Error compensation in two-step triangular-pattern phase-shifting profilometry

Jia, Peirong; Kofman, Jonathan; English, Chad

doi:10.1016/j.optlaseng.2007.11.004

Cited by 25 publications

(14 citation statements)

References 15 publications

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“…The literature on phase error is divided into three categories, namely, harmonic compensation methods [4], phase-shifting compensation methods [1][2][3]5,14], and gamma model compensation methods [6][7][8][9][10][11][12][13][14][15][16][17][18]. The gamma model compensation methods are currently a significant and challenging research focus.…”

Section: Introductionmentioning

confidence: 99%

Digital fringe image gamma modeling and new algorithm for phase error compensation

Cui

Zhao

et al. 2014

Optik

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Section: Introductionmentioning

confidence: 99%

Digital fringe image gamma modeling and new algorithm for phase error compensation

Cui

Zhao

et al. 2014

Optik

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“…Secondly, phase calculation is different, with our method being based on the calculation of an arctangent function of the phase, whereas the triangular method computes the intensity ratio to obtain the phase. Thirdly, our method is immune to the non-sinusoidal phase error, whereas the measurement accuracy of the triangular method is limited by the gamma nonlinearity [6] . Two traditional sinusoidal fringes are tested to compare the performance of the proposed approach and the traditional phase-shifting fringe methods.…”

mentioning

confidence: 99%

“…These methods have a simple computation for the intensity ratio and rapid calculation speed. However, they are highly sensitive to noise, nonlinearities, and projector and camera defocus [6] . Our proposed method and the triangular pattern method differ in three ways.…”

mentioning

confidence: 99%

Linear sinusoidal phase-shifting method resistant to non-sinusoidal phase error

Cui¹,

Liao²,

Dai³

et al. 2012

中国光学快报

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Non-sinusoidal phase error is common in structured light three-dimensional (3D) shape measurement system, thus we perform theoretical and experimental analyses of such error. The number of non-sinusoidal waveform errors in a 2π phase period is the same as the number of steps of the phase-shifting algorithm; no errors occur within the one-phase period. Based on our findings, a new structured light method, the linear sinusoidal phase-shifting method (LSPS), that is resistant to non-sinusoidal phase error is proposed. Experiments show that the non-sinusoidal waveform error is reduced to an almost negligible level (0.001 rad) using the proposed LSPS.OCIS Optical non-contact three-dimensional (3D) shape measurement techniques have been developed to obtain 3D contours. With the recent advancement in digital display technology, 3D shape measurement based on digital projection units has been rapidly expanding [1−2] . However, the challenge remains to be in area of developing a system with an off-the-shelf projector, such as liquid crystal display (LCD) and digital mirror device (DMD), for high-quality 3D shape measurement. One of the major issues is the nonlinear response of the projection engines of projectors [1−10] . Projector gamma calibration is usually needed to perform high-quality 3D shape measurement using a digital fringe projection and phase-shifting method [2−10] . This is because the commonly used commercial video projector is a nonlinear device purposely designed to compensate for human vision [7] . A variety of techniques have been developed for nonlinear phase errors [2−12] . These include the two-step triangular-pattern phase-shifting algorithm and the error compensation method [5−6] , which can reduce periodic measurement errors due to gamma nonlinearity as well as projector and camera defocus. In this letter, the detailed mathematical model for sinusoidal phase shifting was developed to predict the effects of non-unitary gamma on phase-measuring profilometry [3] . Zhang et al. developed a compensation method that needs to calibrate an error look-up table (LUT) and is based on the assumption of periodic phase error [9−10] . In general, the abovementioned methods need an additional compensatory step to reduce phase error. A new method with defocusing binary structured patterns can be used to eliminate nonlinear gamma [7] ; however, controlling the proper defocusing degree to achieve high accuracy is difficult using this method [8] . Guo et al. proposed a gamma correction method using a simple one-parameter gamma function technique by statistically analyzing the fringe images [11] . These techniques significantly reduce the phase error caused by nonlinear gamma. Nevertheless, these compensation methods still have residual error value that cannot be ignored in accurate measurement. In addition, the actual gamma of the projector is very complicated and is not the only factor that causes nonsinusoidal waveforms. Our experiments show that the nonlinear gamma of the projector changes over pixels, and mu...

