## 1 Introduction  
The mechanical properties of advanced high strength steels (AHSS) are greatly influenced by the grain size and the composition of the metallurgical phases. Both grain size refinement and the introduction or creation of secondary phases (e.g., martensite, bainite, pearlite) are mechanisms to strengthen AHSS. Hence, control of grain size, and control of secondary phase volume fraction are essential to master the mechanical properties. For consistent behavior of the product in forming processes, the mechanical properties, and hence the microstructure and composition, should remain constant. Therefore, real-time monitoring and control of the production process is important but challenging due to the harsh conditions. A potential way to measure the grain size and the secondary phase volume fraction in an inline manner during steel hot rolling is via laser ultrasonics (LUS). A complicating factor, however, is that the temperature varies during the process, affecting the ultrasonic properties as damping and wave velocity. Since the proposal to use LUS as a new contactless measurement method for non-destructive testing of metals [1; 2; 3; 4; 5], the technology has been developed over the years to become a mature technology for a wide range of applications, such as corrosion monitoring [6], delamination detection in reinforced polymers [7], and in the determination of material properties [8; 9; 10; 11]. Whereas in conventional transducer-based ultrasonic characterization a contact probe is used, LUS employs a laser pulse to generate an ultrasonic wave in the medium by ablating a small fraction of the sample material. The propagating ultrasonic wave can be recorded by a measuring laser. The resulting measurement scheme is contactless, making it suitable for inline measurements in a steel mill, where the movement and temperature of the steel strip are a challenge for conventional transducers. Details on the physical background and practical applications of LUS techniques are described in several books and articles, e.g., [12; 13; 14; 15; 16]. Various LUS systems have been developed and used in offline systems [5; 10; 17; 18; 19] or as inline systems in steel mills [20]. Grain size and metallurgical composition are among the key factors determining material properties, such as strength, deformability, hardening and toughness, but also for detecting the formation of corrosion and pitting. Grain sizing. and time-varying aspects such as growth, deformation, recovery, and recrystallization have been studied in a variety of metals, such as manganese alloys [5], cobalt alloys [21], nickel alloys [9; 22], aluminum [19; 23] and stainless steels [24; 25; 26; 27]. Monitoring of the metallurgical composition is especially important in dual phase (or multiphase) steels, where formability and strength depend on the phase ratio and phase distribution [28; 29; 30; 31; 32]. Efforts to model the ultrasonic wave propagation in materials with a microstructure have mainly focused on calculating attenuation and wave velocities in 3D, but backscattering has also been considered. Increasing computational power and the development of sophisticated computational methods such as finite difference (FD) or finite-difference time-domain (FDTD) methods [33; 34] and finite element methods (FEM) [24; 35; 36; 37], have enabled the modelling and computation of large three-dimensional samples. In these studies, materials with (poly)crystalline structures, consisting of different phases, or with inclusions, voids or cracks have been modelled. Our investigation presents a model-based study to evaluate the capability of the LUS method to measure these grain size and metallurgical composition (apart from experimental measurement uncertainties). The study addressed the (inter-)dependencies of such a measurement, for example, to temperature.