High-speed phase-shifting profilometry under fluorescent light
Introduction
Phase-shifting profilometry (PSP) is able to measure the 3-D shape of an object accurately by using temporally phase-shifted fringe patterns and achieve high resolution due to pixel-by-pixel phase calculation [1], [2], [3], [4], [5]. Comparing with the transform-based profilometry using a single fringe pattern [6], [7], [8], [9], [10], the PSP is also simpler to implement and preserves edges [5]. Thus PSP has been widely applied in areas such as reverse engineering, advanced manufacturing, and security protection, etc. [2]. The PSP's measurement error mainly comes from the phase error generated by the projector nonlinear response (i.e., gamma distortion), which can be reduced by either using a large number of phase-shifted fringe patterns or using a small number of fringe patterns combined with techniques based on a lookup table [11], a gamma model [12,13] or a pre-coding [14,15], etc.
This paper presents a new measurement error source in PSP, the phase error generated by the fluorescent light presenting in the environment. The PSP system usually involves two different light sources, the projecting light source and the environmental light source. The projecting light may vary slowly in a long period of time, which may generate a time-independent phase error in PSP [16], [17], [18]. The projecting light can be assumed to be temporally stable in a short capture time used in high-speed PSP. When the projecting light is powered by a LED light source with the direct current, it only generates an ignorable phase error about 0.02 rad in high-speed PSP [19]. On the contrary, PSP typically works under the fluorescent light powered by ballasts with the alternating current (AC) frequency of 50 Hz (UK) or 60 Hz USA) [20]. Therefore, the fluorescent light flickers with a double frequency of 100 Hz or 120 Hz, respectively [21]. It is difficult to filter this double frequency because of the very low frequency resolution and the energy leakage, especially for high-speed PSP using a small number of fringe patterns. Such light flickering may lead to a non-ignorable phase error, and then generate a measurement error.
Traditional PSP often captures sinusoidal patterns with a speed less than 120 frames per second (fps) [11], which does not generate obvious phase error for PSP with an image acquisition rate lower than the fluorescent light frequency, as will be analyzed in detail in Section 2. However, when the capture speed increases, even to a few thousands fps in binary-projection high-speed PSP with projector defocusing [1], we have observed non-ignorable phase errors up to 0.12 rad.
Intuitively, the fluorescent light problem can be resolved by using near-infrared patterns [22,23] or turning off the fluorescent light source. Near-infrared light projector has been used in 3-D measurement devices such as Kinect I [24] and LiDAR [25]. However, near-infrared light sources have relatively low intensity and require higher cost [22], making visible light projector a common choice. In addition, the fluorescent light source is commonly used for illumination for manufacturing lines, public areas, etc., where PSP may be applied. Thus, investigating and solving the fluorescent light problem for accurate and high-speed PSP is of importance.
In this paper, we first mathematically describe the fluorescent light problem, and model the PSP phase error due to this problem, from which, the non-ignorable phase error in high-speed PSP is clearly revealed. Next, we propose a fluorescent light error suppression (FLES) algorithm to suppress the phase error according to different sampling speed situations, which is experimentally verified on high-speed PSP.
The rest of this paper is organized as follows. Section 2 analyzes the fluorescent light problem in PSP. Section 3 presents the FLES algorithm. Section 4 provides experiments, Section 5 gives conclusions.
Section snippets
Basics of PSP
In traditional N-step PSP, a set of phase-shifted sinusoidal patterns are first projected by a projector, and then captured by a camera [1], [2], [3], [4], [5]. We emphasize that there are two types of intensity, instantaneous intensity and captured intensity. The latter is the integration of the former during the exposure time interval.
The instantaneous intensity of the sinusoidal patterns reaching the camera image sensor can be described bywhere
Fluorescent light error suppression (FLES) algorithm
As has been analyzed and simulated, the fluorescence light as a new error source could cause non-ignorable phase error. In this section, we propose a FLES algorithm to make it immune to the error. According to three different speed situations, we will use the traditional dual 4-step algorithm, a constructive 4-step algorithm, or a postponed dual 4-step algorithm, respectively. As we only consider v ∈ (100, 5100), and with and , we have Δ ∈ (0, 2π)to be considered because
Experiments
Our experiment system uses a TI DLP Discovery 6500 projector with a resolution of 1920 × 1080, and a Basler CMOS acA800 camera with a resolution of 800 × 600. The camera is placed with a distance about 1.5 m from the fluorescent light source, and captures a flat white board with a distance of about 60 cm. There are six fluorescent light sources with total power of 168 W. By using the method given in Ref. [34], a set of four phase-shifted binary patterns are designed with the fringe period of 36
Conclusions
In this paper, a new error measurement error source from fluorescent light is mathematically analyzed and experimentally verified for the first time. In the normal activity places, such as public areas and offices, the RMS phase error from this error source can be up to 0.12 rad, which generates obvious wrinkles in the measured 3-D shapes.
A FLES algorithm is proposed to suppress the phase error. Three sub-algorithms of the traditional 4-step, the consecutive dual 4-step and the postponed dual
CRediT authorship contribution statement
Dongliang Zheng: Conceptualization, Methodology, Software, Writing - review & editing. Qian Kemao: Conceptualization, Validation, Writing - original draft. Jing Han: Formal analysis. Jing Wang: Validation, Software. Haotian Yu: Investigation, Software. Lianfa Bai: Supervision.
Declaration of Competing Interest
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
Acknowledgments
This research is supported by the Natural Science Foundation of Jiangsu Province (BK20160693), the National Natural Science Foundation of China (61971227 and 61727802), the Key Research & Development Programs in Jiangsu China (BE2018126).
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