🔬 applied physics

Determination of Nanoparticle and Microdroplet Parameters in Levitating Microdroplets of Suspension by Speckle Image Analysis Using Convolutional Neural Networks

This study demonstrates that convolutional neural networks can effectively analyze laser speckle images from levitating microdroplets to simultaneously determine droplet diameter, nanoparticle concentration, and nanoparticle size, offering a viable data-driven approach for multi-parameter optical diagnostics of suspension systems.

Original authors: Yaroslav Shopa, Kwasi Nyandey, Daniel Jakubczyk

Published 2026-04-09

📖 5 min read🧠 Deep dive

CC BY 4.0

Original authors: Yaroslav Shopa, Kwasi Nyandey, Daniel Jakubczyk

Original paper licensed under CC BY 4.0 (http://creativecommons.org/licenses/by/4.0/). ✨ This is an AI-generated explanation of the paper below. It is not written or endorsed by the authors. For technical accuracy, refer to the original paper. Read full disclaimer

The Big Idea: Reading the "Fingerprint" of a Floating Drop

Imagine you have a tiny, floating drop of liquid (like a microscopic raindrop) suspended in mid-air. Inside this drop, there are thousands of tiny particles, like dust or nanoparticles.

The scientists in this paper wanted to answer a tricky question: Can we look at the pattern of light bouncing off this drop and figure out exactly what's inside it?

Specifically, they wanted to know three things just by looking at the light:

How big is the drop?
How many particles are inside? (Concentration)
How big are the particles? (Size)

The Problem: The "Static" Noise

Usually, when light hits a rough surface or a messy mixture, it creates a chaotic, grainy pattern called laser speckle. Think of it like the static on an old TV or the glittery, shifting pattern you see when sunlight hits a rippling pool of water.

For a long time, scientists thought this "static" was just noise—random mess that didn't tell them much. It's like trying to read a book where the letters are constantly shuffling around.

However, the researchers realized that this "noise" actually contains a hidden code. The specific way the light dances depends on the size of the drop and the particles inside. But the code is so complex and subtle that a human eye (or a standard computer program) can't crack it.

The Solution: The "Super-Student" AI

To solve this, the team used a Convolutional Neural Network (CNN).

The Analogy:
Imagine you are trying to teach a child to recognize different types of clouds.

Old Method: You give the child a rulebook: "If it's fluffy and white, it's a cumulus. If it's dark and flat, it's a stratus." This is hard because clouds change shape.
The CNN Method: You show the child thousands of pictures of clouds and say, "You figure out the patterns yourself." The child (the AI) starts noticing tiny details you didn't even think about—like the specific way the light hits the edge of a cloud or the texture of the bottom. Eventually, the child becomes an expert at identifying clouds just by looking at the picture, without needing a rulebook.

In this paper, the "child" is the AI. They fed it hundreds of thousands of laser speckle images from floating drops. The AI learned to spot the invisible patterns that link a specific light pattern to a specific drop size or particle count.

The Experiment: The Floating Lab

The scientists used a special device called an electrodynamic trap. Think of it as an invisible force field that holds a single drop of liquid in mid-air, so it doesn't touch anything.

They filled these drops with Titanium Dioxide (a white powder often used in paint and sunscreen) mixed in a thick liquid. They then shined a green laser through the drop and took pictures of the resulting "sparkle" pattern.

The Results: How Well Did the AI Do?

The AI was tested on three different tasks, and the results were like a video game getting harder:

1. Level 1: Guessing the Drop Size (The Easy Win)

Result: The AI was excellent at this.
Why: The size of the drop changes the "big picture" of the light pattern, like how a large drum sounds different from a small one. The AI got this right about 94% of the time (an error of less than 6%).

2. Level 2: Guessing the Particle Size (The Medium Win)

Result: The AI was very good at this too.
Why: Even though the particles are tiny, they change the "texture" of the sparkle. The AI learned to distinguish between drops with tiny particles vs. medium-sized particles.

