## 1 Introduction
This has the advantage being non-invasive, non-destructive, and can measure interface inside a machine where desired surfaces are inaccessible. Reflection and transmission coefficients are defined as the proportion of an incident wave reflected from or transmitted through the interface, respectively. The reflection coefficient depends on the amount of solid contact. The acoustic impedance of air is significantly small, compared to solid materials, and so the air gap at the interface causes more incident energy to reflect. Increasing the nominal contact pressure leads to an increase in the number of the asperities in contact, therefore less incident energy is reflected and more energy transmitted [18]. [PERSON] [24] and [PERSON] [19] used a spring model, where the interface is treated as a distributed stiffness, to demonstrate that the reflection coefficient of an imperfect contact (incomplete contact) is dependent on the interfacial stiffness. Authors have studied both normal and tangential interface stiffness in the linear regime using either longitudinal or transverse polarised ultrasound, respectively [18; 19; 20; 21; 22; 23; 25; 26; 27]. Both elastic and plastic rough surface contact models have been used to predict interface stiffness compared to ultrasonic measurement [15; 28; 29]. [PERSON] et al. [15; 28] presented a spring-damper model in a parallel configuration to address the effect of ultrasound attenuation. However, the results were still far beyond those predicted by the GW model. [PERSON] et al. [30] modeled the interface as a layer of equivalent materials such as viscoelastic materials. Their study is accurate in cases where the Poisson's ratio of the layer model is known. The principle has been modified by [PERSON] et al. [31], [PERSON] et al. [32] and [PERSON] et al. [17]. These studies have been based around the linear response of an interface to an ultrasonic wave. The pressures generated by the wave and the resulting deflections are normally very small and so the process is elastic and reversible. However, in recent years there have been a number of studies based around higher power ultrasound that causes nonlinear behaviour. The nonlinear behaviour may originate from the material itself, as the stress-strain relationship of the medium exceeds [PERSON]'s law (nonlinear elasticity) [33; 34]. Alternatively, the interface may also be a source of nonlinearity. If the wave is of sufficient power, it can cause opening and closing of the air gaps and this can lead to the generation of higher harmonics in the reflected/transmitted waves. This is known as Contact Acoustic Nonlinearity CAN [35; 36; 37]. In Section 2, a description of the higher harmonics generation (mechanics of CAN) is described. [PERSON] [38] studied one-dimensional nonlinear wave propagation through identical contacting materials by considering the concept of CAN. He defined an analytical relation between the incident wave and the relative surface approach of the interface. [PERSON] et al. [39] used [PERSON]'s findings to propose a nonlinear nominal contact pressure-relative surface approach relationship using a polynomial Taylor series to define the linear and nonlinear interfacial stiffnesses using the reflection coefficient. Nonlinear interfacial stiffness is important when a high-power ultrasound is employed to define the interface. The wave itself causes a distortion of the interface and hence a linear model can no longer describe the proper interface response. In previous studies only through transmission methods had been used to measure the nonlinear interfacial stiffness. The aim of this paper is to evaluate linear and nonlinear interfacial stiffnesses measured with a reflection method to demonstrate that they are both based on the same fundamental relationship between contact pressure and relative surface approach. The result is compared to published experimental work using through transmission.