## 1 Introduction  
Gas-liquid two-phase flow is a common phenomenon occurring in petroleum, chemical, refrigeration and power generation industries [1; 2; 3]. Due to the unstable flow, heat and mass transfer process, the flow pattern and interface structure of two-phase flow are usually complex [4; 5; 6]. Therefore, the two-phase flow parameters are difficult to measure quickly and accurately [7]. However, the knowledge of local parameters of two-phase flow plays a critical role in the studies of the heat and mass transfer characteristics and mechanism of the gas-liquid two-phase, the development of two-phase modeling research, the optimization of two-phase flow patterns and the safety and stability of equipment operation [8; 9; 10]. The theoretical models, including the two-fluid model and interfacial area transportation model, rely heavily on the advanced measurement techniques to provide benchmark database and possibility of inspecting new phenomenon and physical laws. The flow parameters including phase distribution, void fraction, interfacial area concentration (IAC), bubble size, velocity, etc. of two-phase flow have great impacts on the heat and mass transfer characteristics, the reaction efficiency and operation safety of multiple chemical applications [11; 12; 13; 14; 15]. Hence, it is particularly necessary to develop and utilize accurate, fast and convenient methods to explore the two-phase flow details. Currently, the measurement methods of local two-phase flow parameters can be divided into the following two categories: (1) the photography and image process techniques, having the advantage of lack influence on the flow, usually called visual measurement [16; 17; 18] and (2) the point by point measurement [3; 19; 20], in which optical or electrical signal that can be altered by involved phases. However, the first kind of methods is only applied to systems where the flow channel or vessel is transparent, unless the photography employs high energy ray to penetrate metal walls [21; 22]. Besides, it is hard for visual measurements to distinguish bubbles at different depths when bubbles are overlapped in complex two-phase flow [23]. Nevertheless, this method has contributed greatly in the identification of flow regimes, track of simple bubbly flow and determination of bubble condensation rate in phase changing flows [23; 24; 25; 26; 27; 28]. For the second category of methods, one of its important kinds is the wire-sensor mesh [29; 30; 31; 32; 33] where a matrix of measurement points is created at the cross points of two arrays of parallel mesh wires. Electrical signals from the wire-sensor mesh are collected and then analyzed by a program to get void fraction, bubble size, bubble velocity and so on across the whole flow field. Another kind is the sensor probe including single-sensor probe, double-sensor probe, four-sensor probe and other multiple-sensor probes [34; 35; 36; 37; 38; 39; 40; 41; 42]. Moving the probe across the two-phase flow field, local flow parameters at different positions can be measured. Although both the wire-sensor mesh and sensor probe interfere measurements affect the original two-phase flow field, this intrusion can be limited by a great extent with very thin wires or probes. Moreover, compared with the visual measurement, the point-to-point sensors are easier to be adopted online for practical opaque tube and vessel and more complex two-phase flow. In the above-mentioned method, only two sensors apart from the probe shell are used in the double-sensor probe, and thus two series of signals can be collected. In the simple measurement theorem of double-sensor probe, it is assumed that the direction of interface and velocity of bubbles (or interface) are both in parallel to the connection between the two sensors' tips.