spad op• Data kinds: counts → counts
• Call: import fullseye as fs; fs.ledger.tcspc_coates_correct(hist, cycles) (to call the implementation directly, import photoncount; photoncount.tcspc_coates_correct(hist, cycles); from the registry, opsphoton.get("tcspc_coates_correct"))
Undo TCSPC pile-up exactly (Coates's estimator) — the early-photon bias.
Classical TCSPC records at most one photon per excitation cycle: the first one. Late bins are therefore starved, because the cycles in which an early photon arrived never reach them, and the measured histogram is biased toward short arrival times — a dToF depth read straight off a piled-up histogram is *too close*, and a fluorescence lifetime is *too short*.
Coates's estimator inverts that exactly. With N_k the measured counts in bin k and C the number of excitation cycles, the number of cycles that survived to reach bin k is D_k = C - sum_{j<k} N_j, the per-cycle detection probability in that bin is p_k = N_k / D_k and the pile-up-free per-cycle intensity is lambda_k = -ln(1 - p_k). This op returns C * lambda_k — the histogram the same scene would have produced if the detector could record every photon — so it is directly comparable to the measured one.
This is an exact inverse, not a linearisation: build a histogram from a known lambda through the forward model N_k = C * exp(-sum_{j<k} lambda_j) * (1 - exp(-lambda_k)) and Coates returns lambda to machine precision (measured max relative error 1.6e-15 in the tests, on a pile-up so severe that the last bin was suppressed to 14.8% of its true counts).
*hist* is the 1-D measured histogram (counts per bin); *cycles* the number of excitation cycles (laser pulses) that produced it.
Raises ValueError: negative, non-finite or non-1-D *hist*, a non-positive or non-integer *cycles*, a histogram whose total exceeds *cycles* (impossible: at most one photon per cycle — a sure sign that *cycles* is wrong or the data are not first-photon TCSPC), and any bin that consumed every remaining cycle (p_k = 1, where -ln(0) is inf).
• 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
• poc_dtof_ranging — py -3.11 examples/poc_dtof_ranging.py
counts as input)tcspc_irf_convolve · tcspc_background_subtract · tcspc_stats · dtof_depth · lifetime_fit · lifetime_phasor
spad)spad_deadtime_apply · spad_deadtime_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.