Particle size analysis is crucial across many fields, with light scattering techniques offering a relatively easy and precise method for optical characterization. Laser diffraction (LD) is a common technique, using a laser beam to illuminate a particle suspension and measuring the angle-dependent scattered light to infer particle size distribution. While precise, commercial LD particle size analyzers (PSAs) are large, complex, expensive (50-200k€), and require trained personnel and maintenance, limiting their use in online industrial applications. These limitations stem from the need for a large distance between the sample and detectors for angular resolution, the use of expensive lasers and numerous detectors, and the reliance on single scattering approximations which are inaccurate for concentrated suspensions. Multiple scattering corrections are complex and time consuming. Alternative techniques like dynamic light scattering (DLS) and nanoparticle tracking analysis (NTA) are suitable for submicron particles but have their own limitations. DLS is low resolution and unsuitable for polydisperse samples, while NTA, though overcoming some DLS limitations, still focuses on individual particles. This paper proposes a novel, miniaturized PSA addressing these limitations using a CMOS image sensor and machine learning to analyze the angular distribution of scattered light, similar to LD, but overcoming its size, cost, and concentration limitations.

Existing particle size analysis methods based on light scattering include laser diffraction (LD), dynamic light scattering (DLS), and nanoparticle tracking analysis (NTA). LD PSAs are widely used but are bulky, expensive and limited to dilute suspensions due to the single-scattering approximation used in analysis. DLS is suitable for submicron particles but has limitations with polydisperse samples. NTA overcomes some limitations of DLS but still focuses on individual particles. Lens-free imaging systems using CMOS sensors have been explored for direct particle imaging, but these typically analyze individual particle holograms or diffraction patterns rather than the angular distribution of scattered light from an ensemble of particles. The use of machine learning in overcoming the multiple scattering effects in concentrated suspensions has been previously shown to be effective.

The core innovation is a small form factor angular spatial filter (ASF), a 5 mm diameter, 17 mm long polymer rod with an array of holes of varying diameters. The cut-off angle (θe) for each hole is determined by its diameter (D) and length (L): θe = arctan(D/L). The ASF collects scattered light up to predefined θe values, enabling reconstruction of the cumulative angular scattering profile. This design, created using a polymer extrusion technique, offers high flexibility in design and overcomes challenges of other fabrication methods (3D printing, photolithography, micro-machining) for achieving high L/D ratios required for measuring larger particles. The PSA uses a collimated red LED (632.8 nm) to illuminate the sample, with the scattered light collected by the ASF and a CMOS image sensor array. The ASF was designed with 23 holes (112-800 µm diameter), allowing measurement of scattering angles from 0.29° to 2.02° in water (after correcting for refraction at the flow cell wall). To address multiple scattering effects at high concentrations, one side of the ASF is polished, creating a large aperture to collect the full angular spectrum. The inner walls are coated with black acrylic paint to minimize reflection and crosstalk. Data analysis was performed using MATLAB and Python, with a random forest algorithm used for particle size prediction. Measurements were conducted on glass beads of various sizes (13-150 µm) and concentrations (1-40 mg/ml), with the highest concentration for the smallest particles being limited to 10 mg/ml due to signal-to-noise ratio concerns.

The proposed ultra-compact PSA, based on the novel ASF and a random forest algorithm, effectively predicts particle size in suspensions. Experiments with glass beads of varying sizes and concentrations demonstrated the device's capability to correct for multiple scattering effects. Mean absolute percentage errors (MAPE) in particle size prediction were 5.09% without concentration as an input parameter and 2.5% with concentration as an input parameter. When only spherical particles were considered, the MAPE without concentration as an input reduced significantly to 0.72%. The device’s compact size (on the order of ten centimeters) and low cost, stemming from the use of readily available consumer electronics, represent a significant advancement over existing commercial systems. The ability to work effectively with high concentrations eliminates the need for sample dilution and simplifies the measurement process.

The results demonstrate that the proposed PSA successfully addresses the limitations of existing commercial LD PSAs. The use of a compact ASF and a machine learning algorithm allows for accurate particle size prediction even in high-concentration suspensions, avoiding the need for complex multiple scattering correction models. The device’s small size and low cost open up new possibilities for online and in-line industrial process monitoring, where traditional PSAs are impractical. The accuracy achieved, especially when considering only spherical particles, suggests that the method could be refined further with more advanced machine learning models and potentially tailored to specific particle shapes and materials. The device’s performance could be further improved by using more sensitive image sensor arrays for smaller particles, where signal-to-noise ratio becomes a significant factor.

This work presents a novel, ultra-compact particle size analyzer that overcomes the limitations of existing commercial systems. The use of a miniature angular spatial filter, a CMOS image sensor, and machine learning enables accurate particle size prediction in a cost-effective and compact device. The results show promising accuracy in various concentration ranges and pave the way for in-situ applications in various industries. Future work could focus on further optimization of the machine learning model, exploring the use of more sensitive image sensors, and expanding the device's capabilities to accommodate broader ranges of particle sizes and shapes.

While the proposed PSA shows promising results, some limitations exist. The current design's accuracy is somewhat dependent on the sphericity of the particles, with accuracy decreasing for non-spherical particles. The highest measurable concentration for smaller particles is limited by the signal-to-noise ratio. Further improvements in the sensitivity of the CMOS sensor could expand this range. Also, the current ASF design is optimized for a specific size range; the design would need modification for measurement of particles outside this range.