typed op• Data kinds: counts → counts
• Call: fullseye.apply(img, "tb_tcspc_coates_correct", a=0.5, b=0.5) (the 2-D model is one image plus two scalar knobs a,b∈[0,1])
*The figure is the actual output on a synthetic 128×128 input. Left: input, right: output. Point clouds are drawn as a top-down scatter (brightness = z), 1-D series as a line plot, volumes as the maximum-intensity projection along z, videos as the middle frame, complex images as magnitude; return values that are not pictures are shown as the values themselves.*
*Knob a does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
*Knob b does not change the output (measured: identical at 0.1 / 0.5 / 0.9).*
Stages (the ops that come before → this op, left to right):
▸ tb_tcspc_coates_correct: stages (docs site)
On other images (synthetic scene / photo / coins. Top row: inputs, bottom row: their outputs. Knobs at default):
▸ tb_tcspc_coates_correct: other inputs (docs site)
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).
Typed bridge of the photon op tcspc_coates_correct into the 2-D evolution registry: the same implementation, called under the op(v, a, b) convention. This op has no tunable parameter; a and b are 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.
The program below has been verified to run (same input as the figure). In Studio's help this block becomes buttons that load and run it on the spot.
img_to_counts 0.50 0.50 tb_tcspc_coates_correct 0.50 0.50
▸ Load this pipeline · Load & run
The examples below call the underlying ledger op tcspc_coates_correct. This bridge op is the same implementation adapted to the fn(v, a, b) convention, so the behaviour carries over unchanged (only the call form differs).
• photon_timeresolved — py -3.11 examples/photon_timeresolved.py
• poc_dtof_ranging — py -3.11 examples/poc_dtof_ranging.py
counts as input)identity · tb_spad_deadtime_apply · tb_spad_deadtime_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_project_points · tb_render_point_depth · tb_statistical_outlier_removal · tb_radius_outlier_removal · tb_voxel_grid_downsample
*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.