"Phase error compensation for a 3-D shape measurement system based on the phase shifting method," Opt. Eng., (2007)

[10] S Zhang and PS Huang, "Phase error compensation for a 3-D shape measurement system based on the phase shifting method," Opt. Eng., 46(6), 063601, 2007; doi:10.1117/1.2746814

This paper describes a novel phase error compensation method for reducing the measurement error caused by nonsinusoidal waveforms in phase-shifting methods. For 3-D shape measurement systems using commercial video projectors, the nonsinusoidal waveform of the projected fringe patterns as a result of the nonlinear gamma of projectors causes significant phase measurement error and therefore shape measurement error. The proposed phase error compensation method is based on our finding that the phase error due to the nonsinusoidal waveform depends only on the nonlinearity of the projector’s gamma. Therefore, if the projector’s gamma is calibrated and the phase error due to the nonlinearity of the gamma is calculated, a lookup table that stores the phase error can be constructed for error compensation. Our experimental results demonstrate that by using the proposed method, the measurement error can be reduced by 10 times. In addition to phase error compensation, a similar method is also proposed to correct the nonsinusoidality of the fringe patterns for the purpose of generating a more accurate flat image of the object for texture mapping. While not relevant to applications in metrology, texture mapping is important for applications in computer vision and computer graphics.

"High-resolution real-time three-dimensional shape measurement," Opt. Eng., (2006)

[7] S Zhang and PS Huang, "High-resolution real-time three-dimensional shape measurement," Opt. Eng., 45(12), 123601, 2006 ; doi: 10.1117/1.2402128 

We describe a high-resolution, real-time 3-D shape measurement system based on a digital fringe projection and phase-shifting technique. It utilizes a single-chip digital light processing projector to project computer-generated fringe patterns onto the object, and a high-speed CCD camera synchronized with the projector to acquire the fringe images at a frame rate of 120 frames/ s. A color CCD camera is also used to capture images for texture mapping. Based on a three-step phaseshifting technique, each frame of the 3-D shape is reconstructed using three consecutive fringe images. Therefore the 3-D data acquisition speed of the system is 40 frames/ s. With this system, together with the fast three-step phase-shifting algorithm and parallel processing software we developed, high-resolution, real-time 3-D shape measurement is realized at a frame rate of up to 40 frames/ s and a resolution of 532
500 points per frame

"Novel method for structured light system calibration," Opt. Eng., (2006)

[4] S Zhang and PS Huang, "Novel method for structured light system calibration," Opt. Eng., 45(8), 083601, 2006; doi:10.1117/1.2336196

System calibration, which usually involves complicated and time-consuming procedures, is crucial for any 3-D shape measurement system. In this work, a novel systematic method is proposed for accurate and quick calibration of a 3-D shape measurement system we developed based on a structured light technique. The key concept is to enable the projector to “capture” images like a camera, thus making the calibration of a projector the same as that of a camera. With this new concept, the calibration of structured light systems becomes essentially the same as the calibration of traditional stereovision systems, which is well established. The calibration method is fast, robust, and accurate. It signifi- cantly simplifies the calibration and recalibration procedures of structured light systems. This work describes the principle of the proposed method and presents some experimental results that demonstrate its performance.

"Fast three-step phase-shifting algorithm," Appl. Opt., (2006)

[3] PS Huang and S Zhang, "Fast three-step phase-shifting algorithm," Appl. Opt., 45(21), 5086-5091, 2006 (Cover Feature); doi: 10.1364/AO.45.005086

We propose a new three-step phase-shifting algorithm, which is much faster than the traditional three-step algorithm. We achieve the speed advantage by using a simple intensity ratio function to replace the arctangent function in the traditional algorithm. The phase error caused by this new algorithm is compensated for by use of a lookup table. Our experimental results show that both the new algorithm and the traditional algorithm generate similar results, but the new algorithm is 3.4 times faster. By implementing this new algorithm in a high-resolution, real-time three-dimensional shape measurement system, we were able to achieve a measurement speed of 40 frames per second at a resolution of 532
500 pixels, all with an ordinary personal computer.

"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.