"Motion induced phase error reduction using a Hilbert transform," Opt. Express (2018)

 [117] Y. Wang, Z. Liu, and C. Jiang, and S. Zhang, "Motion induced phase error reduction using a Hilbert transform," Opt. Express 26(26), 34224-34235 (2018); doi:10.1364/OE.26.034224

Abstract

The motion of object could introduce phase error and thus measurement error for phase-shifting profilometry. This paper proposes a generic motion error compensation method based on our finding that the dominant motion introduced phase error doubles the frequency of the projected fringe frequency, and Hilbert transform shifts the phase of a fringe pattern by $\pi/2$. We apply Hilbert transform to phase-shifted fringe patterns to generate another set of fringe patterns, calculate one phase map using the original fringe patterns and another phase map using Hilbert transformed fringe patterns, and then use the average of these two phase maps for 3D reconstruction. Both simulation and experiments demonstrated the proposed method can substantially reduce motion-introduced measurement error.

"Double-pattern triangular pulse width modulation technique for high-accuracy high-speed 3D shape measurement," Opt. Express (2017)

Y. Wang, C. Jiang, and S. Zhang, "Double-pattern triangular pulse width modulation technique for high-accuracy high-speed 3D shape measurement," Opt. Express 25(24), 30177-30188 (2017); doi:10.1364/OE.25.03177

Abstract

Using 1-bit binary patterns for 3D shape measurement has been demonstrated advantageous over using  8-bit sinusoidal patterns in terms of achievable speeds. However, the phase quality generated by binary pattern(s) typically  is not  high if only a small number of phase-shifted patterns is used. This paper proposes a method to improve the phase quality  by representing each pattern with the difference of two binary patterns:  the first binary pattern is generated by triangular pulse width modulation (TPWM) technique, and the second being $\pi$ shifted from the first pattern is also generated by TPWM technique. The phase is retrieved by applying a three-step phase-shifting algorithm to the difference patterns. Through optimizing the modulation frequency of the  triangular carrier signal, we demonstrate that high-quality phase can be generated for a wide range of fringe periods (e.g., from 18 to 1140 pixels) with only six binary patterns. Since only 1-bit binary patterns are required for 3D shape measurement, this paper will present a real-time 3D shape measurement system that can achieve 30 Hz.

"Digital micromirror transient response influence on superfast 3D shape measurement," Opt. Laser Eng., (2014)

[63] Y. Wang*, B.  Bhattacharya, E. H. Winer, P. Kosmicki, W. H. El-Ratal, and S. Zhang, "Digital micromirror transient response influence on superfast 3D shape measurement," Opt. Laser Eng. 58, 19-26, 2014; doi: 10.1016/j.optlaseng.2014.01.015

Abstract

Nowadays, the high speed (e.g., kilo-Hertz) refreshing rate of the digital micro-mirror device (DMD) has enabled superfast 3D shape measurement using the binary defocusing technique. This research finds that when the system reaches its extreme binary pattern refreshing rate, the transient response of the DMD induces a coupling effect (i.e., two neighboring patterns blend together) that may cause substantial measurement error. Since this transient response repeats itself, this systematic measurement error is substantially reduced to a negligible level when the timing between the projector and the camera is properly adjusted. Experimental results are presented to demonstrate the observed phenomena, and the success of utilizing the proposed method to overcome the problems associated with the transient response of the DMD.

"High-resolution, high-speed, three-dimensional video imaging with digital fringe projection techniques," Journal of Visualized Experiments, (2013)

L. Ekstrand*, N. Karpinsky*, Y. Wang*, and S. Zhang, "High-resolution, high-speed, three-dimensional video imaging with digital fringe projection techniques," Journal of Visualized Experiments (JoVE), (82), e50421, 2013. (Associated with Video Illustrations) (invited); doi: 10.3791/50421

Digital fringe projection (DFP) techniques provide dense 3D measurements of dynamically changing surfaces. Like the human eyes and brain, DFP uses triangulation between matching points in two views of the same scene at different angles to compute depth. However, unlike a stereo-based method, DFP uses a digital video projector to replace one of the cameras. The projector rapidly projects a known sinusoidal pattern onto the subject, and the surface of the subject distorts these patterns in the camera’s field of view. Three distorted patterns (fringe images) from the camera can be used to compute the depth using triangulation.

