## 1 Introduction  
Surface mount technology (SMT) is now a widely-used method for mounting discrete electronic components (or packages) on a printed circuit board (PCB) to interconnect with smaller-size and finer-pitch components using the solder joints. To implement the SMT, an infrared (IR) solder reflow process with well-controlled heating and cooling temperatures has been used for mounting the electronic components on the PCB with solder joints (or paste). However, there exists a problem with PCB warpage in such device assembly during the solder reflow process. The excessive warpage of the PCB would result in some solder joint defects, such as short or open circuits, or thermal-mechanical strains in the PCB, seriously influencing the reliability of the PCB assembly [1]. The main factor causing the thermal-mechanical strains is a coefficient of thermal expansion (CTE) mismatch between the electronic components and the PCB, which would have a great deal of influence on the reliability of solder joints in microelectronic packages [2]. Therefore, methods to effectively measure and further control or even reduce the PCB warpage in the reflow process are of utmost importance. In 1997, a real-time strain-gauge probe method for measuring and recording the in-process deformation of packages during a simulated solder reflow process was developed [3]. Strain gauges have been widely used in measuring the mechanical strain on a PCB due to their reliable and easy-to-use characteristics. Appropriately selected locations adhered with a strain gauge are very important for accurately measuring the strains on packages [4]. A method for evaluating the strain gauges used in printed circuit board assemblies was proposed for mechanical strain monitoring [5]. Mechanical-strain gauge data measuring on a package and a PCB under a 4-point bending test has been used for the finite element model's verification [6]. Strain gauges were applied to monitor the mechanical strains developed across all four corners of a lidless flip-chip ball grid array (BGA) package during a heatsink mounting process [7]. Strain gauge measurements were also carried out for the PCB assembly under thermal loading to validate the finite element simulation results [8]. Regarding full-field measurements, the optical shadow moire system has been used for out-of-plane deformation (or warpage) measurements in a PCB assembly and electronic components [9; 10; 11]. This optical method has been effectively and successfully used to measure the full-field out-of-plane deformations of electronic packages, and the PCB under different temperatures, by studying the residual strain in the epoxy molding compound in plastic BGA packages [12; 13] and the warpage of a CPU socket [14]. However, there is no out-of-plane deformation measurement available in the literature for a PCB assembly using stain gauges during a solder reflow process.  
In order to monitor the warpage variation of a PCB assembly in real time under heating and cooling during a solder reflow process, especially in a conventional IR oven (although some of such preliminary results have been reported in [15; 16]), a warpage measurement of a PCB with strain gauges during the reflow process will be proposed in this study. Its feasibility will be evaluated by the shadow moire system and finite element method (FEM) analysis.