3. Level 3: Guessing the Concentration (The Hard Mode)

Result: This was tricky. The AI could tell the difference if the concentration was very different (e.g., 1 drop of paint vs. 20 drops of paint), but it struggled if the amounts were close together.
Why: The signal for "how many particles" is very faint, like trying to hear a whisper in a noisy room. Also, it was hard to mix the liquid perfectly, so the "ground truth" wasn't always 100% accurate.

The Boss Battle: Doing It All at Once
Finally, they asked the AI to guess all three things at the same time (Size of drop, Size of particles, and Number of particles).

Result: It worked! The AI successfully sorted the drops into 27 different categories simultaneously.
The Catch: Sometimes the AI got confused between similar categories (like mixing up a drop with 5 particles and a drop with 6 particles), but it was still able to make a very educated guess.

Why Does This Matter?

This is a "proof of concept." It's like proving that a new type of car engine works in a test track before putting it in a real car.

Real World Application: Imagine a factory that sprays paint or medicine into the air as a mist (aerosol). Currently, it's hard to check if the droplets are the right size or if the medicine is mixed evenly without stopping the machine and taking samples.
The Future: With this AI method, we could shine a laser at the mist in real-time and instantly know: "Hey, the droplets are too big," or "The medicine concentration is too low," all without touching the spray.

Summary

The scientists took a chaotic, messy pattern of light (laser speckle) and used a smart computer (AI) to decode it. They proved that you can "read" the hidden secrets of a floating drop—its size and what's inside it—just by analyzing the sparkle. It's a major step toward creating smart sensors that can monitor the air, clouds, and industrial sprays in real-time.

1. Problem Statement

The optical response of a suspension microdroplet is a complex inverse problem. Unlike bulk suspensions, a microdroplet acts as a finite dielectric object and a weak optical resonator, modifying the incident light field through morphology-dependent resonances. Consequently, the scattered light pattern (speckle) is governed not only by the properties of the suspended nanoparticles (size, concentration) but also by the droplet's own geometry and optical structure.

Challenge: Retrieving specific suspension parameters (droplet diameter, nanoparticle concentration, nanoparticle size) from scattered-light patterns is difficult because the information is distributed across a complex, stochastic texture rather than distinct, easily identifiable observables.
Goal: To determine if Convolutional Neural Networks (CNNs) can perform data-driven recognition of these parameters from laser speckle images of single levitating microdroplets, moving from single-parameter to multi-parameter classification.

2. Methodology

Experimental Setup

System: Single microdroplets of monodisperse $TiO_2$ nanoparticle suspensions in diethylene glycol (DEG) were levitated in a custom-built Linear Electrodynamic Quadrupole Trap (LEQT).
Conditions: The droplets were slowly evaporating. The experiment assumed negligible changes in droplet diameter and suspension concentration during the observation window (evaporation rate was low enough to maintain stability).
Materials:
- Nanoparticles: $TiO_2$ with diameters of 100 nm, 250 nm, and 500 nm.
- Concentrations: Mass concentrations of 1, 5, and 20 mg/mL.
- Droplet Sizes: Varied ranges (e.g., 65–130 $\mu$ m).
Imaging: A 514 nm (green) diode laser illuminated the droplet. Speckle patterns were recorded by a CCD sensor at ~10 fps with a 20 ms exposure time (shorter than the autocorrelation decay time to ensure static speckle capture).
Preprocessing:
- Background subtraction (average of 100 images without a droplet).
- 2-D Gaussian smoothing.
- Normalization (0–1) to remove brightness dependencies caused by droplet position or power fluctuations.
- Dataset construction: ~1.5 million speckle images were collected. Independent test sets were created from experimental runs not used in training to ensure generalization.

