"Trapezoidal phase-shifting method for three-dimensional shape measurement," Opt. Eng., (2005)

[2] PS Huang, S Zhang, and F-P Chiang, "Trapezoidal phase-shifting method for three-dimensional shape measurement," Opt. Eng. 44(12), 123601, 2005; doi:10.1117/1.2147311

We propose a novel structured light method, namely a trapezoidal phase-shifting method, for 3-D shape measurement. This method uses three patterns coded with phase-shifted, trapezoidalshaped gray levels. The 3-D information of the object is extracted by direct calculation of an intensity ratio. Compared to traditional intensityratio-based methods, the vertical or depth resolution is six times better. Also, this new method is significantly less sensitive to the defocusing effect of the captured images, which makes large-depth 3-D shape measurement possible. If compared to sinusoidal phase-shifting methods, the resolution is similar, but the data processing speed is at least 4.5 times faster. The feasibility of this method is demonstrated in a previously developed real-time 3-D shape measurement system. The reconstructed 3-D results show similar quality to those obtained by the sinusoidal phase-shifting method. However, since the data processing speed is much faster
4.6 ms per frame, both image acquisition and 3-D reconstruction can be done in real time at a frame rate of 40 fps and a resolution of 532
500 points. This real-time capability allows us to measure dynamically changing objects, such as human faces. The potential applications of this new method include industrial inspection, reverse engineering, robotic vision, computer graphics, medical diagnosis, etc.