lifetime opcounts → tableimport fullseye as fs; fs.ledger.lifetime_fit(decay, bin_ps=100.0, background=None, min_counts=1.0, start_bin=None) (実装を直接呼ぶなら import photoncount; photoncount.lifetime_fit(decay, bin_ps=100.0, background=None, min_counts=1.0, start_bin=None)、台帳から引くなら opsphoton.get("lifetime_fit"))Mono-exponential fluorescence lifetime from a TCSPC decay histogram.
Fits I(t) = A*exp(-t/tau) + b by a Poisson-weighted log-linear least
squares: the background is removed, the logarithm of the remaining counts
is linear in t with slope -1/tau, and each bin is weighted by its own
counts because var(ln N) ~ 1/N — which is exactly the Poisson error bar
:func:photon_uncertainty reports.
The fit starts at the peak bin by default (or at start_bin if given):
the rising edge before the peak is the instrument response convolved with the
decay, not the decay, and including it flattens the log slope and so biases
the lifetime long. Measured on a 2000 ps decay blurred by a 600 ps IRF
(256 bins x 100 ps): starting at the peak (bin 4) gives 2008.0 ps (+0.40%),
forcing start_bin=0 gives 2100.7 ps (+5.0%) — a 12x worse bias from four
extra bins. Only bins with more than min_counts counts after background
removal take part (the
logarithm of 0 is -inf, and single-count tail bins carry almost no
information but huge log-scatter).
background is the flat pedestal per bin; None (default) estimates it as
the median of the last decile of bins, which for a decay is tail. Pass
0.0 to state that the data are already background free.
Returns a dict: lifetime_ps · amplitude (the fitted A at t=0
of the fit window, in counts per bin) · background (the level used) ·
start_bin · n_bins_used · r_squared (of the weighted log fit).
Ground truth: on a noiseless exponential the recovery is exact —
lifetime_ps came back as 2000.000000000 ps for tau = 2000 ps (256
bins x 100 ps), a measured relative error of 0.0, with r_squared 1.0.
That stays true when the histogram is built by integrating the exponential
over each bin rather than sampling it, because bin integration multiplies
every bin by the same constant and so cannot change the slope.
With Poisson noise the log-linear estimator is biased high, and the size
of the bias is worth knowing: at 20000 total photons, seed 0,
min_counts=1 gives 2058.8 ps (+2.9%) from 133 bins, and raising
min_counts to 10 gives 2047.3 ps (+2.4%) from 94 bins. Averaged over
seeds 0-19 at min_counts=10 the mean is 2014.3 ps (+0.72% systematic
bias) with a 18.2 ps (0.9%) seed-to-seed spread — so seed 0 is a
2-sigma-high draw, and the bias, not the scatter, is the thing to remember.
It comes from E[ln N] < ln E[N] in the sparse tail; a full Poisson MLE
would remove it and is not what this op does.
Raises ValueError: negative, non-finite or non-1-D decay, a
non-positive bin_ps, a negative background / min_counts, a start_bin
outside the histogram, fewer than 2 usable bins after the background and
threshold cuts (a straight line needs two points), a degenerate fit (all
usable bins at the same time), and — instead of returning a negative
lifetime — a fitted slope that is zero or positive, i.e. a profile that does
not decay.
py -3.11 examples/photon_timeresolved.pytable を入力に取れる)—
lifetime)Provenance: photoncount.py — PHOTON operator registry. この per-op ノートは tools/opdocs.py md が自動生成(手編集しない)。
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.