An ultra-compact particle size analyser using a CMOS image sensor and machine learning

The study addresses the need for compact, low-cost, and robust particle size analyzers (PSAs) capable of operating in industrial environments and at higher concentrations than traditional laser diffraction (LD) systems. Conventional techniques such as dynamic light scattering (DLS) and nanoparticle tracking analysis (NTA) are effective for submicron particles but have limitations with polydispersity and the influence of large particles. LD PSAs are widely used for particles from hundreds of nanometres to millimetres but are typically large, complex, expensive, and often restricted to dilute suspensions due to reliance on single-scattering models; multiple scattering at higher concentrations leads to size underestimation. Existing multiple scattering correction algorithms are computationally intensive and not ideal for online use. The authors propose a novel PSA that leverages a CMOS image sensor, an LED source, and a compact angular spatial filter (ASF) to capture angle-resolved cumulative scattering signals, combined with a machine learning (random forest) model to predict particle size, aiming to overcome size, cost, and multiple-scattering limitations of traditional LD instruments.

The paper reviews key optical particle sizing methods: DLS, which derives hydrodynamic size from Brownian motion but struggles with polydisperse samples and sensitivity to large particles; NTA, which tracks individual particles to estimate size from diffusion and mitigates some DLS limitations. LD PSAs are highlighted as the predominant method for larger particles, using forward scattering patterns interpreted via Fraunhofer or Mie theory (requiring refractive indices), but they are large, costly, and typically limited to dilute suspensions due to single-scattering assumptions. Multiple scattering in concentrated systems causes apparent angle increases and size underestimation; while correction algorithms exist, they are complex and slow for online deployment. Machine learning has been shown to predict particle size from angular scattering and concentration data even at high concentrations, suggesting a path to bypass explicit optical models and complex corrections while enabling industrial, online applications.

Core concept: Introduce an angular spatial filter (ASF) comprising an array of apertures (holes) with different diameters D and a common length L that act as low-pass angular filters with cut-off angle θc = arctan(D/L). The ASF, paired with a CMOS image sensor, measures cumulative forward-scattered light up to discrete θc values, enabling reconstruction of the cumulative angular scattering profile. Detected angles are corrected for refraction through the flow cell using Snell’s law (accounting for water’s refractive index), mapping ASF-defined angles in air to effective scattering angles in the sample medium. The ASF is designed so that smaller θc (larger L/D) captures scattering from larger particles that scatter at smaller angles. Fabrication: The ASF was fabricated from PMMA using a drill-and-draw (polymer extrusion) technique inspired by micro-structured polymer optical fibers. A PMMA rod was machined to a 60 mm diameter, holes were drilled with desired patterns, the preform was annealed at 80 °C for a week, and then drawn to canes of 5 mm diameter and 50 mm length. The final ASF used has 23 holes with diameters from 112 to 800 µm and length L = 17 mm, yielding cut-off angles in air from approximately 0.38° to 2.7°; after refraction correction in water, the effective range is about 0.29° to 2.02°, suitable (per Mie theory) for particles ~10–125 µm. The inner walls were coated with black acrylic paint to increase absorption and reduce reflections and crosstalk. One side was polished along the length to create a large-aperture channel permitting collection of the full forward-scattered angular spectrum, aiding analysis of multiple scattering at high concentrations. Residual reflection and diffraction in holes were observed but did not impede angular discrimination; diffraction can be reduced by scaling D and L proportionally. Instrument design: A fiber-coupled red LED (λ ≈ 632.8 nm) was collimated to a ~10 mm beam to illuminate particles suspended in water within a flow cell. The ASF, mounted in a holder directly on a CMOS image sensor, collected both scattered and unscattered light; the CMOS captured raw images containing discrete bright regions corresponding to ASF apertures. Data acquisition used the CMOS sensor array; data processing and analysis were performed in MATLAB and Python. Measurement protocol and samples: Glass bead suspensions with known size distributions (e.g., commercial samples spanning ~13–150 µm) were measured across concentrations from 1 to 40 mg ml⁻¹, with the smallest size range limited to ≤10 mg ml⁻¹ due to signal constraints. Before each measurement, 200 ml of water was circulated through the flow cell and five images were acquired separated by 20–60 s. Raw ASF images provided cumulative angular scattering intensities up to each aperture’s θc. Machine learning: A random forest model was trained on features extracted from the raw ASF images (angularly cumulative scattering intensities) to predict the volume median diameter (D50) of the particle population. The model optionally included concentration as an input to account for multiple scattering, enabling correction of concentration-dependent broadening of the scattering lobe.

