Light Stability Score

• Light Stability Score is a quantitative metric family that aggregates multiple light instability measures into a normalized, interpretable score across various scientific fields.
• It is computed using domain-specific formulas that assess geometric, dynamical, or statistical instabilities, guiding decisions in areas such as black hole stability and topological photonics.
• The score supports applications like quality flagging, device design trade-offs, and benchmarking in real-time instrumentation and computational video analysis.

The Light Stability Score (LSS) is a quantitative metric family used to assess, rank, and compare the stability, consistency, or robustness of light-related phenomena across diverse scientific domains. Variants of the Light Stability Score have been independently introduced in astrophysics, photonics, gravitational physics, and computer vision to unify geometric, dynamical, or statistical diagnostics of light-related stability into a single interpretable figure of merit. The metric takes distinct mathematical forms and empirical protocols depending on the context, but its unifying principle is to condense multiple dimensions of "light stability" into a bounded, dimensionless score to guide design, evaluation, or interpretation.

1. Theoretical Motivation and General Definition

Stability under perturbation or fluctuation is a central concern in photonic device engineering, observational astronomy, gravitational physics, and computational video analysis. A Light Stability Score is devised to:

• Quantify robustness against disorder, noise, or instabilities (e.g., photonic bandstructures, astrophysical backgrounds, photon-trapping geometries).
• Provide a normalized criterion ([0,1] or unbounded) aggregating geometric, temporal, or statistical diagnostics.
• Enable direct ranking, scheduling, quality-flagging, or benchmarking.

Key formal characteristics of all Light Stability Score variants are:

• Aggregation of one or more quantitative instability or fluctuation measures (e.g., Lyapunov exponents, wavepacket breakup times, temporal brightness deviations).
• Normalization for comparability across systems, parameter regimes, or observation conditions.
• Interpretation boundaries for operational or scientific decision-making (e.g., “excellent,” “acceptable,” or “warning” regimes).

2. Light Stability Score in Gravitational Physics

In the context of nonlinear stability of black holes with stable light rings, the Light Stability Score $S_L$ specifically quantifies the resilience of photon-trapping orbits in spherically symmetric metrics under radial perturbations (Guo et al., 2024). The construction is based on the interplay between geometric instability (Lyapunov exponent) and dynamical decay (quasinormal mode damping):

• For a metric $$ds^2 = -N(r) e^{-2\delta(r)} dt^2 + dr^2/N(r) + r^2 d\Omega^2$$, circular photon orbits ("light rings") at $r = r_c$ satisfy $V_{\rm eff}'(r_c) = 0$, with stability set by the sign of $V_{\rm eff}''(r_c)$.
• The Lyapunov exponent $\lambda$ governing geodesic instability is

$$\lambda = \sqrt{-\frac{V_{\rm eff}''(r_c)}{2\,\dot t_c^2}},$$

where $\dot t_c = 1/\sqrt{N(r_c) e^{-2\delta(r_c)}}$.

• The quasinormal decay rate $\gamma = -\operatorname{Im}\omega_0$ emerges from the dominant (linearized) perturbation mode.
• The Light Stability Score is defined as

$S_L = \frac{\gamma}{|\lambda| + \gamma}.$

Here, $S_L \to 1$ signals strong decay (robust stability), $S_L \to 0$ identifies strong instability, and intermediate values denote marginal cases.

A systematic workflow to compute $S_L$ involves:

1. Extracting $N(r), \delta(r)$, and $V_{\rm eff}(r)$ from the metric.
2. Locating light ring radii ($V_{\rm eff}'(r_c) = 0$), evaluating $V_{\rm eff}''(r_c)$.
3. Computing $\lambda$ and numerically extracting $\gamma$ from linearized wave evolution.
4. Scoring using $S_L$ and interpreting the value for stability diagnostics.

This approach enables direct comparison of the trapping stability of black holes or exotic compact objects under scalar perturbations, integrating both local orbit instability and global wave damping.

3. Light Stability Score in Topological Photonics

In topological photonic devices, the Light Stability Score offers a mathematically explicit guide for the design of robust slow-light edge modes in the presence of fabrication disorder (Karcher et al., 2023):

• For a Chern insulator with engineered multiple edge-mode winding (winding number $n$), the subband bandwidth is $\Delta_n \approx \Delta/(2n+1)$, and the bare group velocity is $v_e \sim \Delta_n a / (2\pi)$.
• On-site disorder of strength $w$ induces an energy-dependent group velocity renormalization but not backscattering.
• The wavepacket breakup time (over which a bandwidth-$\delta\epsilon$ pulse remains coherent) is

$$\tau_{\rm break} \sim \frac{(\Delta_n)^3}{w^2\,(\delta\epsilon)^2\,v_e}.$$

• The Light Stability Score is defined as

$$S = \tau_{\rm break} \Delta_n = \frac{(\Delta_n)^4}{w^2\,v_e\,(\delta\epsilon)^2}.$$

This score scales as $n^{-4}$, reflecting quadruple suppression of instability with increased winding.

