The optical setup employs a 1,550 nm single-mode distributed feedback (DFB) laser diode (ThorLabs-L1550P5DFB) equipped with a package-integrated monitoring photodiode. To ensure sufficient power and signal enhancement during particle passage, the laser beam is focused using a doublet lens (AC254-030-C), achieving a measured spot diameter of 80 μm at its waist with an initial power of 4.7 mW. The propagation axis of the laser is set at an angle of 80 ° relative to the channel flow. The laser is mounted on a 3-axis linear stage (ZaberTech T-LSM050A) to allow precise micrometer-scale alignment. The SMI signal is acquired by monitoring variations in the photodiode current using a custom-made transimpedance amplifier and recorded at a sampling rate of 2 MHz using an acquisition card (DAQ NI-6361).

To achieve single-particle alignment and ensure a constant flow of individual particles through the laser sensing volume, a custom-made PDMS microfluidic chip was fabricated, specifically designed to perform hydrodynamic focusing (HF) for particle alignment. The channel structure was created using photolithography, and its dimensions were verified using a profilometer, confirming a consistent height of 70 µm and a width of 80 µm. For particle isolation via HF, the flow rates are set at 5 μL/min for the sheath flow and 10 μL/min for the sample flow. The velocity profile inside the chip was estimated through simulations in COMSOL to determine the range of particle speeds within the chip. To verify the correct operation of the HF system, the microfluidic chip is mounted on an inverted microscope, allowing real-time monitoring of the channel and flow using a high-speed camera.

Inspired to simulate human blood cells for flow cytometry experiments, synthetic 2, 4, and 10 µm monodisperse polystyrene particles are used, each with a coefficient of variation of 1.8% in its diameter. For each particle size, a 4% concentration was prepared in 1 mL of deionized water (DI) and introduced into the channels using a microfluidic control system (Fluigent MFCS-EZ) equipped with multiple flow rate sensors (Fluigent Flow Unit M+) with a precision of ± 0.2 mL/min, allowing precise adjustment of the flow rate during experiments.

To construct a robust database containing the induced modulation caused by particle transit, all potential particle events were recorded in real-time using a Python-based acquisition routine. The collected signals were then analyzed to segment the time intervals corresponding to each particle’s passage for further analysis. Additionally, to increase the size of the dataset and improve model generalization, multiple augmentation techniques were applied.

The data acquisition system (DAQ) was configured with a sampling frequency of 2 MHz, chosen to cover the expected Doppler frequency peaks range while retaining higher-order harmonics and transient components, and to provide a comprehensive dataset for both algorithm development and later decimation analysis. Each acquisition window captured 8.192 ms (16,384 samples) to ensure full coverage of the slowest particle transits while limiting unrelated signal content. A real-valued FFT of the full segment with a rectangular window was applied to identify the characteristic Doppler peaks. This configuration balanced detection reliability, computational efficiency, and preservation of amplitude information in low-SNR conditions (Rapuano and Harris, 2008). To define a broad frequency range of interest, the expected particle velocity was estimated through numerical simulations. Based on Equation 1, a detection range from 5 kHz to 100 kHz was established, broad enough to avoid missing Doppler peaks outside the expected range while still allowing effective filtering of irrelevant frequencies. A threshold level for peak detection was determined experimentally by analyzing the noise level when only deionized (DI) water was flowing. Segments that met the detection criteria were stored for further processing.

Following the approach described in Sierra-Alarcón et al. (2024), an offline adaptive spectrogram algorithm was employed to extract only the signal segments corresponding to particle transits. For each detected event, the spectrogram parameters were adjusted based on the estimated particle velocity and transit duration. A Gaussian fit was then applied to verify whether the observed modulation matched the expected signal shape defined in Equation 3.

To support this validation, the signal-to-noise ratio (SNR) was evaluated using Equation 7, providing initial evidence that the signal amplitude decreases as particle size decreases (Figure 5). The SNR was estimated by comparing the average power of segments containing particle-induced modulation, x p ( t ) , with those containing only noise signal, x np ( t ) .

The final dataset included 700 labeled samples for each particle size (2, 4, and 10 µm), with each sample spanning 1.25 ms (2,500 data points), capturing the complete transit event while excluding irrelevant portions of the signal. P signal = 1 N ∑ i = 1 N x p i 2 (5) P noise = 1 N ∑ i = 1 N x np i 2 (6) S N R d B = 10 ⋅ log 10 P signal − P noise P noise (7)

A combination of the following data augmentation techniques was randomly applied to represent possible variation in the real raw signals while preserving the essential characteristics of the modulations.

• Additive Noise: Gaussian noise is added to the signal to reduce the SNR in each sample. The noisy signal is given by Equation 8:

To reduce signal dimensionality and suppress embedded noise, all samples were processed using a band-pass filter based on the previously defined frequency ranges. A decimation step was then applied, reducing the sampling rate by a factor of 4, to 500 kHz. This reduction aimed to decrease data size without significantly altering the signal characteristics. Additionally, the filtered signals were scaled by a factor of 10, selected after testing different values (1, 5, 10, 20) for its ability to accelerate convergence by increasing gradient magnitudes, without affecting classification accuracy or altering the relative shape of the signals (LeCun et al., 2012). This formatted signal was then used for the next data representation approaches.

