## 1 Introduction  
Optical microscopy, together with histology, has long been used to assess the pathology of suspicious regions of tissue. For a histological examination, tissue needs to be prepared through multiple chemical staining procedures to highlight specific target structures before being observed. Normally, several hours to a few days are required to complete the process. Therefore, this requirement of tissue characterization during operation time has been challenged. Furthermore, the tissue usually loses its biological functions after being stained. Several studies were conducted by using elastography as an alternative tissue characterization modality [1; 2; 3; 4]. Each of the modalities applies various loading approaches on the sample and result in strain distribution, which is observed by the imaging method. Magnetic resonance elastography (MRE) is sensitive to the magnetic property of the water and fat content of the tissue. MRE can achieve whole-body imaging with high penetration and low spatial resolution. Meanwhile, optical coherence elastography (OCE) can achieve a higher resolution (up to the diffraction limit of the optical wavelength) and low penetration (about 1 mm). Ultrasound elastography (USE) has been one of the most popular modalities thank to its ability to integrate into ultrasound systems. The USE is mainly divided into three groups: strain imaging methods, shear wave elastography, and B-mode elastography. With externally normal stress applied, the mechanical strain induced along the direction of the mechanical stress is measured (Young's modulus) in strain imaging [5] while shear wave created and propagated in a direction perpendicular to the mechanical stress is measured (shear modulus) in shear wave elastography [6]. Verasonic's research scanner is able to integrate different array transducers from the various manufacturers. The system is widely used in many studies because of its flexibility in sequencing and data processing modification [5; 7; 8]. B-mode elastography measures the speed of longitudinal waves, which is used to estimate bulk modulus. Each tissue characterization modality has advantages and disadvantages in deployment in clinical applications and also plays a different role in filling the gap in terms of spatial resolution among them. Among the elastography modalities, B-mode elastography, using a single element transducer, has been utilized for tissue characterization on a microscale owing to its high spatial resolution and simplicity. Due to the correlation of elasticity and speed of sound in the tissue [9], the acoustic velocity of longitudinal waves has been considered to be a parameter for tissue characterization. The single element transducer scans the area of interest of the sample to achieve two-dimensional sound-speed images. Several authors have reported the use of scanning acoustic microscopy (SAM) for the tissue characterization of various anatomical regions [10; 11; 12; 13; 14; 15]. During the early stages of tissue characterization by SAM, several studies have calculated acoustic velocity [16; 17; 18]. In histology and pathology, thin slices of tissue from about several micrometers to several tens of micrometers thick were used for characterization. The interferential method has been the most popular method, where the distance between two reflections at the tissue is under one wavelength. In this method, the phases of the two reflections are compared with the reference phases, which are determined from the substrate without the tissue. The reference phases are identical at every position if the substrate surface and scanning line of the transducer are parallel. However, determining the reference phases has been a challenge, due to the slope of the scanning stage. There have been numerous attempts to solve this problem [19]. The plane function has been widely used in previous studies. In this method, the slope of the stage on each axis was compensated by the time lags among three points without the tissue [20; 21].