pyfli.phasor.phasorSEPL.locus#

locus.py#

Build Single-Exponential Phasor Locus (SEPL) arrays — the parametric curve traced in the (g, s) plane as τ sweeps from 0 to ∞.

The term “SEPL” (pronounced sepal) was introduced by Michalet 2021 for all such curves, whether they are the canonical universal semicircle or deformed variants arising from gating / binning / truncation.

Functions

`build_loci`(cfgs, **kwargs)	Compute SEPL curves for a list of configs in one call.
`build_locus`(cfg, *[, tau, filter_finite])	Compute the full SEPL for the given acquisition configuration.
`sepl_center_radius_discrete`(cfg)	Analytically compute the circle centre (gc, sc) and radius r of the discrete SEPL L_N (Michalet 2021, Sec.
`tau_grid`(cfg[, power])	Return a non-uniform τ grid in [tau_min_ns, tau_max_ns].
`universal_semicircle`([n_pts])	Return (g, s) coordinates of the universal semicircle.

tau_grid(cfg, power=1.5)[source]#

Return a non-uniform τ grid in [tau_min_ns, tau_max_ns].

The grid is denser at small τ (where the locus curves sharply near (1,0)) using a power-law spacing.

Parameters:

cfg (AcquisitionConfig)
power (float) – Exponent for the nonlinear spacing. 1.0 = linear; >1 = finer at small τ.

Returns:

tau

Return type:

1-D ndarray (length = cfg.n_tau_pts)

build_locus(cfg, *, tau=None, filter_finite=True)[source]#

Compute the full SEPL for the given acquisition configuration.

Parameters:

cfg (AcquisitionConfig) – Fully describes the experiment (mode, T, harmonic, gates, …).
tau (1-D array, optional) – Custom τ grid in ns. If None, tau_grid(cfg) is used.
filter_finite (bool) – If True (default), remove any (g, s) pairs where either component is non-finite (NaN / ±Inf). Useful for modes that become undefined at τ → 0 for certain parameter sets.

Returns:

g (1-D ndarray) – Real phasor coordinate.
s (1-D ndarray) – Imaginary phasor coordinate.
tau (1-D ndarray) – Corresponding lifetime values in ns.

Return type:

tuple[NDArray[float64], NDArray[float64], NDArray[float64]]

build_loci(cfgs, **kwargs)[source]#

Compute SEPL curves for a list of configs in one call.

Useful for overlaying several acquisition scenarios on the same plot.

Parameters:

cfgs (list[AcquisitionConfig])
kwargs (passed verbatim to build_locus.)

Return type:

list of (g, s, tau) tuples, same order as *cfgs*.

universal_semicircle(n_pts=300)[source]#

Return (g, s) coordinates of the universal semicircle.

The universal semicircle is defined by: (g − ½)² + s² = (½)², s ≥ 0
and is parameterised by the angle θ ∈ [0, π]:: g = ½ + ½·cos(θ), s = ½·sin(θ)

Parameters:: n_pts (int) – Number of samples (default 300).
Returns:: g, s
Return type:: 1-D ndarray

sepl_center_radius_discrete(cfg)[source]#

Analytically compute the circle centre (gc, sc) and radius r of the discrete SEPL L_N (Michalet 2021, Sec. III C 1).

For a binned PSED with N bins and harmonic n, the phasor traces:

z_N(τ) = (1 − x) / (1 − x·e^{iφ})

where x = e^{−T/(N·τ)} and φ = 2π·n/N.

This Möbius transform of the real interval (0, 1) traces an arc of a circle with parameters (derived analytically by equating coefficients in the expanded circle equation):

gc = 1/2 sc = −(1/2) · tan(φ/2) r = √(gc² + sc²) = (1/2) / cos(φ/2)

The arc converges to the universal semicircle as N → ∞ (φ → 0).

Parameters:: cfg (AcquisitionConfig) – Requires: N_bins, harmonic.
Returns:: gc, sc, r – Circle centre coordinates and radius.
Return type:: float