Ericok Ozan Burak, Cemgil Ali Taylan, Erturk Hakan
J Opt Soc Am A Opt Image Sci Vis. 2018 Jan 1;35(1):88-97. doi: 10.1364/JOSAA.35.000088.
Characterization of nanoparticle aggregates from observed scattered light leads to a highly complex inverse problem. Even the forward model is so complex that it prohibits the use of classical likelihood-based inference methods. In this study, we compare four so-called likelihood-free methods based on approximate Bayesian computation (ABC) that requires only numeric simulation of the forward model without the need of evaluating a likelihood. In particular, rejection, Markov chain Monte Carlo, population Monte Carlo, and adaptive population Monte Carlo (APMC) are compared in terms of accuracy. In the current model, we assume that the nanoparticle aggregates are mutually well separated and made up of particles of same size. Filippov's particle-cluster algorithm is used to generate aggregates, and discrete dipole approximation is used to estimate scattering behavior. It is found that the APMC algorithm is superior to others in terms of time and acceptance rates, although all algorithms produce similar posterior distributions. Using ABC techniques and utilizing unpolarized light experiments at 266 nm wavelength, characterization of soot aggregates is performed with less than 2 nm deviation in nanoparticle radius and 3-4 deviation in number of nanoparticles forming the monodisperse aggregates. Promising results are also observed for the polydisperse aggregate with log-normal particle size distribution.
根据观测到的散射光对纳米颗粒聚集体进行表征会导致一个高度复杂的反问题。即使正向模型也非常复杂，以至于无法使用基于经典似然的推理方法。在本研究中，我们比较了四种基于近似贝叶斯计算（ABC）的所谓无似然方法，这些方法仅需要正向模型的数值模拟，而无需评估似然。具体而言，对拒绝抽样、马尔可夫链蒙特卡罗、群体蒙特卡罗和自适应群体蒙特卡罗（APMC）在准确性方面进行了比较。在当前模型中，我们假设纳米颗粒聚集体相互之间分隔良好，且由相同大小的颗粒组成。使用菲利波夫粒子聚类算法生成聚集体，并使用离散偶极近似来估计散射行为。结果发现，尽管所有算法产生的后验分布相似，但APMC算法在时间和接受率方面优于其他算法。利用ABC技术并在266纳米波长下进行非偏振光实验，对烟灰聚集体进行表征，纳米颗粒半径偏差小于2纳米，形成单分散聚集体的纳米颗粒数量偏差为3 - 4 。对于具有对数正态粒度分布的多分散聚集体也观察到了有前景的结果。
