7 Lifetime Features (Fit-Free)
Phasor analysis provides a fast, model-free view of lifetimes by transforming fluorescence decays into phasor coordinates through a Fourier transform. This approach is considered “fit-free” because it does not require iterative curve fitting or predefined decay models—each decay is mapped directly to a point on the phasor plot. It has the nice property that mono-exponential decays fall on the universal semicircle while mixtures lie inside as linear combinations, so clusters reveal distinct species and their fractional contributions. FLIM Playground currently extracts cell-level phasor features: g, s, Tau_phase, Tau_mod, g_2nd (2nd harmonic), and s_2nd. (Datasets extracted before this feature was renamed use Tau_m, which Data Analysis still recognizes.)
Fit-free features in the final dataset are prefixed by the combination of the feature extractor name (i.e. Lifetime fit free) and the channel name, allowing Data Analysis to group the features. For example, Lifetime fit free_nadh: G means the \(g\) coordinate for this cell in the NAD(P)H channel.
7.1 Preprocessing
It sums up all the pixel decays belonging to the same cell ROI labeled by the ROI mask as one decay curve1. The phasor features are calculated from the summed decay curve.
Two preprocessing steps are then applied, and they are independent of each other:
- Offset subtraction is applied to every decay curve, regardless of the chosen calibration method. For each cell, the offset is estimated as the mean of the last 10% of the time bins of that cell’s own decay curve, subtracted from the curve, and any resulting negative values are clipped to zero. Note that this per-cell baseline is unrelated to the
offsetparameter fitted during lifetime fitting. - IRF shifting is applied only when the chosen calibration method is IRF shift calibration. The IRF is shifted using the shift values as described in the Shift IRF step. Under fluorescence lifetime standard calibration, no IRF shift is applied.
7.2 Phasor features
7.2.1 Step 1: raw phasor coordinates
The reference implementation from phasorpy assumes the decay curve comes from one period and time bins are evenly spaced (untruncated). So, their calculation is frequency (\(f\)) and time (\(T\)) independent. However, there are cases when the decay curve is truncated due to the deadtime of the system. For example, when the laser frequency is \(f = 0.08\) GHz, the theoretical period is \(T = 12.5\) ns, but in practice the time window is truncated to \(T = 10\) ns. FLIM Playground applies a custom implementation to the truncated decay curve. (The sample_phase option can be used to account for the truncation but it does not handle the second or higher harmonics)
Untruncated decay curve
It uses the phasor_from_signal function from the phasorpy package to calculate the uncalibrated phasor coordinates g_raw and s_raw, g_raw_2nd and s_raw_2nd, the first and second harmonics’ real and imaginary parts, from the cell decay curve.
Either g_irf, s_irf, g_irf_2nd, and s_irf_2nd from the IRF, or ref_mean, ref_real, ref_imag from the fluorescence lifetime standard, depending on the chosen calibration method, are calculated using the same function.
Mathematically, the raw phasor coordinates are calculated as (copied from the phasorpy documentation):
\[ F_{\mathrm{DC}}=\frac{1}{K}\sum_{k=0}^{K-1}F_k,\quad g_{\mathrm{raw}}=\frac{1}{F_{\mathrm{DC}}}\frac{1}{K}\sum_{k=0}^{K-1}F_k\cos\!\left(2\pi h \frac{k}{K}\right),\quad s_{\mathrm{raw}}=\frac{1}{F_{\mathrm{DC}}}\frac{1}{K}\sum_{k=0}^{K-1}F_k\sin\!\left(2\pi h \frac{k}{K}\right) \] where \(K\) is the number of time bins, \(F_k\) is the decay curve, and \(h\) is the harmonic number.
Truncated decay curve
The phasor coordinates of the IRF and the decay curves of both harmonics are calculated using the time axis \(t_k = k\,(T/K)\;\;(k=0,\ldots,K-1)\) and the angular frequency \(\omega = 2\pi\,hf\):
\[ g_{\mathrm{raw}} =\frac{\sum_{k=0}^{K-1} F_k \cos\!\big(\omega\, t_k\big)} {\sum_{k=0}^{K-1} F_k},\quad s_{\mathrm{raw}} =\frac{\sum_{k=0}^{K-1} F_k \sin\!\big(\omega\, t_k\big)} {\sum_{k=0}^{K-1} F_k} \]
This formula is equivalent to the untruncated formula when \(fT = 1\).
For the fluorescence lifetime standard, the phasor coordinates are calculated using phasorpy’s phasor_from_signal and the sample_phase option is set to \(\omega t_k\).
7.2.2 Step 2: calibrated phasor coordinates
To get the calibrated phasor coordinates g, s, g_2nd, and s_2nd, FLIM Playground uses either
from phasorpy import phasor
g, s = phasor.phasor_divide(g_raw, s_raw, g_irf, s_irf)
g_2nd, s_2nd = phasor.phasor_divide(g_raw_2nd, s_raw_2nd, g_irf_2nd, s_irf_2nd)or
from phasorpy import lifetime
g, s = lifetime.phasor_calibrate(g_raw, s_raw, ref_mean, ref_real, ref_imag, frequency=laser_rate, lifetime=reference_dye_lifetime)
g_2nd, s_2nd = lifetime.phasor_calibrate(g_raw_2nd, s_raw_2nd, ref_mean, ref_real, ref_imag, frequency=laser_rate, lifetime=reference_dye_lifetime, harmonic=2)The laser_rate is specified during the fov metadata extraction and the configuration interface.
7.2.3 Step 3: phasor-derived lifetime
Tau_phase and Tau_mod are calculated using the first harmonic’s phasor coordinates g and s.
import numpy as np
w = 2 * np.pi * laser_rate
phi = np.arctan2(s, g)
mod = np.sqrt(g**2 + s**2)
tau_phase = 1/w * np.tan(phi)
tau_mod = 1/w * np.sqrt(1/mod**2 - 1)\[ \phi = \operatorname{atan2}(s,\,g), \mathrm{mod} = \sqrt{g^{2}+s^{2}}, \tau_{\phi} = \frac{\tan \phi}{\omega}, \tau_{\mathrm{mod}} = \frac{1}{\omega}\sqrt{\frac{1}{\mathrm{mod}^{2}}-1} \]
Because \(\omega\) is derived from the laser rate in GHz, Tau_phase and Tau_mod are expressed in nanoseconds. Note that this differs from the Lifetime fit extractor, whose lifetime columns are exported in picoseconds.