ParticleTensorAI® – TSTOF and Light-Scattering Signals

ParticleTensorAI® builds on the physics of time-dependent light scattering. A moving droplet or particle interacts with a shaped light beam and produces a scattered-light signal that changes over time. The Time-Shift Time-of-Flight (TSTOF) method uses the timing of such signals to characterise individual particles. ParticleTensorAI® uses the same general type of optical information as the basis for AI-based signal-sequence analysis.

When light interacts with a particle, part of the light is scattered. The recorded signal depends on the particle and on the optical measurement arrangement, including the shape of the light field and the position of the detector.

If the particle moves through the illuminated region, it passes through different parts of the light field. The detector therefore records a changing intensity over time. In this way, the spatial interaction between the particle and the light is converted into a time-dependent signal.

The measured waveform is influenced by the particle’s motion through the light field. Its temporal structure can include changes in signal intensity and timing. The exact signal shape also depends on the particle’s optical properties and the position from which scattered light is detected.

This means that a light-scattering signal is not simply a measure of brightness. Its time structure contains information about how the particle interacts with the shaped beam as it moves through the measurement region.

TSTOF combines time-shift and time-of-flight measurements. In a typical arrangement, a particle passes through two spatially separated light beams. Detectors record the resulting time-dependent scattered-light signals.

• The time of flight is obtained from the delay between signals associated with the two separated light beams. When the beam separation is known, this delay provides information about particle velocity.
• The time shift between signals recorded at different detector positions depends on the interaction between the particle and the light field. This timing information can be used together with the time-of-flight measurement to determine particle properties.

In a common TSTOF configuration, multiple detectors record signals from different scattering directions. The measured time relationships can be evaluated to determine particle size and velocity. For transparent or semi-transparent materials, the method can also provide information related to refractive index or solid fraction, depending on the measurement configuration.

TSTOF is a counting method: its classical evaluation identifies signals associated with individual particles and uses their timing to calculate particle properties. ParticleTensorAI® uses a different analysis strategy. It can retain a section of one or more detector signal streams and arrange the data as a Particle Tensor for AI evaluation.

This distinction concerns how the recorded signals are processed. Both approaches rely on optical light-scattering information, while ParticleTensorAI® focuses on evaluating patterns across buffered signal sequences without requiring every particle interaction to be separated into an individual event first.

The information that can be extracted depends on the optical setup, detector positions, particle flow, material, and evaluation method. Signal timing and shape may be used to investigate particle size and velocity. With suitable data and a validated AI model, ParticleTensorAI® can also investigate classifications or material-related properties.

These outputs require validation for the relevant measurement conditions. A signal pattern alone does not guarantee a particular result; its interpretation depends on the physical measurement and the method used to analyse it.

A detailed description of the TSTOF measurement principle, its technical foundations, and its comparison with other laser-based methods is available in the following open-access article:

Walter Schaefer, Lingxi Li, Patrick Stegmann, and Masaru Terada, “Technical Report on the TSTOF Measurement Method: Technical Basics, Historical Development, and Comparison with Other Laser-Based Measurement Methods,” Photonics, 13(1), 56, 2026. Read the article.