Machine Learning Architecture

Model: A custom Convolutional Neural Network (CNN) based on a residual multi-branch texture classifier.
- Structure: Extracts local texture patterns, refines them via skip-connected blocks, analyzes them in two parallel feature streams, fuses the streams, and classifies based on the global texture signature.
- Training: Performed in MATLAB (2023a) using Stochastic Gradient Descent with Momentum (SGDM) on dual NVIDIA RTX 3090 GPUs.
- Validation: Used independent datasets and Grad-CAM (Gradient-weighted Class Activation Mapping) to verify that the network focused on speckle features rather than experimental artifacts (avoiding the "Russian tank fallacy").

Classification Tasks

The study progressed through three levels of complexity:

Single-Parameter: Classifying droplet diameter, NP concentration, or NP diameter separately.
Two-Parameter: Simultaneous classification of (Diameter + Concentration) and (Concentration + NP Diameter).
Three-Parameter: Simultaneous classification of all three parameters (Total 27 classes).

3. Key Results

A. Droplet Diameter Classification

Performance: Achieved high reliability with an estimated accuracy better than 6%.
Observation: Diameter manifests strongly as vertical spatial frequency in speckle patterns. The CNN successfully predicted expected diameter values within the error limits of the shadowgraphy ground truth.
Robustness: The model generalized well even when tested on image series containing minor artifacts, though accuracy dropped slightly.

B. Nanoparticle Concentration Classification

Performance: More difficult to resolve than diameter.
Constraint: Unambiguous classification required concentration classes to be separated by a factor of at least ~4 (e.g., distinguishing 1 mg/mL from 5 mg/mL was feasible; finer distinctions were not).
Cause: Concentration effects are encoded in subtler speckle features. Additionally, experimental uncertainty in initial concentration estimation (~50%) limited the precision of the ground truth labels.

C. Nanoparticle Diameter Classification

Performance: Successfully classified for the selected cases (100, 250, 500 nm) at a fixed mass concentration.
Nuance: The study noted that at fixed mass concentration, changing NP diameter inherently changes the number of particles and scattering cross-section. Despite this mixing of effects, the CNN could unambiguously distinguish the particle sizes.

D. Multi-Parameter Classification

Two-Parameter: Successfully classified pairs of parameters (e.g., Concentration vs. Diameter) with unambiguous results, though faint "echoes" (misclassifications) appeared where one parameter's features dominated the other.
Three-Parameter: Successfully classified all 27 combinations (3 diameters $\times$ 3 concentrations $\times$ 3 NP sizes).
Conclusion: The CNN successfully learned to disentangle the complex, overlapping features of the speckle patterns to identify multiple physical parameters simultaneously.

4. Significance and Contributions

Proof of Principle for Inverse Problems: The study demonstrates that CNNs can solve non-trivial inverse problems in aerosol physics, retrieving multiple physical parameters from complex, stochastic speckle patterns where traditional feature engineering fails.
Multi-Parameter Diagnostics: It establishes a viable route for simultaneous optical diagnostics of free suspension microdroplets. This is a significant step toward analyzing complex, real-world aerosol systems (e.g., water-based droplets with varying compositions).
Methodological Robustness: The use of independent test sets and Grad-CAM validation confirms that the network learns physical correlations rather than experimental artifacts.
Scalability: The authors note that the number of classes is limited primarily by computational resources, suggesting the method can be scaled to even more complex systems with finer parameter resolutions.

5. Limitations and Future Work

Concentration Uncertainty: The accuracy of concentration classification is currently limited by the difficulty of precisely preparing and verifying initial suspension concentrations.
Parameter Coupling: In the NP diameter tests, the effect of particle size was coupled with particle number (due to fixed mass concentration). Future work aims to decouple these variables.
Real-World Application: While the current study uses a model system ( $TiO_2$ in DEG), the ultimate goal is to apply this method to complex, water-based aerosols found in atmospheric science and industrial processes.

In summary, this paper validates that laser speckle analysis combined with CNNs is a powerful, data-driven tool for the non-invasive, multi-parameter characterization of levitating microdroplets, offering a promising alternative to conventional optical diagnostic methods.