Unlike other 3D measurement methods, DFP techniques lead to systems that tend to be faster, lower in equipment cost, more flexible, and easier to develop. DFP systems can also achieve the same measurement resolution as the camera. For this reason, DFP and other digital structured light techniques have recently been the focus of intense research (as summarized in1-5). Taking advantage of DFP, the graphics processing unit, and optimized algorithms, we have developed a system capable of 30 Hz 3D video data acquisition, reconstruction, and display for over 300,000 measurement points per frame. Binary defocusing DFP methods can achieve even greater speeds.

Diverse applications can benefit from DFP techniques. Our collaborators have used our systems for facial function analysis9, facial animation10, cardiac mechanics studies11, and fluid surface measurements, but many other potential applications exist. This video will teach the fundamentals of DFP techniques and illustrate the design and operation of a binary defocusing DFP system.

"Optimal fringe angle selection for digital fringe projection technique," Appl. Opt., (2013)

[55] Y. Wang*, and S. Zhang, "Optimal fringe angle selection for digital fringe projection technique," Appl. Opt. 52(29),  7094-7098, 2013; doi: 10.1364/AO.52.007094

Abstract

Existing digital fringe projection (DFP) systems mainly use either horizontal or vertical fringe patterns for three-dimensional shape measurement. This paper reveals that these two fringe directions are usually not optimal where the phase change is the largest to a given depth variation. We propose a novel and efficient method to determine the optimal fringe angle by projecting a set of horizontal and vertical fringe patterns onto a step-height object and by further analyzing two resultant phase maps. Experiments demonstrate the existence of the optimal angle and the success of the proposed optimal angle determination method.

"Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques," Opt. Laser Eng. 2014

B. Li*, Y. Wang*, J. Dai, and W. Lohry*, and S. Zhang, "Some recent advances on superfast 3D shape measurement with digital binary defocusing techniques," Opt. Laser Eng. 54, 236-246, 2014 (invited); doi:10.1016/j.optlaseng.2013.07.010

The digital binary phase-shifting technique has been demonstrated for its merits over the conventional sinusoidal phase-shifting method in terms of measurement speed and simplicity. Yet, the measurement depth range is small when a squared binary method is used. Our recent research focuses on improving its measurement accuracy without sacrificing measurement speed, and increasing its depth range without losing measurement quality. This paper will summarize our recent work on the following three major areas: (a) realization of kHz 3D shape measurement with binary phase-shifting methods; (b) binary pattern improvement with pulse width modulation and binary dithering/halftoning techniques; and (c) applications of superfast 3D shape measurement techniques. Principle of each technique will be presented, and experimental results will be shown to verify its performance.

"Flexible real-time natural 2D color and 3D shape measurement," Opt. Express, 2013;

P. Ou, B. Li*, Y. Wang*, and S. Zhang, "Flexible real-time natural 2D color and 3D shape measurement," Opt. Express,21(14), 16736-16741, 2013; doi: 10.1364/OE.21.016736

The majority of existing real-time 3D shape measurement systems only generate non-nature texture (i.e., having illumination other than ambient lights) that induces shadow related issues. This paper presents a method that can simultaneously capture natural 2D color texture and 3D shape in real time. Specifically, we use an infrared fringe projection system to acquire 3D shapes, and a secondary color camera to simultaneously capture 2D color images of the object. Finally, we develop a flexible and simple calibration technique to determine the mapping between the 2D color image and the 3D geometry. Experimental results demonstrate the success of the proposed technique.  

