typed op• Data kinds: counts → counts
• Call: fullseye.apply(img, "tb_spad_deadtime_apply", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
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
:func: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*.
Typed bridge of the photon op `spad_deadtime_apply into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. a drives dead_time_ns (default 50); b` is unused.
• 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.
• (none yet)
counts as input)identity · tb_spad_deadtime_correct · tb_tcspc_coates_correct · tb_tcspc_irf_convolve · tb_tcspc_background_subtract · tb_dtof_depth · tb_countrate_to_counts · tb_counts_to_countrate
typed)tb_points_to_voxel · tb_estimate_point_normals · tb_iss_keypoints · tb_angle_3points · tb_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal
*Provenance: ops.py — 2D 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.