Shape measurement for BGA using whole-space tabulation method with FPGA memory board

Whole-space tabulation method (WSTM) is a technique to relate the phase of a projected grating and the coordinates at each pixel of a camera. The relation data of all the pixels are obtained in the whole-space where a reference plane is moved. The relation data are stored in tables. Thereby, WSTM is high speed and accurate shape measurement method because the coordinates are obtained by only looking up the tables without any complex calculation. Even when the brightness distribution of the projected grating is warped from a cosinusoidal wave, correct coordinates are provided. However, the WSTM needs huge memories for the phase-coordinate tables such as 10 GB in the case of a VGA image and 2000 tables at each pixel. Therefore, we developed an FPGA memory board to store the table and to refer the table in real-time. In the case of a ball grid array (BGA), it is necessary to measure the shape of the balls with high accuracy and high speed without the influence of halation. It is also necessary to measure the coplanarity of the balls without distortion. The influence of halation can be reduced with combining the 3D shape measured with several cameras set at different positions. It is easy to realize them using the WSTM. In this paper, it is confirmed that accurate shape measurements for a BGA can be performed using the WSTM with an FPGA memory board.