Fisher-Information-Driven Adaptive Acquisition for Photon-Efficient FLIM: A Dual-Implementation Framework for TCSPC and Programmable Time-Gating

TL;DR

This work tackles photon-limited FLIM by formulating a unified Fisher-information-based framework that treats temporal sampling as an optimizable design under a fixed photon budget. It derives a Poisson-counting observation model for time-domain FLIM with bi-exponential decays convolved by the instrument response, and introduces a nuisance-robust effective FI via the Schur complement to handle IRF/background uncertainty. An adaptive two-stage design procedure selects temporally optimized sampling (maximizing $U(d)=\log \det(F_{\mathrm{eff}})$) and allocates the remaining photons accordingly, with two practical implementations: TCSPC re-binning and programmable time-gating. Simulations and Monte Carlo studies show improved photon efficiency over uniform sampling, robustness to nuisance mismatch, and estimator performance approaching the Cramér–Rao lower bound, enabling hardware-friendly, information-driven FLIM acquisition without modifications. This framework provides a principled path to dose-aware, high-precision FLIM maps in live-cell and tissue applications.

Abstract

We present a Fisher-information (FI) framework for photon-efficient fluorescence lifetime imaging microscopy (FLIM) that treats temporal sampling as a controllable design variable under a fixed photon (dose) budget. Starting from a Poisson photon-counting model for bi-exponential fluorescence decays convolved with a finite instrument response function (IRF) and including additive background, we derive FI for both time-binned TCSPC histograms and programmable time-gated acquisitions. To ensure robustness when nuisance parameters such as IRF width, temporal offset, and background level are uncertain, we compute an effective FI using a Schur-complement marginalization and select hardware-feasible temporal designs by maximizing D-optimal criteria over candidate libraries. Across instrument-agnostic simulations spanning IRF broadening and increasing background fractions, FI-driven temporal designs consistently improve photon efficiency relative to uniform sampling, while nuisance-aware planning yields more stable gains under mismatch than naive optimization. Monte Carlo studies with maximum-likelihood estimation confirm that higher effective FI translates into reduced estimator variance and improved parametric map quality at fixed photon budgets. Finally, we map the same FI core to two practical deployment pathways: adaptive re-binning for TCSPC FLIM and adaptive gate placement/width selection for time-gated FLIM, enabling information-theoretic acquisition without hardware modification.

Figures (6)

• Figure 1: FI-driven adaptive acquisition. A low-dose scout acquisition initializes parameter beliefs, which are used to compute the effective FI for candidate temporal samplings. The next sampling design is chosen by optimizing an information-theoretic utility under constraints, and the remaining photon budget is allocated accordingly.
• Figure 2: CRLB for $a$ vs $a$ under uniform binning and an FI-optimized proxy (early-time--dense). Lower is better.
• Figure 3: RMSE of $a$ vs signal photons $N$ (Monte Carlo). FI-optimized sampling reduces error at fixed $N$.
• Figure 4: Relative degradation of precision under IRF width mismatch. Nuisance-aware planning (effective FI) is more robust than naive planning.
• Figure 5: Phantom validation template: estimated $a$ vs ground truth (synthetic placeholder). Replace with dye-mixture or lifetime-standard phantom data.