"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

"Phase error compensation for 3-D shape measurement with projector defocusing," Appl. Opt., (2011)

Y. Xu*, L. Ekstrand*, J. Dai, and S. Zhang, "Phase error compensation for 3-D shape measurement with projector defocusing," Appl. Opt., 50(18), 2572-2581, 2011; doi: 10.1364/AO.50.002572

"Three-dimensional profilometry with nearly focused binary phase-shifting algorithms," Opt. Lett. (2011)

L. Ekstrand* and S. Zhang, "Three-dimensional profilometry with nearly focused binary phase-shifting algorithms," Opt. Lett. 36(23) 4518-4520, 2011  (Cover feature); doi: 10.1364/OL.36.004518

This Letter investigates the effects of different phase-shifting algorithms on the quality of high-resolution three-dimensional (3-D) profilometry produced with nearly focused binary patterns. From theoretical analyses, simulations, and experiments, we found that the nine-step phase-shifting algorithm produces accurate 3-D measurements at high speed without the limited depth range and calibration difficulties that typically plague binary defocusing methods. We also found that the use of more fringe patterns does not necessarily enhance measurement quality.

"Holovideo: Real-time 3D range video encoding and decoding on GPU," Opt. Laser Eng. (2012)

N. Karpinsky* and S. Zhang, "Holovideo: Real-time 3D range video encoding and decoding on GPU," Opt. Laser Eng.50(2), 280-286, 2012; doi: 10.1016/j.optlaseng.2011.08.002

We present a 3D video-encoding technique called Holovideo that is capable of encoding high-resolution 3D videos into standard 2D videos, and then decoding the 2D videos back into 3D rapidly without significant loss of quality. Due to the nature of the algorithm, 2D video compression such as JPEG encoding with QuickTime Run Length Encoding (QTRLE) can be applied with little quality loss, resulting in an effective way to store 3D video at very small file sizes. We found that under a compression ratio of 134:1, Holovideo to OBJ file format, the 3D geometry quality drops at a negligible level. Several sets of 3D videos were captured using a structured light scanner, compressed using the Holovideo codec, and then uncompressed and displayed to demonstrate the effectiveness of the codec. With the use of OpenGL Shaders (GLSL), the 3D video codec can encode and decode in realtime. We demonstrated that for a video size of 512 512, the decoding speed is 28 frames per second (FPS) with a laptop computer using an embedded NVIDIA GeForce 9400 m graphics processing unit (GPU). Encoding can be done with this same setup at 18 FPS, making this technology suitable for applications such as interactive 3D video games and 3D video conferencing. 

"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.

High-resolution, high-speed three-dimensional shape measurement using projector defocusing," Opt. Eng., 2011

[28] Y. Gong* and S. Zhang, "High-resolution, high-speed three-dimensional shape measurement using projector defocusing," Opt. Eng., 50(2), 023603, 2011; doi: 10.1117/1.3534798

We present a high-resolution, high-speed three-dimensional (3-D) shape measurement technique that can reach the speed limit of a digital fringe projection system without significantly increasing the system cost. Instead of generating sinusoidal fringe patterns by a computer directly, they are produced by defocusing binary ones. By this means,with a relatively inexpensive camera, the 3-D shape measurement system can double the previously maximum achievable speed and reach the refreshing rate of a digital-light-processing projector: 120

"High-resolution three-dimensional profilometry with binary phase-shifting methods," Appl. Opt., (2011)

S. Zhang, "High-resolution three-dimensional profilometry with binary phase-shifting methods," Appl. Opt., 50(12), 1753-1757, 2011; doi: 10.1364/AO.50.001753

This paper presents a novel pixel-level resolution 3D profilometry technique that only needs binary phase-shifted structured patterns. This technique uses four sets of three phase-shifted binary patterns to achieve the phase error of less than 0.2%, and only requires two sets to reach similar quality if the projector is slightly defocused. Theoretical analysis, simulations, and experiments will be presented 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. 

