SprayQuantAI® uses the classical TSTOF (Time-Shift-Time-of-Flight) [1][2] measurement principle and non-coherent light scattering to measure individual droplets in sprays and flows. From the time-resolved optical signal of each detected droplet, the system can determine droplet size, droplet velocity and droplet rate.
The classical analytical approach requires only a small number of mathematical operations, making it particularly suitable for real-time spray monitoring and implementation directly inside compact measurement electronics.
Technical Background of the SprayQuantAI® Measurement Principle
SprayQuantAI® uses non-coherent light scattering and the TSTOF measurement principle to characterize droplets in sprays and flows. The basic configuration of the measurement probe consists of a single laser line and a high-speed optical detector.
For each detected droplet, the measurement probe records a time-resolved light-scattering signature. Characteristic parameters of this signal are used to calculate droplet size and velocity. In addition, the number of detected droplet events within a defined evaluation interval provides the droplet rate.
More advanced SprayQuantAI® configurations can use AI-based signal processing to evaluate additional characteristics of the light-scattering signal. Signal shape and structure can therefore provide additional information about droplet or particle properties and, depending on the application and calibration, material composition [3][4].
From a Light-Scattering Signal to Droplet Size and Velocity
When a droplet passes through the laser line, part of the incident light is scattered toward the optical detector. The detector records a time-dependent light-scattering signal S(t), which can be approximated by a Gaussian function with two characteristic signal parameters:
- A – amplitude of the light-scattering signal
- σ – temporal width of the light-scattering signal
Together, signal amplitude and temporal width describe the optical signal strength and the residence time of the droplet inside the illuminated measurement region
The amount of scattered light detected while a droplet passes through the laser line can be represented by the time integral of the measured light-scattering signal:
In the simplified model, the integrated optical signal is approximately proportional to the cross-sectional area of the droplet. Because the cross-sectional area scales with d², the droplet diameter can be derived from the product of signal amplitude and temporal signal width:
Here, Cd is the droplet-size calibration constant determined experimentally using reference measurements during the calibration process.
Droplet velocity is related to the temporal width of the detected light-scattering signal. A faster droplet passes through the laser line in a shorter time and therefore produces a narrower optical signal. A slower droplet remains within the illuminated measurement region for a longer period and produces a wider signal.
The constant Cv is the velocity calibration factor determined during the manufacturing and calibration process.
Consequently, every detected droplet event can be assigned a pair of physical quantities (d, v). Signal amplitude and signal width are evaluated jointly for size determination, whereas velocity is determined primarily from the temporal signal width.
In addition to droplet size and velocity, SprayQuantAI® can determine the droplet rate. The droplet rate is calculated from the number of detected individual droplet events within the selected evaluation interval.
The measurement can therefore distinguish changes in local droplet concentration from changes in mean droplet size or velocity. This capability is particularly useful for analysing spatial spray profiles and monitoring dynamic atomization processes.
Real-Time Spray Monitoring
The measurements presented here show how characteristic parameters of a single light-scattering signal can be converted into physical quantities such as droplet size and droplet velocity. Because the required calculations are computationally simple, they can be implemented directly in the measurement electronics. Physical droplet quantities can therefore be provided with a typical temporal resolution of approximately 100ms.
This makes SprayQuantAI® suitable for detecting changes in the atomization process in real time and for integrating droplet size, velocity and droplet-rate measurements into existing spray monitoring and process-control systems.
References
[1] W. Schaefer, L. Li, P. Stegmann, and M. Terada, “TSTOF測定法に関する技術報告書：第一部 ─ 技術的基礎、歴史的発展、および他のレーザー測定法との比較,” J. Coat. Technol. Res., vol. 61, no. 3, Art. no. 100, 2026. [Online]. Available: https://jcot.or.jp/download/61-03-2.pdf
[2] W. Schaefer, L. Li, P. Stegmann, and M. Terada, “Technical report on the TSTOF measurement method: Technical basics, historical development, and comparison with other laser-based measurement methods,” Photonics, vol. 13, no. 1, Art. no. 56, 2026, doi: 10.3390/photonics13010056.
[3] W. Schaefer and L. Li, “Particle characterization by analyzing light scattering signals with a machine learning approach,” Appl. Opt., vol. 63, no. 29, pp. 7701–7711, Oct. 2024, doi: 10.1364/AO.531346.
[4] A. M. A. Doan, W. Schaefer, V. Chernoray, W. Schaefer, and V. Chernoray, “Analysis of the light scattering of a colloid droplet on a Gaussian beam to determine the suspension concentration,” in Proc. ILASS-Europe, Lund, Sweden, 2025.