# Laser-Ultrasound-Based Grain Size Gauge for the Hot Strip Mill
## 2 Materials and Methods  
### The Generation Event Method  
The ultrasonic method/algorithm developed herein is an adaptation of the multiple echo method, wherein the frequency-dependent attenuation is evaluated, after which the  
Figure 1: Schematic of the principle for laser ultrasonic grain-size measurement. (**a**) The ultrasound is generated in the sample by a generation laser hitting the surface with a short optical pulse. (**b**) The ultrasonic response of the sample is acquired with the detection laser collecting several backwall echoes. (**c**) The frequency-dependent attenuation is calculated for the backwall echoes. (**d**) The third-order frequency-dependent attenuation \(b\) is transferred by a calibration curve plotting known attenuation vs. grain sizes. grain size is calculated using a calibration curve. The unique aspect of this new method is that the reference spectrum that is used for the attenuation calculation is the actual generation event. Typically, with epicentric LUS measurements, the surface movement during the generation/ablation is too large to fit within the dynamic range of the interferometer. This is especially prominent when the sample is at room temperature, since the surface moves significantly due to the thermal expansion. However, during a trial measurement campaign in a hot strip mill in 2018 [10], it was empirically observed that the LUS measurement conditions in the hot strip mill were so favorable that the surface movement of the generation/ablation could be fully measured. Figure 2 shows ten LUS measurements on a strip, where the generation event is the first peak at 0.7 us and the three following peaks are the consecutive backwall echoes with a peak-to-peak separation of ~2.4 us. The measurement of the whole strip contains more than a thousand shots, but only ten A-scans are shown for clarity. The reason why the generation event could be measured in the mill is believed to be due to the material temperature at the generation spot being close to the melting temperature, which limits the available surface movement by thermal expansion. During ablation, the uppermost part of the surface is heated to the melting point. Considering that surface movement is proportional to the temperature change AT, the change at the generation point for a sample starting at room temperature is almost 1000 degrees larger than for the strip in the mill, which starts at ~1000 \({}^{\circ}\)C.  
Figure 3 displays the frequency content of the ten generation events presented in Figure 2, as well the consecutive backwall echoes. The data clearly shows that the higher frequencies are attenuated more than the lower frequencies. In the method/algorithm developed herein, the measured generation event serves as the reference spectrum for the following attenuation analysis. Therefore, the online system is self-calibrating in the sense that if the generation laser pulse characteristics, or any of the environmental factors, change, then the system will automatically adapt. This is because the spectrum for the generation event that is used for evaluation will mirror these changes. However, using the generation-event spectrum as a reference requires that the method for calculating the grain size can cope with the effects from diffraction, which is mainly managed by using only adequately high frequencies when fitting the data to Equation (3). Additionally, if the grain size is relatively small, then the US attenuation will be low, and several echoes will have a high enough signal-to-noise ratio (SNR) and can serve as input to the attenuation analysis. If, on the other hand, the grain size is relatively large, the grain scattering effects will be larger than the diffraction effects. In this case, the measurement may only contain one  
Figure 2: Ten typical bandpass\(-\)filtered A\(-\)scans from an online measurement in a hot strip mill [10]. The first peak at 0.7 us is the generation event, and the following peaks are the consecutive backwall echoes.