荧光介质内滤光效应时空通量演化的解析马尔可夫链
Analytical Markov Chain for Spatiotemporal Flux Evolution of the Inner Filter Effect in Fluorescent Media
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中文总结 AI 辅助
研究多组分荧光介质内滤光效应的光谱扭曲问题，提出基于时空解耦的解析马尔可夫传输模型，降低计算复杂度，能评估瞬态衰减时间光谱、预测稳态波长光谱畸变，与MC模拟匹配，可加速参数筛选等。
中文摘要 AI 辅助
在多组分荧光介质中表征发射和衰减时间光谱对于识别材料固有特性和优化探测器至关重要。然而，二次内滤光效应（IFE）引起的波长演化会扭曲这些可观测光谱。蒙特卡罗（MC）光线追踪虽能模拟这种扭曲，但积累足够的跟踪统计数据需很长计算时间，阻碍了高维空间中的参数优化。本文提出一种基于时空解耦的解析马尔可夫传输模型。通过拉普拉斯变换将连续域上的多重嵌套卷积积分转换为离散马尔可夫转移矩阵，将计算复杂度从与波长 bins $N_{\lambda}$ 和级联阶数 $n$ 相关的指数规模 $\mathcal{O}(N_{\lambda}^n)$ 降至线性规模 $\mathcal{O}(N_{\lambda} + n)$。所得代数解将瞬态衰减时间光谱评估为伽马波包的连续叠加，并预测IFE在亚秒时间尺度内驱动的稳态波长光谱畸变。在正交和正面光谱仪配置上的验证表明，计算光谱与MC模拟的线形匹配。该模型可作为快速前向引擎，加速参数空间筛选，提供早期探测器设计参考，并作为事件顶点重建算法的物理约束输入。
英文摘要
Characterizing emission and decay time spectra in multi-component fluorescent media is essential for identifying intrinsic material properties and optimizing detectors. However, wavelength evolution from the secondary inner filter effect (IFE) distorts these observable spectra. While Monte Carlo (MC) ray-tracing can simulate this distortion, accumulating adequate tracking statistics requires long computation times, which hinders parameter optimization within high-dimensional spaces. This paper presents an analytical Markovian transport model based on spatiotemporal decoupling. A Laplace transform converts the multi-nested convolution integrals over continuous domains into a discrete Markov transition matrix, reducing the computational complexity from an exponential scale with respect to wavelength bins $N_λ$ and cascade order $n$, $\mathcal{O}(N_λ^n)$, to a linear scale, $\mathcal{O}(N_λ + n)$. The resulting algebraic solutions evaluate transient decay time spectra as a continuum superposition of Gamma wave packets and predict steady-state wavelength spectrum distortions driven by the IFE within a sub-second timescale. Validations across orthogonal and front-face spectrometer configurations show that the calculated spectra match MC simulations in lineshape. This model can serve as a fast forward engine to accelerate parameter space screening, provide early-stage detector design references, and act as a physics-constrained input for event vertex reconstruction algorithms.
