lifetime op• Datenarten: counts → table
• Aufruf: import fullseye as fs; fs.ledger.lifetime_phasor(decay, bin_ps=100.0, harmonic=1, background=0.0) (die Implementierung direkt: import photoncount; photoncount.lifetime_phasor(decay, bin_ps=100.0, harmonic=1, background=0.0); aus dem Register: opsphoton.get("lifetime_phasor"))
Phasor-(Frequenzbereichs-)Darstellung eines Abklingvorgangs — die fitfreie Sicht.
> Die ausführliche Beschreibung unten ist der Originaltext — Zusammenfassung und Überschriften sind übersetzt.
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 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. 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.
• Leitfaden zur Familie photon_timeresolved
• Katalog der Beispieldaten (Download-URLs / Lizenzen) — 2-D nutzt skimage.data (BSD/Public Domain) plus synthetische Bilder, 3-D nennt Download-URLs echter Datenquellen (Stanford, PDS, …).
• Herkunft und Literatur der Operatoren — die Quellen der Forschung/Verfahren, auf denen diese Operatorfamilie beruht.
• Der kanonische Algorithmus (Autor, Jahr) und seine Anwendungen stehen im Familienleitfaden oben.
• photon_timeresolved — py -3.11 examples/photon_timeresolved.py
table als Eingabe)—
lifetime)*Provenance: photoncount.py — PHOTON Operator-Registry. Diese Notiz wird von tools/opdocs.py md erzeugt (nicht von Hand bearbeiten).*
© 2026 Kazufumi Furuse — Fullseye operator documentation. Licensed under Apache-2.0.