# Flavi Detection on a Tilted Particleboard by Use of the Spec-Radiation Method
## 1 Introduction
The large furniture manufacturers want to meet this demand and, at the same time, to reduce the costs of production, which often works through material savings, and thus ever thinner or less dense particleboards are being used whilst ensuring that the furniture can withstand loads. During the production process of a particleboard, air inclusions and imperfectly glued regions can strongly influence the load capacity [17]. Manufacturers must then test their wood products non-destructively to guarantee the high demands of the furniture industry. The first to deal with the detection of delaminations or flaws in wood-based materials by ToF measurements were [18; 19]. In today's modern particleboard industry, particleboards are tested directly in the running production process. However, due to pressing and gluing, these boards have temperatures of up to 100 \({}^{\circ}\)C and vapors can still escape, which might damage the receivers [17]. This leaves air-coupled ultrasound as a testing method, with large distances to the particleboard of \(>\)100 mm. If a pulse excitation is used, sufficient time must be allowed between one ultrasonic pulse and the next. Otherwise, reflections of the previous ultrasonic pulse between the transmitter and the particleboard or between the particleboard and the receiver will superimpose the actual signal. In worst cases, a standing wave could occur, making evaluation difficult or else falsifying it. A tilted arrangement is preferred if a high repetition speed of the ultrasonic pulse is needed. As an example: If a panel material moving at 5 m/s over the production line is to be inspected with a measuring point distance of 20 mm, a repetition frequency of 250 Hz is required. However, efforts are being made to achieve a much smaller measuring point distance in order to detect flaws even more accurately. This method circumvents the problem posed by reflections. In this case, either the transmitter and receiver are tilted at an angle to the particleboard or vice versa. In this way, the ultrasonic pulse is reflected away from the actual sound path after hitting the particleboard. However, this makes evaluation more difficult, as the sound propagates through the particleboard at a different angle according to [PERSON]'s law of refraction due to the impedance difference [20]. There are different ways of presenting the measured information from the receiver. The three most common ones are, according to [21], A-, B- and C-scans. In an A-scan, the information of a measuring point is plotted over time. A B-scan shows the information of a line of measured points over time, e.g., as an amplitude image. In a C-scan, the ToF, amplitudes or phases of an area of measured points are displayed. This is particularly suitable if a visual representation of possible flaws and their positions in the plane of a particleboard is desired. However, the sound waves diffract at delaminations, making it increasingly difficult to detect the delaminations as the measuring plane moves further away from the surface of the particleboard [22]. To reproduce the sound path, techniques of acoustic holography can be used, which can calculate the sound propagation in space by solving the wave equation. Since the invention of holography by [23], it has been continuously developed and is used today in the most diverse methods. Acoustic holography enables the sound distribution to not only be displayed in the measuring plane as a C-scan, but also to be calculated back from the measuring plane directly on the air layer on the surface of the particleboard. This can be done, for example, with the re-radiation method [8; 24; 25; 26; 27; 28; 29] or the spec-radiation method for parallel planes [30]. With these radiation methods, it is possible to identify flaws that are smaller than the wavelength of the acoustic wave [8; 28] and to use a grid point distance in the measuring plane that is larger than the flaw [28]. As mentioned, this type of evaluation has only been possible for planes that are parallel-oriented to one another.