## 1 Introduction  
The acoustic nonlinearity parameter (\(\beta\)) is widely used for diagnosing and inferring material damage and it can be measured using displacement amplitudes of fundamental and second-order harmonics waves [1; 2; 3; 4; 5; 6; 7; 8; 9; 10; 11]. The exact value of an acoustic nonlinearity parameter is called the absolute acoustic nonlinearity parameter. To measure the absolute acoustic nonlinearity parameter, it is necessary to measure the extremely small displacement amplitudes of the second harmonic frequency component [12]. However, such experimental measurement methods are complicated and practically difficult to apply in the field. Hence, the relative acoustic nonlinearity parameter available for relative comparison is frequently measured using the voltage amplitude of the device, measuring the detected ultrasonic wave. Nevertheless, measurement of the absolute acoustic nonlinearity parameter is indispensable for quantitative characterization of materials. There are two ways to obtain the absolute acoustic nonlinearity parameter: a direct method and an indirect method. The direct method is used to measure the displacement amplitude of the ultrasonic wave directly or to use a calibration to convert the detected voltage signal amplitude into the displacement amplitude [12]. The indirect method is used to estimate the absolute acoustic nonlinearityparameter of a test material by measuring the ratio of relative acoustic nonlinearity parameters between the test material and the reference material, where the absolute acoustic nonlinearity parameter of the reference material is known [13]. This indirect method, introduced in the aforementioned paper, is simpler than the direct method, but requires the assumption that the voltage-displacement proportionality coefficients (VDCs) of the test and reference materials are the same. The VDC indicates the proportionality coefficient between the detected voltage signal amplitude of ultrasonic wave and the displacement amplitude of that wave, which is dependent on the material properties and the sensitivity of the receiving transducer. If the experimental conditions are kept constant for two similar materials, an indirect method can be applied to them because the VDCs of the two materials are almost the same. On the other hand, if the test and reference materials are dissimilar, an indirect method cannot be applied even if the experimental conditions are kept consistent because the VDCs of the two materials are different. In particular, the material dependency of the VDC is critical in the case of contact detection. For example, in the case of contact reception of ultrasonic waves using piezoelectric transducers, energy loss due to impedance mismatching can occur when ultrasonic energy is converted into electrical energy, so that the VDC varies if the material's acoustic impedance is different. Therefore, to overcome the limitation of the previously proposed indirect method, a non-contact detection method using a laser interferometer has been proposed for longitudinal waves [14]. Since the interferometer obtains an output directly proportional to the ultrasonic displacement, its proportionality is independent of the material. Meanwhile, many studies have investigated the acoustic nonlinearity parameter of surface acoustic waves [3; 4; 15; 16; 17; 18; 19]. In this regard, an indirect method to measure the acoustic nonlinearity parameter of surface acoustic waves has also been studied for the case of similar test and reference materials [3]. Unfortunately, however, when a surface acoustic wave is transmitted and received using wedges as a contact technique, this method cannot be applied for dissimilar materials because of the constraints mentioned above. This paper proposes a fully non-contact surface acoustic wave technique using lasers for the indirect measurement of the acoustic nonlinearity parameter. This technique allows the application of the indirect method even when the test and reference materials are dissimilar.