E2S UPPA, CNRS, TOTAL, LFCR UMR5150, Universite de Pau et des Pays de l'Adour, Anglet, France.
Institut des Sciences de la Terre d'Orléans, CNRS, Université Orléans, 1A rue de la Férollerie, 45071, Orléans, France.
Eur Phys J E Soft Matter. 2021 Dec 2;44(12):146. doi: 10.1140/epje/s10189-021-00146-2.
The autocorrelation function is a statistical tool that is often combined with dynamic light scattering (DLS) techniques to investigate the dynamical behavior of the scattered light fluctuations in order to measure, for example, the diffusive behavior of transparent particles dispersed in a fluid. An alternative approach to the autocorrelation function for the analysis of DLS data has been proposed decades ago and consists of calculating the autocorrelation function starting from difference of the signal at different times by using the so-called structure function. The structure function approach has been proven to be more robust than the autocorrelation function method in terms of noise and drift rejection. Therefore, the structure function analysis has gained visibility, in particular in combination with imaging techniques such as dynamic shadowgraphy and differential dynamic microscopy. Here, we show how the calculation of the structure function over thousands of images, typical of such techniques, can be accelerated, with the aim of achieving real-time analysis. The acceleration is realized by taking advantage of the Wiener-Khinchin theorem, i.e., by calculating the difference of images through Fourier transform in time. The new algorithm was tested both on CPU and GPU hardware, showing that the acceleration is particularly large in the case of CPU.
自相关函数是一种常用的统计工具，通常与动态光散射（DLS）技术结合使用，以研究散射光波动的动力学行为，例如，测量在流体中分散的透明粒子的扩散行为。几十年来，人们提出了一种替代自相关函数的方法来分析 DLS 数据，该方法包括通过使用所谓的结构函数，从不同时间的信号中计算自相关函数。与自相关函数方法相比，结构函数方法在噪声和漂移抑制方面具有更强的稳健性。因此，结构函数分析在与动态阴影照相术和差动动态显微镜等成像技术相结合的情况下，越来越受到关注。本文展示了如何通过利用维纳-辛钦定理（即通过在时间上进行傅里叶变换计算图像之间的差值），加速数千张图像（这些技术中典型的数量）的结构函数计算，以实现实时分析。该新算法在 CPU 和 GPU 硬件上进行了测试，结果表明在 CPU 情况下，加速效果尤其明显。
