A novel method of generating phase-shifting sinusoidal fringes for 3D shape measurement

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  • This work proposes a technique for generating sinusoidal fringes for high-speed three-dimensional shape measurement using phase-shifting algorithm. The mechanism of generating sinusoidal fringes is mathematically analyzed, and the specific way of projection is proposed. A sinusoidal fringe is generated by expanding the inverted image of a filled binary sinusoidal pattern in a specified direction, and the phase shift is realized by switching the backlight sources of a set of binary sinusoidal patterns which made on a slide. Using four-step phase-shifting method, the phase error caused by the angle of the light expansion direction deviating from the ideal direction in the solution results is analyzed, which provides a basis for the adjustment requirements of the expansion direction. Compared to existing high frame rate projection methods, this technique has the following characteristics: 1) Sinusoidal fringes obtained are not approximate but theoretically guaranteed, regardless of whether the projection is defocused or not, 2) Convenient phase shifting process, 3) No mechanical moving parts required, 4) No need to consider laser Speckle. At the same time, the method has the advantages of simple structure, convenient control, low cost, and easy miniaturization, so it is very suitable for occasions where size and cost need to be limited, such as in some commercial applications.

Abstract

In this paper, a new generating technique of sinusoidal fringes for 3D shape measurement is presented. Specifically, a sinusoidal fringe is generated by expanding the inverted image of a filled binary sinusoidal pattern in a specified direction, and further, the phase shift is realized by switching the backlight sources of a set of sinusoidal patterns. In theory, sinusoidal fringes can be formed whether the projection is focused or defocused. Moreover, the technique has the potential for high frame rates due to the way the phase shift is performed. In particular, since the high shape precision of the binary sinusoidal pattern and the high accuracy of the phase shift can be easily realized by the photolithography process, the technique is very easy to implement.

Introduction

The 3D shape measurement technique using sinusoidal fringe projection and phase-shifting method has been used in many fields. In the early days, a sinusoidal fringe was produced by using a grating with sinusoidal intensity transmission as the Slide object, and phase shift was achieved by mechanical movement [1,2]. Nowadays, digital fringe projection (DFP) technology has been widely used for fringe projection, and since it can display arbitrary patterns by programming, it is easy to project sinusoidal fringes and achieve accurate phase shifting.

In recent years, high-speed measurement of 3D shape of target has become an important research direction [3], [4], [5], [6], [7], [8], [9], [10], [11]. To perform high-speed 3D shape measurement using sinusoidal fringe projection and phase-shifting algorithm, it is necessary to project fringe patterns at high frame rate. Although an off-the-shelf projector has the advantage of being convenient to use, its projection frame rate is relatively low because it works in grayscale display mode, usually up to 120 Hz or slightly higher. Lei and Zhang [12] generated sinusoidal fringes by sending binary square wave grating patterns to a defocused digital projector, which was based on the fact that the approximate sinusoidal fringes could be obtained when the projection was at a certain degree of defocus. In fact, the defocus acts as a low-pass filter, and the fundamental frequency component of the square wave is retained while other harmonic components are suppressed. Zhang et al. [13] applied the DLP Discovery technology to square-wave binary defocus projection. Since the 1-bit image switching rate of DLP Discovery technology is up to tens of kHz, it can be used to achieve ultra-fast 3D shape measurement. In their experiment, the DLP worked at a switching rate of 2000Hz, and a 3D shape measurement speed of 667 Hz was achieved by using a three-step phase shift method. However, the sinusoidal fringe obtained by defocusing the square wave binary pattern is approximate, and when the frequency is very low, the sinusoidal characteristics will be more difficult to guarantee. Therefore, various improved binary patterns based on defocusing projection to obtain sinusoidal fringes have also been proposed. Ayubi et al. [14] used sinusoidal pulse width modulation (SPWM) technique to generate binary patterns. Wang and Zhang [15] proposed a technique called optimal pulse width modulation (OPWM). Zuo et al. [16] proposed the technique called tripolar SPWM, which can obtain better sinusoidal fringes at a small defocus level. The binary patterns in these techniques are all modulated in one dimension(1D). Lohry and Zhang [17] proposed a 2D(two-dimensional) area modulation technique, which can greatly improve the quality of 3D shape measurement even when the projector is nearly focused. Dai and Zhang [18] use dither technology to generate binary dithered patterns, which can be used for projection to generate high-quality sinusoidal fringes. Lohry and Zhang [19] applying the random dithering technique to generate the desired binary patterns. Although these 2D methods can be used to generate sinusoidal fringes with higher quality, they require more complex display control of DLP. Anyway, the defocus projection method based on DLP discovery technology has already been widely used in the research of high-speed 3D measurement and has become the most mainstream projection method [20], [21], [22], [23]. However, since the method of generating sinusoidal fringes by defocusing requires a reasonable defocusing level, it is more or less inconvenient in use.

