## 1 Introduction  
Owing to the rapid development in the manufacturing industry, such as automobile and aerospace applications, measuring the surface displacement of complex mechanical structures and new materials is important. The surface displacement can be further translated into strain and stress, which is the key parameter for design, manufacturing, and quality control [1]. A dynamic full-field and highly sensitive measurement of displacement is the foundation of rapid and optimization design. The measurement of a three dimensional displacement, along three mutually orthogonal directions, can be classified as out-of-plane and in-plane displacements. However, the in-plane displacement component is more important than the out-of-plane displacement component in many practical problems [2]. Information on in-plane displacement is helpful in determining [PERSON]'s modulus and [PERSON]'s ratio of materials [3; 4]. In-plane rotations, which can be determined by in-plane displacement, is an essential component of the geometrical metrology [5; 6; 7]. Under similar testing conditions, residual stress, obtained from in-plane displacements, has higher precision than that obtained from out-of-plane displacement [8]. Optical measurement techniques have been widely used in displacement measurements because they are non-contact, full-field, and highly sensitive. Advanced optical methods include, digital image correlation (DIC) [9; 10], Moire interferometry [11], and digital speckle pattern interferometry (DSPI) [3; 12]. The sensitivity of Moire interferometry and DSPI is higher than that of DIC, and the set-up of DSPI is simpler than that of Moire interferometry. Because of the high sensitivity and flexibility of DSPI, it has been well-accepted in experimental mechanics, displacement and displacement measurements, and strain measurements. In DSPI, in-plane displacement is measured by evaluating the phase difference of two recorded speckle interferograms under load. The surface under the test is illuminated from two symmetrical directions with a single direction of observation [13], or is observed from two symmetrical directions with a single direction of illumination [14]. The measurement of a surface displacement in two orthogonal directions is often required for the complete characterization of displacement. In traditional DSPI, in-plane displacement is measured in the single direction, depending on the illumination or observation direction. For example, if the surface is illuminated from two symmetrical directions, the measured displacement is in the vector direction, which is the subtraction of the vector directions of the two illumination beams. To measure the displacement in the perpendicular direction, the illumination beams must be rotated 90 degrees around the viewing axis. To make a system sensitive to displacement in two orthogonal directions, two pairs of beams, with different directions, should sequentially illuminate the surface. Thus, two separate interferograms can be recorded and combined vectorially [1; 3; 8; 15]. To avoid cross-interference between the two pairs of beams, they should not illuminate the surface at the same time. Sequential measurement takes more time than usual, making the simultaneous measurement of transient or non-repeatable events, that require displacement in two orthogonal directions, unsuitable. Therefore, an interferometer, capable of measuring two in-plane displacements at the same time, is needed. By using two cameras and two orthogonal polarized dual-beam illumination sets, cross-interference between the two pairs of beams can be avoided, allowing the measurement of the two interferograms at the same time [2]. However, the effectiveness of this method depends on the surface not changing the polarization of the incident beams, which is not always the case [16]. The spatial coherence of the laser can also be used to avoid cross-interference [12].