lifetime opcounts → tableimport fullseye as fs; fs.ledger.lifetime_phasor(decay, bin_ps=100.0, harmonic=1, background=0.0) (実装を直接呼ぶなら import photoncount; photoncount.lifetime_phasor(decay, bin_ps=100.0, harmonic=1, background=0.0)、台帳から引くなら opsphoton.get("lifetime_phasor"))Phasor (frequency-domain) representation of a decay — the fit-free view.
FLIM’s standard fit-free tool. With omega = 2*pi*harmonic/window and bin
centres t_k::
g = sum(h_k * cos(omega*t_k)) / sum(h_k)
s = sum(h_k * sin(omega*t_k)) / sum(h_k)
For a single exponential of lifetime tau under periodic excitation the
exact analytic phasor is g = 1/(1+(omega*tau)^2),
s = omega*tau/(1+(omega*tau)^2), which traces the universal
semicircle (g - 1/2)^2 + s^2 = 1/4 as tau runs from 0 to infinity.
A multi-exponential decay falls strictly inside that circle — which is why
semicircle_residual is returned: it is the honest detector of the
single-exponential assumption that :func:lifetime_fit cannot give you.
Returns a dict: g · s · modulation m = sqrt(g^2+s^2) ·
phase_rad · omega_per_ps · tau_phi_ps = tan(phase)/omega ·
tau_m_ps = sqrt(1/m^2 - 1)/omega · semicircle_residual
= (g-1/2)^2 + s^2 - 1/4 (0 on the circle, negative inside) ·
total_counts. tau_phi_ps is None — not a negative number — when
the phase is not in (0, pi/2), and tau_m_ps is None when the
modulation is 0 or >= 1; both mean “this is not a decaying single
exponential”, which is information, not a failure.
Honest accuracy: the analytic formula is the continuous integral over one
excitation period, while this op sums over bins, so the two differ by the
midpoint-rule error. Measured on an exactly bin-integrated single exponential
(tau = 2000 ps, 256 bins x 100 ps, i.e. a 25.6 ns period): g is
0.805809 against the analytic 0.805830 (-2.0e-05), s is 0.395653 against
0.395561 (+9.2e-05), tau_phi_ps comes back as 2000.52 ps (+0.026%),
tau_m_ps as 1999.74 ps (-0.013%) and semicircle_residual is
+6.07e-05. Quadrupling to 1024 bins over the same window divides the residual
by exactly 16.00 (to 3.79e-06) and the tau_phi error by 16 — the
O(bin^2) midpoint behaviour, not a bias in the op.
And the reason semicircle_residual earns its place: the same window with
a two-component decay (equal photon budgets at 500 ps and 4000 ps) gives
a residual of -0.0924, i.e. 1500x further inside the circle than the
single-exponential round-off. :func:lifetime_fit would have returned one
confident number for that same histogram.
Raises ValueError: negative, non-finite, non-1-D or all-zero decay,
a non-positive bin_ps, a harmonic outside [1, bins//2] (above
Nyquist the phasor is aliased and meaningless), a negative background, and
a background subtraction that removes every count.
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.