Fringe projection profilometry can provide high-speed surface inspection and 3D-shape-measurement capabilities. It has wide applications in the automotive, aerospace, semiconductor, and other industries. In particular, the application of this technology to product-quality inspection and process control can yield tremendous cost savings and reduce lead times

Fringe projection profilometry is based on the principle that periodic fringe patterns can be projected onto an object's surface, and the distorted patterns caused by its depth variation recorded from different directions. The phase distributions of these patterns are often recovered by phase-shifting techniques^{1,2} or methods based on Fourier-transformation analysis. To reconstruct the object surface, an algorithm must convert the phase map into coordinates, a process know as system calibration.

Two phase-height calibration techniques are commonly used in fringe projection profilometry:^{3,4} unwrapping the phase continuously along its vertical orientation and absolute phase calibration.^{5,6} The former depends on the phase difference between neighboring calibration planes. Absolute phase calibration, on the other hand, introduces an additional image that is used to determine special reference points where phase is constant for all calibration planes. Though the point coordinates in the phase map are usually decimal, it is common to determine the phase-height relationship by the integer coordinate of the point. Unfortunately, this degrades the system accuracy greatly.

We have introduced a linear interpolation in the absolute phase calibration algorithm to improve system accuracy. During calibration, a circle point is projected onto the object to get the special points, as shown in Figure 1. We can obtain the reference-point coordinates (*x*_{n}, *y*_{n}), which are decimal and have unknown phase. However, because the phases of the points four neighboring pixels are known, as shown in Figure 2, linear interpolation can be used to determine its absolute phase. The absolute unwrapping phase of the calibration planes can then be obtained and the phase-height look-up table decided.

**Figure 1.** Calibration involves the identification of special reference points where the phase is constant for all calibration planes.

**Figure 2.** The linear interpolation algorithm is used to get the reference point's absolute phase from the phases of its four neighbors.

Two 15mm planes were measured using different calibration techniques: the conventional algorithm and the linear interpolation algorithm. The results were as follows:

Compared with the conventional algorithm, therefore, ours has improved measurement accuracy.

Shuangyun Shao, Hao Yu

Beijing Jiaotong University

Beijing, China