In some high-speed 3D measurement research, mechanical methods [24], [25], [26], [27] were used to project fringes. In these mechanical methods, a high-speed rotating grating is used as the projected object, and a synchronization device is used to control the exposure of the camera to control the phase shift. Among them, Hyun and Zhang [26] achieve a 3D measurement frame rate of 3000 Hz by using a mechanical projector, and the same hardware prototype system could potentially achieve a 3D shape measurement speed of 10,000 Hz. Although these methods could reach a high projection speed, the defects caused by mechanical movement are obvious.

Laser interference was also used to project fringes in high-speed 3D measurement. Schaffer et al. [28] used Mach-Zehnder interferometer to generate fringes, and employed an acousto-optic deflector to deflect the fringes to obtain phase-shifting. Although the fringe was actually shifted with a rate of 400Hz in the designed experiment, the potential rate can reach 200kHz. However, this method is not easy to use because it is complicated to perform the phase shift accurately. Li et al. [29] used fiber interference to generate fringes, and used a high speed Lithium Niobat (LN) electro optical modulator to achieve high speed phase shift. This method can theoretically perform the 3D measurement frame rate in GHz, but due to the laser power, the prototype system just achieved 3D shape measurement at a rate of 100 Hz. Generally, in the methods of using laser interference to generate phase shift fringes, the objective speckles on the image sensor will reduce the measurement accuracy, and the measurement system is easy to be disturbed. In addition, these methods are relatively expensive.

Some techniques generate high speed projection by switching projection channels, including the methods to arrange multiple channels for parallel projection [30,31], those to combine several fringe projection units with beam splitters [32,33], and those to use LED (Light Emitting Diode) linear array to illuminate a grating plate step by step [34]. All of these techniques preset projection channels, each channel contains an independent LED backlight, and projects a specific fringe. The phase shift is achieved by switching channels, and the channel switching is performed by turning on and off the LEDs, so by selecting LEDs with high speed response characteristics, it is easy to obtain extremely high projection frame rates, which can theoretically reach more than tens of MHz. In these methods, the fringes are approximately sinusoidal, and some are even non-periodic sinusoidal. Furthermore, due to the complexity of the implementation process, these LED-based techniques are not easy to apply.

Our goal is to obtain a high frame rate projection method, which has the following characteristics: 1) Sinusoidal fringes can be projected regardless of defocusing, 2) Convenient phase shifting process, 3) No mechanical moving parts required, 4) No need to consider laser Speckle. In this paper, we propose a projection method with these characteristics. In this method, we still use LEDs as the backlight sources and realize phase shift by switching LEDs. A Slide with a set of sinusoidal patterns is used, and we call the patterns filled binary sinusoidal patterns because they are produced by filling sine waveform. In theory, if a filled binary sinusoidal pattern is used as the projection object, a sinusoidal fringe can be generated under focusing conditions by expanding light in the direction of the amplitude of the filled binary sinusoidal pattern. Further, if N filled binary sinusoidal patterns satisfying the N-step phase-shifting relationship are fabricated on one Slide and each pattern has its unique backlight, N-step phase-shifting fringes can be obtained by time-sharing control of the backlight sources. Simulations and experiments demonstrate the feasibility of the proposed method.