A high $S$ implies that topologically protected slow-light propagation persists coherently over many optical cycles despite disorder. The score guides trade-offs between fabrication tolerances, desired velocity, and bandwidth in robust on-chip device design.

4. Light Stability Score in Astroparticle Instrumentation

For atmospheric Cherenkov telescopes utilizing silicon photomultipliers (SiPMs), the Light Stability Score is used as a real-time data quality metric quantifying the agreement between empirical night-sky light background models and actual detector operation (Knoetig et al., 2013):

• The local light condition is parameterized as $$LC(Z_\mathrm{m},A) = \cos Z_\mathrm{m} \cdot A^{2.5}$$ where $Z_\mathrm{m}$ is the moon zenith angle and $A$ the illuminated fraction.
• The predicted camera DC current is $I_\mathrm{pred} = \alpha LC + \beta$, compared against measured $I_\mathrm{obs}$.
• With the relative current deviation $$\delta I = (I_\mathrm{obs} - I_\mathrm{pred})/I_\mathrm{pred}$$ and night-to-night gain RMS $\sigma_\mathrm{gain}$, the score is

$$S = 1 - \max\left(|\delta I|, \sigma_\mathrm{gain}\right).$$

• $S$ near 1 indicates excellent observational stability and model fidelity; $S < 0.8$ signals warning or outlier conditions.

By fusing background modeling and hardware stability verification, this Light Stability Score enables automated, reproducible scheduling, quality flagging, and performance benchmarking for long-term monitoring of bright sources under varying night-sky illumination.

5. Light Stability Score in Video Relighting Evaluation

In computational video relighting, the Light Stability Score as defined in "Hi-Light" (Liu et al., 30 Jan 2026) addresses the absence of robust quantitative metrics for perceptual temporal lighting consistency:

• For an $N$-frame video, frames are converted to grayscale and "bright" pixels ($G_t(x,y) \ge T$, with $T = 125$) are selected.
• Three time series are formed:
  • Mean suprathreshold lightness $I_t$,
  • Number of bright pixels $C_t$,
  • First differences $\dot{I}_t = I_{t+1} - I_t$.
• Temporal unsmoothness for each series $s$ is normalized:

$$M^{(s)} = \frac{1}{N_s-1}\sum_{i=1}^{N_s-1}|s_{i+1}-s_i|,\quad R^{(s)} = \max s_i - \min s_i,\quad U^{(s)} = M^{(s)}/R^{(s)}.$$

• The per-signal smoothness score is

$S^{(s)} = \exp(-\lambda_s U^{(s)})$

with empirically tuned $\lambda$.

• The Light Stability Score aggregates the three:

$$\mathrm{LSS} = \frac{1}{3}[S^{(I)} + S^{(C)} + S^{(\dot{I})}]$$

bounded in $[0,1]$.

Empirically, LSS correlates perfectly (rank coefficient $\rho=1.0$) with human judgment of flicker, and demonstrates stability to hyperparameter variation. Methodological ablations confirm the utility of its three-signal structure and exponential normalization. LSS provides a full-reference, interpretable, and application-specific benchmark for evaluating relighting consistency in video synthesis.

6. Comparative Overview and Interpretability

A summary table of Light Stability Score instantiations and their operational meanings is as follows:

Physical System	Mathematical Form	Interpreted Stability Regime
Black hole light rings (Guo et al., 2024)	$S_L = \frac{\gamma}{|\lambda|+\gamma}$	1: strongly stable, 0: unstable
Chern edge slow light (Karcher et al., 2023)	$$S = \frac{(\Delta_n)^4}{w^2 v_e (\delta\epsilon)^2}$$	High: coherent, Low: fragile
FACT SiPM camera (Knoetig et al., 2013)	$S = 1-\max(|\delta I|, \sigma_\mathrm{gain})$	1: excellent, <0.8: warning
Video relighting (Liu et al., 30 Jan 2026)	$\mathrm{LSS} = \frac{1}{3}\sum S^{(s)}$ (see above)	1: smooth, 0: severe flicker

Each variant aggregates contextually relevant measures to operationalize a physically and/or perceptually meaningful light stability metric, tailored to the system's governing equations, observational constraints, or perceptual criteria.

7. Limitations and Prospective Extensions

All Light Stability Score formulations feature domain-specific choices in variable selection, normalization, and aggregation schema. Typical limitations include:

• Dependence on empirical or hand-chosen thresholds or normalization parameters.
• System-specific interpretation of score boundaries; "stable" in one context may not map directly to another.
• Potential insensitivity to instability modes not explicitly targeted (e.g., dark-region flicker in video, as noted in (Liu et al., 30 Jan 2026)).
• For physical systems, geometric-only or dynamical-only measures may miss coupled instabilities.

Proposed extensions include learning-based tuning of thresholds, incorporating deep spatiotemporal models for no-reference scoring, and expanding to multi-channel or semantic region based diagnostics.

A plausible implication is that the Light Stability Score, as a quantitative tool, will see continued adaptation and unification across experimental and theoretical subfields as the requirements for interpretable, operational stability metrics increase. Its rigorous, bounded, and algebraically concise nature makes it an attractive standard for both physical and computational disciplines.