=False) (to call the implementation directly, import photoncount; photoncount.spad_deadtime_apply(rate_hz, dead_time_ns=50.0, paralyzable=False); from the registry, opsphoton.get("spad_deadtime_apply"))
Distort a true photon rate by the detector's dead time (counts lost).
After every detection a SPAD is blind for a recharge (dead) time tau, so the *measured* rate m is always below the *true* incident rate n. Two classical laws, and this op implements both:
• non-paralysable (default) — an arriving photon during the dead time is simply lost: m = n / (1 + n*tau). Monotonic, saturating at 1/tau.
• paralysable (paralyzable=True) — an arriving photon *restarts* the dead time: m = n * exp(-n*tau). This law peaks at n = 1/tau (where m = 1/(e*tau)) and then falls, so a bright scene can read *darker* than a dim one. That is why no inverse op exists for it (see spad_deadtime_correct).
*rate_hz* is a 1-D array of true rates in counts per second; *dead_time_ns* is the dead time in nanoseconds, defaulting to 50 — the middle of the 10-100 ns range a passively quenched SPAD occupies, and a placeholder to be replaced by the datasheet value, never a measurement of your detector. Returns the measured rates as a float64 1-D array of the same length.
Ground truth (pinned in the tests): at n = 1/tau the non-paralysable law gives exactly n/2; the paralysable law's maximum is exactly 1/(e*tau) at n = 1/tau; both reduce to m = n as n*tau -> 0.
Raises ValueError: negative, non-finite or non-1-D *rate_hz*, a non-positive *dead_time_ns*, and a non-bool *paralyzable*.
• photon_timeresolved family guide
• Sample-data catalog (download URLs / licences) — 2-D uses skimage.data (BSD/public domain) plus synthetic images; 3-D lists download URLs for real data sources (Stanford, PDS, …).
• Operator provenance and references — the sources of the research/methods this op family came from.
• The canonical algorithm (author, year) and its uses are named in the family usage guide above.
• photon_timeresolved — py -3.11 examples/photon_timeresolved.py
countrate as input)spad)spad_deadtime_correct · tcspc_coates_correct
*Provenance: photoncount.py — PHOTON operator registry. This per-op note is generated by tools/opdocs.py md (do not hand-edit).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.