- The proposed PSA, using a compact ASF with a CMOS image sensor and LED illumination, accurately predicts particle size from angularly cumulative scattering images via a random forest model. - Validated on glass beads (≈13–125 µm) at various concentrations, achieving mean absolute percentage errors (MAPE) of 5.09% without concentration input and 2.5% when including concentration as a feature. - For datasets restricted to spherical particles, the MAPE without concentration input decreased to 0.72%. - The device demonstrates robustness to multiple scattering at higher concentrations, with the ML approach compensating for concentration-induced broadening of scattering lobes. - The ASF design (5 mm diameter, 17 mm long, 23 apertures) enables discrete angle selection (effective ~0.29–2.02° in water), covering ~10–125 µm particle sizes using cumulative power measurements rather than many discrete detectors. - The prototype exhibits a compact form factor (on the order of ten cm) and uses low-cost consumer electronics, indicating potential for online and in-line industrial monitoring beyond the laboratory.

The findings demonstrate that the ASF-based PSA can address key limitations of conventional LD instruments by drastically reducing system size and component count while maintaining accurate sizing across relevant industrial particle ranges. By encoding angular scattering information into cumulative measurements across a small number of apertures and leveraging machine learning, the approach bypasses the need for explicit optical inverse models and complex multiple-scattering corrections. Including concentration as a model feature significantly improves accuracy, evidencing that the ML model captures concentration-dependent multiple scattering effects. The compact ASF and CMOS-based acquisition enable cost-effective deployment and potential multi-point monitoring in processing environments. The strong performance on spherical glass beads suggests high reliability for well-defined particle systems, and the device retains utility across broader particle types, with accuracy that remains competitive when concentration is accounted for.

The study presents a novel, ultra-compact, and low-cost particle size analyzer that combines an angular spatial filter, a CMOS image sensor, and machine learning to estimate particle size from cumulative angle-resolved scattering. The instrument accurately measured glass bead suspensions (~13–125 µm) and achieved low prediction errors, particularly when concentration information or purely spherical particles were considered. The approach effectively mitigates multiple scattering concerns that limit traditional LD PSAs in concentrated suspensions. Given its small footprint and use of consumer components, the analyzer is well-suited for online and in-line industrial monitoring. Future work may extend the size range and sensitivity—e.g., employing more sensitive image sensors such as single-photon cameras to improve performance for sub-10 µm particles—and further optimize ASF designs for different application ranges.

- Sensitivity limits for small particles: Below ~10 µm, the scattering signal becomes weak relative to noise with the current CMOS sensor, limiting SNR and requiring longer integration times; more sensitive sensors (e.g., single-photon cameras) may be needed. - Concentration constraints: For the smallest size range (13–20 µm), reliable measurements were limited to ≤10 mg ml⁻¹ due to low intensity at higher concentrations with current settings. - ASF non-idealities: Residual reflections and diffraction within ASF holes were observed; Eq. (1) assumes no reflections and square-like filtering and neglects diffraction, introducing deviations from ideal behavior, though angular discrimination was preserved. - Angle correction necessity: Refraction at flow cell interfaces requires angle correction (Snell’s law), adding calibration complexity. - Generalizability: Validation focused on glass bead suspensions; while spherical particle performance is excellent, performance on diverse shapes and materials may vary and requires further validation.