Time-domain spectral analysis is essential for capturing the dynamic behavior of non-stationary signals by revealing how their frequency content evolves over time. Spectrograms were employed due to their effectiveness in detecting transient events and frequency variations. The spectrogram is computed using the Short-Time Fourier Transform (STFT), as defined in Equation 14 S t , f = ∫ − ∞ ∞ x τ w τ − t e − j 2 π f τ d τ (14) where x ( τ ) represents the signal, w ( τ − t ) is the Hamming window centered at time t , and f is the frequency. The computation of S ( f , t ) involves three key parameters: N perseg , which defines the length of the window function w [ n − τ ] ; N overlap , which specifies the overlap between consecutive windows (typically set to half of N perseg to ensure effective detection of transient events); and F range , which determines the frequency range under consideration. The selection of spectrogram parameters was guided by the Doppler frequency range of detected peaks in real particle samples, refining the analysis to focus specifically on the Doppler frequency component and its decay over time (5–40 kHz). This was done while considering the passage duration of the smallest, fastest particles in the dataset. The frequency resolution is given by Equation 15: Δ f = f s N perseg (15) where f s = 500  kHz is the sampling rate. To achieve a target frequency resolution of 1 kHz, the required window length is N perseg = 500 samples. This corresponds to a temporal resolution of approximately 1 ms.

This configuration ensures that short-duration events, such as those caused by 2 μ m particles lasting approximately 1.6 ms, remain visible while preserving spectral integrity.

The choice of spectrograms over alternative representations, such as Mel-Frequency Cepstral Coefficients (MFCCs), was based on their ability to preserve raw time-frequency relationships (Zhao K. et al., 2020; Gourisaria et al., 2024). While MFCCs are effective for auditory perception tasks, they involve dimensionality reduction and feature decorrelation, which can lead to information loss and increased noise sensitivity in non-speech signals. In contrast, spectrograms provide a richer representation, facilitating the extraction of meaningful patterns while maintaining correlated spectral features.

To extract valuable information from both the temporal and frequency domains and to improve differentiation where particle modulation is embedded in noise, the following features were defined:

• Signal Amplitude: The amplitude of the temporal signal correlates with particle size, as larger particles induce higher voltage variations. To ensure robustness against noise-induced peaks, the amplitude is extracted using the envelope of the absolute signal. The envelope is computed using the Hilbert transform (Zhao et al., 2019), providing a smooth upper bound that mitigates the impact of noise peaks.

To qualitatively assess the discriminative capacity of the extracted features, a t-SNE (t-distributed Stochastic Neighbor Embedding) projection was applied to both the handcrafted and spectrogram-based feature sets. This dimensionality reduction technique maps high-dimensional data into a two-dimensional space while preserving local structure, allowing for visual inspection of class separability and the clustering behavior of the features (Maaten and Hinton, 2008). Figure 7 presents the resulting t-SNE plots, where each point corresponds to a sample, and colors indicate particle size classes. The resulting spatial distribution suggests that the extracted features contain sufficient information to support particle size classification.

This model processes spectrograms resized to dimensions 63 × 65 × 1 , which are then passed through a fully connected neural network. The architecture includes a Flatten layer, followed by two dense layers, each using ReLU activation, batch normalization, and L2 regularization with a coefficient λ = 2.5 × 1 0 − 4 to improve generalization (Yang and Shami, 2020; Agrawal, 2021). Dropout is applied after each dense layer to prevent overfitting. The output layer consists of three neurons with softmax activation, corresponding to the three particle size classes. Training was conducted using a batch size of 32 and the Adam optimizer with a learning rate decay initialized at 6 × 1 0 − 4 , using categorical cross-entropy as the loss function. Early stopping was implemented to further reduce overfitting by monitoring validation loss.

All model hyperparameters were optimized via grid search. This included the STFT parameter nperseg = 2 n , with n ∈ [ 7,9 ] , dropout rates p dropout ∈ [ 0.1 , 0.2 ] , and dense layer sizes dense1, dense2 = 2 n , with n ∈ [ 3,8 ] . The optimal configuration, which also reflects the most effective spectrogram resolution, was found to be dense1 = 64, dense2 = 8, p dropout = 0.1 , and nperseg = 128 . This configuration achieved a test accuracy of 97.7% and a validation accuracy of 98.6%.

Following a similar topology to the spectrogram-based model, this version replaces the spectrogram inputs with engineered statistical and frequency-domain features, which are normalized using Z-score scaling. The training methodology remains unchanged, with the L2 regularization coefficient adjusted to λ = 1 × 1 0 − 4 . Hyperparameter tuning explored dense layer sizes defined as dense 1 , dense 2 = 2 n , with n ∈ [ 5,6,7,8,9 ] , and dropout rates p dropout ∈ [ 0.1 , 0.2 ] .

The best configuration was achieved with dense 1 = 128 , dense 2 = 256 , and p dropout = 0.1 . This feature-based model achieved a test accuracy of 97.0% and a validation accuracy of 97.8%.

The 1D Convolutional Neural Network (CNN) model was developed for temporal signal classification, following the band-pass filtering and decimation steps and employing a hierarchical feature extraction strategy. The architecture is composed of three convolutional layers with an increasing number of filters 2 n with n ∈ [ 6 − 8 ] and a kernel size of 5. Each layer uses ReLU activation to capture temporal patterns within the waveform. Batch normalization is applied after each convolutional layer to stabilize the training process, followed by MaxPooling1D (pool size = 2) to reduce dimensionality while preserving relevant temporal features. To prevent overfitting, a dropout rate of p dropout = 0.2 is applied after each pooling layer.

The extracted features were then flattened and passed through a fully connected dense layer with 256 neurons and L2 regularization ( λ = 1 × 1 0 − 4 ) , before reaching the softmax output layer with three neurons corresponding to the particle size classes. The model is trained using the Adam optimizer with a learning rate of 6 × 1 0 − 4 , employing categorical cross-entropy loss. All hyperparameters were tuned via grid search. This CNN model achieved a test accuracy of 98.9% and a validation accuracy of 98.3%.