Superfast three-dimensional (3D) shape measurement with binary defocusing techniques and its applications

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Wang, Yajun
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Song Zhang
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Mechanical Engineering
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High-speed and high-accuracy three-dimensional (3D) shape measurement has enormous potential to benefit numerous areas including advanced manufacturing, medical imaging, and diverse scientific research fields. For example, capturing the rapidly pulsing wings of a flying insect could enhance our understanding of flight and lead to better and safer aircraft designs. Even though there are numerous 3D shape measurement techniques in the literature, it remains extremely difficult to accurately capture rapidly changing events.

Due to the potential for achieving high speed and high measurement accuracy, the digital fringe projection (DFP) techniques have been exhaustively studied and extensively applied to numerous disciplines. Real-time (30 Hz or better) 3D shape measurement techniques have been developed with DFP methods, yet the upper speed limit is typically 120 Hz, the refresh rate of a typical digital video projector. 120 Hz speed can accurately measure the slowly changing objects, such as human facial expressions, but it is far from sufficient to capture high-speed motions (e.g., live, beating hearts or flying insects). To overcome this speed limitation, the binary defocusing technique was recently proposed. Instead of using 8-bit sinusoidal patterns, the binary defocusing technique generates sinusoidal patterns by properly defocusing squared 1-bit binary patterns. Using this technique, kilo-Hertz (kHz) 3D shape measurement rate has been achieved. However, the binary defocusing technique suffers three major limitations: 1) low phase quality due to the influence of high-frequency harmonics; 2) smaller depth measurement range; and 3) low measurement accuracy due to the difficulty of applying existing calibration methods to the system with an out-of-focus projector.

The goal of this dissertation research is to achieve superfast 3D shape measurement by overcoming the major limitations of the binary defocusing technique. Once a superfast 3D shape measurement platform is developed, numerous applications could be benefited. To this end, this dissertation research look into verifying its value by applying to the biomedical engineering field. Specifically, this dissertation research has made major contributions by conquering some major challenges associated with the binary defocusing technique.

The first challenge this dissertation addresses is associated with the limited depth range and low phase quality of the binary defocusing method. The binary defocusing technique essentially generates quasi-sinusoidal fringe patterns by suppressing high-frequency harmonics through lens defocusing. However, the optical engines of the majority of digital video projectors are designed and optimized for applications with large depth of focus; for this reason, good quality sinusoids can only be generated by this technique within a very small depth region. This problem is exacerbated if the fringe stripes are wide. In that case, the high-frequency harmonics cannot be properly suppressed through defocusing, making it almost impossible to generate reasonable quality sinusoids.

To alleviate this problem associated with high-frequency harmonics, an optimal pulse width modulation (OPWM) method, developed in power electronics, is proposed to improve the fringe pattern quality. Instead of projecting squared binary structures, the patterns are optimized, in one dimension perpendicular to the fringe stripes, by selectively eliminating the undesired harmonics which affect the phase quality the most. Both simulation and experimental data demonstrate that the OPWM method can substantially improve the squared binary defocusing technique when the fringe periods are between 30-300 pixels. With this technique, a multi-frequency phase-shifting algorithm is realized that enables the development of a 556-Hz 3D shape measurement system capable of capturing multiple rapidly moving objects.

The OPWM technique is proved successful when the fringe stripe widths are within a certain range, yet it fails to achieve higher-quality fringe patterns when the desired fringe period goes beyond the optimal range. To further improve the binary defocusing technique, binary dithering techniques are proposed. Unlike the OPWM method, the dithering technique optimizes the patterns in both x and y dimensions, and thus can achieve higher-quality fringe patterns. This research demonstrates the superiority of this technique over all aforementioned binary defocusing techniques for high-quality 3D shape measurement even when the projector is nearly focused and the fringe stripes are wide.

The second challenge this dissertation addresses is accurately calibrating the DFP system with an out-of-focus projector. The binary defocusing technique generates quasi-sinusoidal patterns through defocusing, and thus the projector cannot be perfectly in focus. In the meantime, state-of-the-art DFP system calibration assumes that the projector is always in focus. To address this problem, a novel calibration method is proposed that directly relates depth z with the phase pixel by pixel without the requirement of projector calibration. By this means, very high accuracy depth measurement is achieved: for a depth measurement range of 100 mm, the root-mean-squared (rms) error is approximately 70 &mu m.

The third challenge this dissertation addresses is associated with the hardware limitation for the superfast 3D shape measurement technique. The high refresh rate of the digital micro-mirror device (DMD) has enabled superfast 3D shape measurement, yet a hardware limitation has been found once the speeds go beyond a certain range. This is because the DMD cannot completely turn on/off between frames, leading to coupling problems associated with the transient response of the DMD chip. The coupling effect causes substantial measurement error during high-speed measurement. Fortunately, since this type of error is systematic, this research finds that such error can be reduced to a negligible level by properly controlling the timing of the projector and the camera.

The superfast 3D shape measurement platform developed in this research could benefit numerous applications. This research applies the developed platform to the measurement of the cardiac motion of live, beating rabbit hearts. The 3D geometric motion of the live, beating rabbit hearts can be successfully captured if the measurement speed is sufficiently fast (i.e. 200 Hz or higher for normal beating rabbit hearts). This research also finds that, due to the optical properties of live tissue, caution should be given in selecting the spectrum of light in order to properly measure the heart surface.

In summary, the improved binary defocusing techniques are overwhelmingly advantageous compared to the conventional sinusoidal projection method or the squared binary defocusing technique. We believe that the superfast 3D shape measurement platform we have developed has the potential to broadly impact many more academic studies and industrial practices, especially those where understanding the high-speed 3D phenomena is critical.

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Tue Jan 01 00:00:00 UTC 2013