"Three bit representation of three-dimensional range data," Appl. Opt. , (2013)

[54] N. Karpinsky*, Y. Wang*, and S. Zhang, "Three bit representation of three-dimensional range data," Appl. Opt. 52(11), 2286-2293, 2013; doi: 10.1364/AO.52.002286

Abstract

Our previous research has shown that 3D range data sizes can be substantially reduced if they are converted into regular 2D images using the Holoimage technique. Yet, this technique requires all 24 bits of a standard image to represent one 3D point, making it impossible for a regular 2D image to carry 2D texture information as well. This paper proposes an approach to represent 3D range data with 3 bits, further reducing the data size. We demonstrate that more than an 8.2∶1 compression ratio can be achieved with compression root-mean-square error of only 0.34%. Moreover, we can use another bit to represent a black-and-white 2D texture, and thus both 3D data and 2D texture images can be stored into an 8 bit grayscale image. Both simulation and experiments are presented to verify the performance of the proposed technique.

"3D absolute shape measurement of live rabbit hearts with a superfast two-frequency phase-shifting technique," Opt. Express , (2013)

[52] Y. Wang*, J. I. Laughner, I. R. Efimov, and S. Zhang, "3D absolute shape measurement of live rabbit hearts with a superfast two-frequency phase-shifting technique," Opt. Express 21(5), 5822-5832, 2013 (Cover feature)  (Selected for May 22, 2013 issue of The Virtual Journal for Biomedical Optics); doi: 10.1364/OE.21.005822

Abstract

This paper presents a two-frequency binary phase-shifting technique to measure three-dimensional (3D) absolute shape of beating rabbit hearts. Due to the low contrast of the cardiac surface, the projector and the camera must remain focused, which poses challenges for any existing binary method where the measurement accuracy is low. To conquer this challenge, this paper proposes to utilize the optimal pulse width modulation (OPWM) technique to generate high-frequency fringe patterns, and the error-diffusion dithering technique to produce low-frequency fringe patterns. Furthermore, this paper will show that fringe patterns produced with blue light provide the best quality measurements compared to fringe patterns generated with red or green light; and the minimum data acquisition speed for high quality measurements is around 800 Hz for a rabbit heart beating at 180 beats per minute.

"Accurate calibration for 3D shape measurement system using a binary defocusing technique," Opt. Laser Eng., (2013)

L. Merner*, Y. Wang*, and S. Zhang, "Accurate calibration for 3D shape measurement system using a binary defocusing technique," Opt. Laser Eng. 51(5), 514-519, 2013; doi: 10.1016/j.optlaseng.2012.10.015

This paper introduces a novel method to calibrate 3D shape measurement systems that use the binary defocusing technique. Specifically, this method calibrates the pixelwise z as low-order polynomial functions of absolute phase; (x, y) coordinates are calculated from camera calibration with known z value; and the camera is calibrated using the standard flat checkerboard method. Because this method does not require estimation of the projector’s parameters, it can be adopted for any phase measurement system including those employing out-of-focus projectors. Our experiment found that the root-mean squared (rms) error for the depth measurement is less than 70 mm when the measurement depth range is about 100 mm, which is at the same level of the calibration stage +-50 mm.

"Three-dimensional shape measurement with binary dithered patterns," Appl. Opt.,(2012)

Y. Wang* and S. Zhang, "Three-dimensional shape measurement with binary dithered patterns," Appl. Opt. 51(27), 6631-6636, 2012; doi: 10.1364/AO.51.006631

The previously proposed binary defocusing technique and its variations have proven successful for high-quality three-dimensional (3D) shape measurement when fringe stripes are relatively narrow, but they suffer if fringe stripes are wide. This paper proposes to utilize the binary dithering technique to conquer this challenge. Both simulation and experimental results show the phase error is always less than 0.6% even when the fringe stripes are wide and the projector is nearly focused.

"Novel phase coding method for absolute phase retrieval," Opt. Lett., (2012)

Y. Wang* and S. Zhang, "Novel phase coding method for absolute phase retrieval," Opt. Lett. 37(11), 2067-2069, 2012;doi: 10.1364/OL.37.002067

This Letter presents a novel absolute phase recovery technique with phase coding. Unlike the conventional graycoding method, the codeword is embedded into the phase and then used to determine the fringe order for absolute phase retrieval. This technique is robust because it uses phase instead of intensity to determine codewords, and it could achieve a faster measurement speed, since three additional images can represent more than 8
 unique codewords for phase unwrapping. Experimental results will be presented to verify the performance of the proposed technique. 