The projection method proposed in this paper, like other LED-based channel selection methods, has a very high potential projection frame rate. The phase-shifting sinusoidal fringes obtained are not approximate but theoretically guaranteed, regardless of whether the projection is defocused or not. At the same time, the method has the advantages of simple structure, convenient control, low cost, and easy miniaturization, so it is very suitable for occasions where size and cost need to be limited, such as in some commercial applications.

The paper is organized as follows: Section 2 presents the principles behind the proposed method. Section 3 presents the experimental result to verify the feasibility of the method; Section 4 summarizes this paper.

Section snippets

Generating a single sinusoidal fringe from a filled binary sinusoidal pattern

The optical schematic diagram for generating sinusoidal fringes is shown in Fig. 1(a). We first study the case where the projection object contains only one filled binary sinusoidal pattern, as shown in Fig. 1(b). Theoretically, with a conventional projection lens, the sinusoidal pattern can produce an inverted image on the image plane, as shown in Fig. 1(c). If the projection lens is followed immediately by a cylindrical lens whose light expansion direction is parallel to Y, each point of the

Experiments

In order to verify the performance of the proposed approach, a structured light projector used for four-step phase-shifting method was designed, which consists of a Slide printed with four filled binary sinusoidal patterns, four separates backlights, a projection lens F/3.0 with f=30mm, a 5mm × 5mm rectangular diaphragm, and a cylindrical lens with f=30mm. Each sinusoidal pattern on the Slide has a period of 0.4 mm and an amplitude of 0.2 mm, and pitch between patterns is 1mm. Each backlight

Summary

The major advantages of the proposed approach are: (1) Compared with DFP high speed projection method, the sinusoidal fringes can be generated whether the projection is in focus or defocused to a certain extent; (2) compared with other high-speed projection methods that do not use DFP, the proposed Slide scheme is easier to ensure phase-shifting accuracy because the relative positional relationship of the patterns can be very accurate; (3) since LED has a switching speed of the order of 10ns,

Author statements

Under supervision by Huimin Yue, Renjun Peng and Huimin Yue proposed the concept and implementation method of generating phase-shifting fringes, and Renjun Peng completed the experimental data sampling and processing. Mingrui Tian completed the construction of the experimental platform. Li Xu produced the projector display components, and Lifeng Yang performed the projector assembly.

We confirm that the manuscript has been read and approved by all named authors and that there are no other

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

The authors thank Dr. Hua Liu and Professor Xuecai Yu for helpful discussions.

This study was sponsored by National Nature Science Foundation of China (No.61875035), Sichuan science and technology project (2018JY0579). The views expressed in this paper are those of the authors and not necessarily those of the NNSF.

References (37)

  • V Kirschner et al.

    Self-calibrating shape-measuring system based on fringe projection

    Proc. SPIE

    (1997)
  • J Gerber et al.

    Three-coordinate measuring system with structured light

    Proc. SPIE

    (1994)
  • E Wong et al.

    Calibration of an array projector used for high-speed three-dimensional shape measurements using a single camera

    Appl Opt

    (2018)
  • S Heist et al.

    High-speed 3D shape measurement by GOBO projection of aperiodic sinusoidal fringes: a performance analysis

    Proc. SPIE

    (2018)
    S Lei et al.

    Flexible 3-D shape measurement using projector defocusing

    Opt. Express

    (2009)
  • Z Wu et al.

    High-speed three-dimensional shape measurement based on shifting Gray-code light

    Opt Express

    (2019)
  • Z Wu et al.

    High-speed three-dimensional shape measurement based on cyclic complementary Gray-code light

    Opt Express

    (2019)
  • C Zuo et al.

    Micro Fourier transform profilometry (μFTP): 3D shape measurement at 10,000 frames per second

    Opt Lasers Eng

    (2018)
  • S Zhang et al.

    Superfast phase-shifting method for 3-D shape measurement

    Opt Express

    (2010)
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