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“…A pictorial representation of the same with more details is shown in Fig. 3.During the last three decades, fringe projection techniques have developed tremendously due to the contribution of large number of researchers and the developments can be broadly categorized as follows: design or structure of the pattern used for projection [40,41,42,43,44,45,46,47,48,49], method of generating and projecting the patterns [50,51,52,53,54,55,56,57,58,59,60,61,62], study of errors caused by the equipment used and proposing possible corrections [63,64,65,66], developing new fringe analysis methods to extract underlying phase distribution …”

mentioning

confidence: 99%

“…This feature has allowed researchers to come up with design of various kinds of structured patterns and associated processing algorithms for measuring the 3D shapes of objects [40]. Some of the related works include the use of hexagonal grating [41], saw-tooth fringe pattern [42,43], triangular pattern [44], locally adapted projection [45,46], the development of inverse function analysis method that permits projection of any kind of fringe pattern [47], gray-code light projection [48], optimal intensitymodulation projection [49] etc.…”

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confidence: 99%

Fringe projection techniques: Whither we are?

Gorthi

Rastogi

2010

Optics and Lasers in Engineering

1,127

376

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During recent years, the use of fringe projection techniques for generating three-dimensional (3D) surface information has become one of the most active research areas in optical metrology. Its applications range from measuring the 3D shape of MEMS components to the measurement of flatness of large panels (2.5 m × .45 m). The technique has found various applications in diverse fields: biomedical applications such as 3D intra-oral dental measurements [1], non-invasive 3D imaging and monitoring of vascular wall deformations [2], human body shape measurement for shape guided radiotherapy treatment [3,4], lower back deformation measurement [5], detection and monitoring of scoliosis [6], inspection of wounds [7,8] and skin topography measurement for use in cosmetology [9,10, 11]; industrial and scientific applications such as characterization of MEMS components [12,13], vibration analysis [14,15], refractometry [16], global measurement of free surface deformations [17,18], local wall thickness measurement of forced sheet metals [19], corrosion analysis [20,21], measurement of surface roughness [22,23], reverse engineering [24,25,26], quality control of printed circuit board manufacturing [27,28,29] and heat-flow visualization [30]; kinematics applications such as measuring the shape and position of a moving object/creature [31,32] and the study of kinematical parameters of dragonfly in free flight [33,34]; biometric identification applications such as 3D face reconstruction for the development of robust face recognition systems [35,36]; cultural heritage and preservation [37,38,39] etc.One of the outstanding features of some of the fringe projection techniques is their ability to provide high-resolution, whole-field 3D reconstruction of objects in a non-contact manner at video frame rates. This feature has backed the technique to pervade new areas of applications such as security systems, gaming and virtual reality. To gain insights into the series of contributions that have helped in unfolding the technique to acquire this feature, the reader is referred to the review articles in this special issue by Song Zhang, and Xianyu Su et al.A typical fringe projection profilometry system is shown in Fig 1. It consists of a projection unit, an image acquisition unit and a processing/analysis unit. Measurement of shape through fringe projection techniques involves (1) projecting a structured pattern (usually a sinusoidal fringe pattern) onto the object surface, (2) recording the image of the fringe pattern that is phase modulated by the object height distribution, (3) calculating the phase modulation by analyzing the image with one of the fringe analysis techniques (such as Fourier transform Figure 1: Fringe projection profilometry system method, phase stepping and spatial phase detection methodsmost of them generate wrapped phase distribution) (4) using a suitable phase unwrapping algorithm to get continuous phase distribution which is proportional to the object height variations, and finally (5) calibrating the system for m...

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Error compensation in two-step triangular-pattern phase-shifting profilometry

Cited by 25 publications

References 15 publications

Digital fringe image gamma modeling and new algorithm for phase error compensation

Digital fringe image gamma modeling and new algorithm for phase error compensation

Linear sinusoidal phase-shifting method resistant to non-sinusoidal phase error

Fringe projection techniques: Whither we are?

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