## 1 Introduction  
The deterioration of concrete affects the structural integrity of concrete structures and reduces their serviceability. One of the most common types of damage in concrete structures is delamination at the interface between the concrete cover and the embedded steel rebars. The oxide layer around corroded steel rebars produces expansive stresses that initiate cracks with their planes parallel to the rebars (i.e., delamination). In addition, the delamination-like damage usually occurs at bridge deck overlays which include the interface between the topping material layer and structural member. The extent of delamination damage increases over time unless it is appropriately repaired. Delamination damage needs to be detected and characterized at an early development stage to reduce the maintenance cost and improve the serviceability of concrete structures. Studies have demonstrated the potential of nondestructive inspection techniques based on mechanical vibration and elastic wave propagation phenomena to detect damage from concrete structures and further characterize their material properties. The techniques include impact-echo (IE), spectral analysis of surface waves (SASW), and multichannel analysis of surface waves (MASW) [1, 2, 3, 4, 5, 6, 7, 8, 9, 10]. In the IE method, a mechanical impact is applied to excite guided waves and low-frequency vibration modes, and the corresponding responses are collected using a vibration sensor (e.g., an accelerometer or microphone). Then, a specific frequency that corresponds to the zero-group-velocity (ZGV) Lamb wave mode is extracted from the frequency-domain spectrum of the measured response to compute the thickness of concrete pavements and the delamination depth. The SASW computes the phase velocity of Rayleigh waves over a range of frequencies (or wavelengths) using vibration responses collected using two sensors. Furthermore, a shear wave velocity profile over the depth of a layered medium is obtained through an inversion process. The MASW technique uses a multichannel vibration sensor array that enables the spatial sampling of multimodal guided wave responses. The collected array data are processed to obtain experimental phase velocity dispersion curves, where individual wave modes are identified to characterize the material properties. However, it is difficult to estimate the depth of near-surface shallow delamination using these techniques despite their potential. This is partly because these techniques use a mechanical impact source that generates low-frequency (below 20 kHz) resonant vibration modes over the shallow delamination region, and these vibration modes are not favorable for estimating the depth of delamination. In recent years, an air-coupled ultrasonic approach has been demonstrated to be an effective tool for the nondestructive inspection of concrete structures [11; 12; 13; 14]. Lamb waves (plate guided waves) that are favorable for estimating the depth of delamination can be generated by employing ultrasonic frequencies (above 20 kHz). In addition, the noncontact nature of the air-coupled ultrasonic approach facilitates the rapid collection of ultrasonic data over a large inspection area. Recent advances in the micro-electromechanical system (MEMS) technology have enabled the development of a low-cost, high-resolution sensor array system [14]. Air-coupled ultrasonic approaches have been applied to detect and characterize various types of concrete damage, such as internal voids [12], alkali-silica reaction damage [13], and distributed cracks [15]. In this article, we present a method to estimate the depth of near-surface shallow delamination in concrete using a noncontact (air-coupled) MEMS ultrasonic sensor array and an optimization-based data processing approach. The noncontact ultrasonic sensor array system consists of an array of 64 MEMS ultrasonic microphones and a signal-amplifying circuit.