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.
Differential Dynamic Microscopy (DDM) is the combination of optical microscopy to statistical analysis to obtain information about the dynamical behaviour of a variety of samples spanning from soft matter physics to biology. In DDM, the dynamical evolution of the samples is investigated separately at different length scales and extracted from a set of images recorded at different times. A specific result of interest is the structure function that can be computed via spatial Fourier transforms and differences of signals. In this work, we present an algorithm to efficiently process a set of images according to the DDM analysis scheme. We bench-marked the new approach against the state-of-the-art algorithm reported in previous work. The new implementation computes the DDM analysis faster, thanks to an additional Fourier transform in time instead of performing differences of signals. This allows obtaining very fast analysis also in CPU based machine. In order to test the new code, we performed the DDM analysis over sets of more than 1000 images with and without the help of GPU hardware acceleration. As an example, for images of 512 × 512 pixels, the new algorithm is 10 times faster than the previous GPU code. Without GPU hardware acceleration and for the same set of images, we found that the new algorithm is 300 faster than the old one both running only on the CPU.
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