# Pulse Peak Delay-Total Focusing Method for Ultrasonic Tomography on Concrete Structure
## 1 Introduction  
After the rapid rise in the construction of concrete infrastructures in the past, there is now a huge number of old infrastructures that necessitate tremendous budget for their maintenance [1, 2]. Accordingly, the cost to improve old infrastructures increased from 1.3 trillion dollars in 2001 to 4.6 trillion dollars in 2017 in the United States [3]. In order to use this budget efficiently, preemptive maintenance based upon precise status is essential.  
Ultrasonic tomography technique is a popular non-destructive evaluation method to illustrate the inside of concrete structures. One of the ultrasonic tomography techniques is the through-transmission method that measures the time-of-flight or signal attenuation coefficient to depict the internal profile of concrete structures [4, 5, 6, 7, 8]. This method, however, requires to access the opposite surface, which is usually impossible for concrete structure. Another ultrasonic tomography technique is the pulse-echo method that measures the reflected time-of-flight of ultrasonic pulse to describe the inside of concrete [9, 10, 11]. The ultrasonic array system A1040 MIRA is one of the pulse-echo tomography device that has been commonly used to evaluate concrete structures accurately. The MIRA collects ultrasonic signals along multiple paths to visualize the inside of concrete structures [12]. These collected ultrasonic signals are converted into an understandable image by using image reconstruction algorithms [13]. One popular image reconstruction algorithm is TFM (Total Focusing Method), based on the delay-and-sum method [14]. The delay-and-sum method sums up the delayed collected signals according to an appropriate spatial rule for each point on images [15].  
The delayed time is calculated based on the spatial information of transducers and image pixels with a known wave speed and not ultrasonic pulse information [16]. A shortultrasonic pulse with a high frequency has a bare impact on resulting images due to its short pulse duration. However, the MIRA device targeting at concrete structures uses low-frequency ultrasonic pulse to avoid severe signal attenuation [17; 18], which results in long pulse duration, as well as sagging images. Although the MIRA device can handle the frequency of the input electronic signal within a range to change the pulse duration, it is not of great effect on the pulse duration due to a fixed frequency bandwidth of the transducers constituting the MIRA device.  
Cropping resulting images to make up for the sagging phenomenon does not realize the maximum performance of the TFM as the resulting images are still defocused by the long pulse duration. An image reconstruction algorithm embedded in the MIRA called SAFT-C calibrates this phenomenon by means of its own undisclosed way [19; 20]. In this research, the PPD-TFM (Pulse Peak Delay--Total Focusing Method) is proposed to compensate the sagging phenomenon and maximize the performance of the algorithm. A bandwidth filter similar to the transducer in the MIRA is simulated to generate an ultrasonic pulse with a given electronic pulse. A calculated pulse peak delay from the simulated ultrasonic pulse is reflected to the image reconstruction algorithm. Ultrasonic array signals are simulated to validate the proposed method, and an experimental test on a concrete specimen is performed to test the proposed method, as well. The performance of the proposed method is compared with the TFM, as well as the SAFT-C, by means of the PDC (potential damage curve) and API (array performance indicator).