"Comparion among square binary, sinusoidal pulse width modulation, and optimal pulse width modulation methods for three-dimensional shape measurement," Appl. Opt. (2012)

Y. Wang* and S. Zhang, "Comparion among square binary, sinusoidal pulse width modulation, and optimal pulse width modulation methods for three-dimensional shape measurement," Appl. Opt. 51(7), 861-872, 2012; doi:10.1364/AO.51.000861

This paper presents a comparative study on three sinusoidal fringe pattern generation techniques with projector defocusing: the squared binary defocusing method (SBM), the sinusoidal pulse width modulation (SPWM) technique, and the optimal pulse width modulation (OPWM) technique. Because the phase error will directly affect the measurement accuracy, the comparisons are all performed in the phase domain. We found that the OPWM almost always performs the best, and SPWM outperforms SBM to a great extent, while these three methods generate similar results under certain conditions. We will briefly explain the principle of each technique, describe the optimization procedures for each technique, and finally compare their performances through simulations and experiments. © 2012 Optical Society of America

"Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing: Reply to comments," Opt. Lett. (2011)

Y. Wang* and S. Zhang, "Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing: Reply to comments," Opt. Lett. 36(6), 809-809, 2011; doi: 10.1364/OL.36.000809

We found that there were some inaccurate comments in the Comment by Ayubi and Ferrari.

"3D shape measurement technique for multiple rapidly moving objects," Opt. Express, (2011)

Y. Wang*, S. Zhang, and J. H. Oliver, "3D shape measurement technique for multiple rapidly moving objects," Opt. Express,  19(9), 8539-8545, 2011; doi: 10.1364/OE.19.008539

Recently proposed binary defocusing techniques have led to ultrafast speed 3D shape measurement, but they are generally limited to measurement of a single object at a time. Introducing additional gray coded patterns for point-by-point phase unwrapping could permit simultaneous multiple-object measurement. However, when the objects are moving rapidly, the displacement between the first captured pattern and the last can be significant, and pose challenges related to the precisely designed gray codes. This paper presents a new phase unwrapping strategy that combines the conventional spatial phase unwrapping with the gray code to resolve motion related phase unwrapping problems. A system with a speed of 5,000 Hz was developed to verify the performance of the proposed technique.

"Superfast multifrequency phase-shifting technique with optimal pulse width modulation," Opt. Express, (2011)

Y. Wang* and S. Zhang, "Superfast multifrequency phase-shifting technique with optimal pulse width modulation," Opt. Express, 19(6), 5143-5148, 2011(Image of the week of March 21, 2011, OSA Optics InfoBase); doi: 10.1364/OE.19.005149

The technique of generating sinusoidal fringe patterns by defocusing squared binary structured ones has numerous merits for high-speed three-dimensional (3D) shape measurement. However, it is challenging for this method to realize a multifrequency phase-shifting (MFPS) algorithm because it is difficult to simultaneously generate high-quality sinusoidal fringe patterns with different periods. This paper proposes to realize an MFPS algorithm utilizing an optimal pulse width modulation (OPWM) technique that can selectively eliminate high-order harmonics of squared binary patterns. We successfully develop a 556 Hz system utilizing a three-frequency algorithm for simultaneously measuring multiple objects. 

"Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing," Opt. Lett., (2010)

[27] Y. Wang* and S. Zhang, " Optimal pulse width modulation for sinusoidal fringe generation with projector defocusing," Opt. Lett.,  35(24), 4121-4123, 2010; doi: 10.1364/OL.35.004121

Recently, a study showed that generating sinusoidal fringe patterns by properly defocusing binary ones can significantly simplify three-dimensional shape measurement system development and drastically improve its speed. However, when the fringe stripes are very wide, it is very difficult for this technique to achieve high-quality measurement. This Letter presents a method to improve this technique by selectively eliminating high-frequency harmonics induced by a squared binary pattern. As a result, better sinusoidal fringe patterns can be generated with a small degree of defocusing even for wide fringe stripes. Simulation and experiments will be presented to verify the performance of this proposed technique.