"Ultrafast 3-D shape measurement with an off-the-shelf DLP projector," Opt. Express, (2010)

[26] Y. Gong* and S. Zhang, "Ultrafast 3-D shape measurement with an off-the-shelf DLP projector," Opt. Express 18(19), 19743-19754, 2010 (Cover Feature); doi: 10.1364/OE.18.019743

This paper presents a technique that reaches 3-D shape measurement speed beyond the digital-light-processing (DLP) projector’s projection speed. In particular, a “solid-state” binary structured pattern is generated with each micro-mirror pixel always being at one status (ON or OFF). By this means, any time segment of projection can represent the whole signal, thus the exposure time can be shorter than the projection time. A sinusoidal fringe pattern is generated by properly defocusing a binary one, and the Fourier fringe analysis means is used for 3-D shape recovery. We have successfully reached 4,000 Hz rate (80 μs exposure time) 3-D shape measurement speed with an off-the-shelf DLP projector

"High-resolution, real-time 3-D imaging with fringe analysis," Real Time Image Processing, (2012)

[25] N. Karpinsky* and S. Zhang, "High-resolution, real-time 3-D imaging with fringe analysis," Real Time Image Processing,7(1) 55-66, 2012; doi: 10.1007/s11554-010-0167-4

Real-time 3D imaging is becoming increasingly important in areas such as medical science, entertainment, homeland security, and manufacturing. Numerous 3D imaging techniques have been developed, but only a few of them have the potential to achieve realtime. Of these few, fringe analysis based techniques stand out, having many advantages over the rest. This paper will explain the principles behind fringe analysis based techniques, and will provide experimental results from systems using these techniques.

"Composite phase-shifting algorithm for 3-D shape compression," Opt. Eng.. (2010)

[24] N Karpinsky* and S Zhang, "Composite phase-shifting algorithm for 3-D shape compression," Opt. Eng. 49(6), 063604, 2010; doi:10.1117/1.3456632 

With recent advancements in 3-D imaging and computational technologies, acquiring 3-D data is unprecedentedly simple. However, the use of 3-D data is still limited due to the size of 3-D data, especially 3-D video data. Therefore, the study of how to store and transmit the 3-D data in real time is vital. We address a technique that encodes a 3-D surface shape into a single 24-bit color image. In particular, this image is generated by advanced computer graphics tools with two primary color channels encoded as sine and cosine fringe images, and the third channel encoded as a stair image to unwrap the phase obtained from the two fringe images. An arbitrary 3-D shape can then be recovered from a single image. We test 3-D shapes with differing levels of complexity along with various image formats. Experiments demonstrate that, without significantly losing the shape quality, the compression ratio can go up to 1:36.86, compared with the native smallest possible 3-D data representation method.

"Superfast phase-shifting method for 3-D shape measurement," Opt. Express, (2010)

[25] S. Zhang, D. van der Weide, and J. Oliver "Superfast phase-shifting method for 3-D shape measurement," Opt. Express18(9), 9684-9689, 2010. (Selected for July 6, 2010 issue of The Virtual Journal for Biomedical Optics); doi: 10.1364/OE.18.009684

Recently introduced DLP Discovery technology allows for tens of kHz binary image switching, which has great potential for superfast 3-D shape measurement. This paper presents a system that realizes 3-D shape measurement by using a DLP Discovery technology to switch binary structured patterns at very high frame rates. The sinusoidal fringe patterns are generated by properly defocusing the projector. Combining this approach with a phase-shifting method, we achieve an unprecedented rate for 3-D shape measurement: 667 Hz. This technology can be applied to numerous applications including medical science, biometrics, and entertainment.

"Flexible 3-D shape measurement using projector defocusing: extended measurement range," Opt. Lett., (2010)

[23] S. Zhang, "Flexible 3-D shape measurement using projector defocusing: extended measurement range," Opt. Lett. 35(7), 931-933, 2010 (Cover Feature); doi: 10.1364/OL.35.000934

A recently proposed flexible 3D shape measurement technique using a defocused projector [Opt. Lett. 34, 3080 (2009)] shows great potential because of its elimination of projector’s gamma calibration. However, it cannot handle step-height surfaces. I present here a technique to extend its measurement range to an arbitrary shape by integrating a binary coding method. A computational framework is also proposed to tackle the problems related to the defocusing.

"Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques," Opt. Laser Eng., (2010)

[21] S. Zhang, "Recent progresses on real-time 3-D shape measurement using digital fringe projection techniques," Opt. Laser Eng., 48, 149-158, 2010 (Invited). (#2 most cited papers in the past five years 2006-2011, 2007-2012, 2008-2013; #1 most downloaded paper October-December, 2009; January-March, 2010; April-June, 2012; July-September, 2012; January - December 2012 Full Year; January-March, 2013; July-September 2013); doi: 10.1016/j.optlaseng.2009.03.008

Over the past few years, we have been developing techniques for high-speed 3D shape measurement using digital fringe projection and phase-shifting techniques: various algorithms have been developed to improve the phase computation speed, parallel programming has been employed to further increase the processing speed, and advanced hardware technologies have been adopted to boost the speed of coordinate calculations and 3D geometry rendering. We have successfully achieved simultaneous 3D absolute shape acquisition, reconstruction, and display at a speed of 30 frames/s with 300 K points per frame. This paper presents the principles of the real-time 3D shape measurement techniques that we developed, summarizes the most recent progresses that have been made in this field, and discusses the challenges for advancing this technology further.

"Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm," Opt. Eng., (2009)

[19] S Zhang, "Phase unwrapping error reduction framework for a multiple-wavelength phase-shifting algorithm," Opt. Eng.,48(10), 105601, 2009 (Accepted without revision); doi:10.1117/1.3251280

We address a framework to reduce the unwrapping errors of the measurement system using a digital multiple-wavelength phaseshifting algorithm. In particular, the following framework is proposed:
1 smooth the raw phase by smoothing the sine and cosine images of the phase computation of the inverse tangent function;
2 locate and remove the incorrectly unwrapped points by the monotonicity condition of the phase map;
3 obtain the unwrapped phase map for the shortest wavelength without smoothing;
4 detect holes and fill them to preserve as much useful information as possible. Experiments demonstrated that the proposed framework significantly alleviated the measurement errors caused by the phase noise. 

"Flexible 3-D shape measurement using projector defocusing," Opt. Lett., (2009)

[20] S Lei* and S Zhang, "Flexible 3-D shape measurement using projector defocusing," Opt. Lett. 34(20),3080-3082, 2009;doi: 10.1364/OL.34.003080

We present a 3-D shape-measurement technique using a defocused projector. The ideal sinusoidal fringe patterns are generated by defocusing binary structured patterns, and the phase shift is realized by shifting the binary patterns spatially. Because this technique does not require calibration of the gamma of the projector, it is easy to implement and thus is promising for developing flexible 3-D shape measurement systems using digital video projectors. 

"High dynamic range scanning technique," Opt. Eng., (2009)

[18] S Zhang and S-T Yau, "High dynamic range scanning technique," Opt. Eng. 48(3), 033604, 2009; doi: 10.1117/1.3099720

Measuring objects with a high variation range of surface reflectivity is challenging for any optical method: This paper addresses a high dynamic range scanning technique that can measure this type of object. It takes advantage of one merit of a phase-shifting algorithm: pixel-by-pixel phase retrieval. For each measurement, a sequence of fringe images with different exposures are taken: the brightest ones have good fringe quality in the darkest areas while the darkest ones have good fringe quality in the brightest areas. They are arranged from brighter to darker
i.e., from higher exposure to lower exposure. The final fringe images, used for phase retrieval, are produced pixel-by-pixel by choosing the brightest but unsaturated corresponding pixel from one exposure. A phase-shifting algorithm is employed to compute the phase, which can be further converted to coordinates. Our experiments demonstrate that the proposed technique can successfully measure objects with high dynamic range of surface reflectivity variation. 
 

"Digital sinusoidal fringe generation: defocusing binary patterns VS focusing sinusoidal patterns," Opt. Laser, (2010)

[22] S. Lei* and S. Zhang, "Digital sinusoidal fringe generation: defocusing binary patterns VS focusing sinusoidal patterns,"Opt. Laser Eng. 48, 561-569, 2010; doi: 10.1016/j.optlaseng.2009.12.002

There are two approaches to generate sinusoidal fringe patterns with a digital-light-processing (DLP) projector: defocusing binary patterns (DBP), and focusing sinusoidal patterns (FSP). This paper will compare the potential errors for both methods induced by the following factors: (1) degree of defocusing, (2) exposure time, (3) synchronization, and (4) projector’s nonlinear gamma. Experiments show that in most scenarios, the error for the DBP method is smaller than that of the FSP method. Therefore, generating a sinusoidal fringe image using a DBP method seems to be appealing.