# Metrology for Measuring Bumps in a Protection Layer Based on Phase Shifting Fringe Projection
## 1 Introduction  
The development of optical 3D shape measurement methods is rapidly gaining importance in the manufacturing industry due to its capability of measuring and reconstructing real 3D moving objects [1, 2, 3, 4]. Three-dimensional information about shaped objects on silicon wafers, printed circuit boards, or flat panel displays can be obtained in various ways that offer different tradeoffs between speed and resolution/accuracy. Triangulation is often used for the 3D reconstruction of production-worthy metrology [5, 6, 7]. The laser scanning and structured light methods are the two mainstream approaches based on the geometric triangulation principle for determining actual object shapes with high economic performance. In laser scanning, a laser line is projected onto a reference surface and the target object. The absolute positions of both lines on the imaging sensor plane are compared to provide 3D information on the object via a height map. The other widely used method is fringe projection, which encodes the depth information via the deformation of a known fringe pattern projection. Conventional applications have led to the conclusion that, when the same detector is employed for both methods, laser scanning offers superior throughput, while fringe projection has better displacement sensitivity [8]. Several studies have addressed improving the measurement speed and precision of the fringe projection technique to meet the full wafer inspection requirements of the advanced packaging industry [9, 10, 11]. The phase-shifting technique is based on using multiple projections of various stripe patterns to provide continuous phase maps and is the most well-known method for obtaining the absolute phase and corresponding object height. A three-step phase-shifting algorithm is the optimal choice because it requires the minimum number of fringe images for real-time 3D measurement. In most cases, three fringe patterns with a 120\({}^{\circ}\) phase shift to each other are sequentially projected onto the object by a projector, and an area camera is calibrated to grab fringe images of the object. Then, a phase map can be calculated from every three fringe images by phase-wrapping and unwrapping algorithms and is used to decode the 3D shape. Conventional phase shifting method was concerned by the issues of time consuming and limited framerate. A three-row line scan camera has been tested in our previous system setup that was designed to simultaneously acquire three fringe images with a 120\({}^{\circ}\) phase shift in separate rows to achieve continuous scanning and high accuracy in real-time measurement. However, hardware system parameters including the fringe density, fringe projection angle, and magnifications of the projection lens and image collection lens all need to be accurately calculated and strictly adjusted to meet the requirements of the designed phase-shifting algorithm. Three-dimensional imaging systems based on the fringe projection technique measure the absolute phase corresponding to the 3D shape of an object surface. To obtain the shape of the measured object, the absolute phase needs to be converted into depth data. When a small object is being measured, however, the distortion of an ordinary lens complicates the calibration. The inherently nonlinear and spatially variable relationship between the absolute phase of the projected fringe and the object surface depth is an issue for fringe projection technology involving high-accuracy metrology. Telecentric lens with the characteristics of low distortion, better magnification consistency and increased field depth has been proposed as a solution because the size of the object does not change with depth in telecentric imaging; thus, the absolute phase is linear with the depth, which simplifies the calibration process [12; 13; 14; 15; 16; 17; 18; 19].