# AI-Enabled Compact and Efficient Dynamic Light Scattering System for Precise Microparticle Sizing
## 3 Results and Discussion
Figure 2 presents the SEM images of PS spheres with sizes of 200 nm, 400 nm, 600 nm, 900 nm, 1100 nm, and 1400 nm, alongside their corresponding raw scattering intensity signals (blue curve), the smoothed signals after applying Kalman filtering [29] (red curve), and the ACFs of the filtered signals (green curve). Theoretically, the signal should be continuous and free of any interruptions. However, in practical applications, limitations inherent to the acquisition card can lead to step-like distortions in the signal, as shown in the figure. This is a well-recognized issue and represents one of the challenges associated with using low-cost instruments. The raw scattering intensity signals are significantly contaminated by noise due to the low-cost and simple configuration, posing a substantial challenge for subsequent signal processing. As can be seen from the figure, our ACF curve has relatively small differences and does not follow the rule that the larger the particle size, the slower the decay. It is difficult to obtain accurate particle sizes using traditional formula methods. At this point, Kalman filtering technology was used to perform denoising preprocessing on these signals. Subsequently, the ACF was computed from the denoised signals. However, even after the application of Kalman filtering, the persistence of noise was evident, resulting in ACF functions that deviated from the expected exponential decay trend, exhibiting fluctuations. These fluctuations are attributed to the cumulative effect of various instrumental noise sources, which distort the autocorrelation function to such an extent that it becomes infeasible to accurately retrieve the particle size distribution. Furthermore, Supplementary Information Figure S1 provides additional SEM images and the ACFs of processed scattering intensity signals for other sizes, all of which similarly exhibit fluctuations that prevent accurate determination of particle size distributions. In the aforementioned scenario, where the low-cost and simple instrumentation's precision was insufficient, significant noise interference arose, making it challenging to obtain accurate particle size measurements using conventional methods based on the Stokes-Einstein equation [30]. To address this issue, the potential of AI was explored for measuring particle size amidst the substantial noise introduced by the instrument. The model structures of several explored DL models are shown in Figure 3. A DNN model was designed with an input layer [31], three hidden layers, and an output layer (Figure 3a). The input layer accepts a 1 \(\times\) 200 input vector. The first hidden layer comprises 30,000 neurons, followed by the second hidden layer with 18,000 neurons, and the third hidden layer with 10,000 neurons. The output layer contains a single neuron, providing the regression result. Figure 3b shows a 1D-CNN model, leveraging its inherent advantages in processing time-series data [32], which accepts a 1D ACF signal of size 1 \(\times\) 20,000 as input [33]. The model, constructed using the Keras library [34], consists of two sequential convolutional layers with 32 and 64 filters, respectively, both employing a kernel size of 3 and ReLU activation functions. Following each convolutional layer, max-pooling layers with a pool size of 2 are utilized to reduce dimensionality. Subsequently, a flattening operation transforms the pooled features into a 1D vector, which is then processed by a dense layer comprising 256 neurons with ReLU activation. The output layer consists of a single neuron with a linear activation function, specifically designed for the regression task of predicting particle size [35]. Figure 2: SEM image, raw scattering intensity signals (blue curve), the smoothed signals after applying Kalman filtering (red curve), and the ACFs (the number of lags is 1 ms) of the filtered signals (green curve) for the PS spheres with the diameters of (**a**) 200 nm, (**b**) 400 nm, (**c**) 600 nm, (**d**) 900 nm, (**e**) 1100 nm, and (**f**) 1400 nm.