1. Introduction

The proliferation of distributed industrial robots and self-driving automobiles has generated an increasing demand for 3D imaging solutions characterized by miniaturization, low-cost, and power efficiency. Structured illumination-based 3D imaging and reconstruction offer a swift and precise extraction of a target's 3D profile information [1,2,3,4]. In this context, digital light processing (DLP) technology and liquid crystal display (LCD) technology have emerged as principal projection technologies for 3D reconstruction, meeting the diverse application needs of various scenes and accommodating the projection of different structured light pattern shapes [5,6]. However, their projection processes involve pre-defined pixel-by-pixel image pattern coding and frame-to-frame image memory caching to facilitate variable light pattern formation. For objects with intricate surface topology and varied size accuracy distributions, encoding and projecting multiple image frames of structured light patterns with different shapes or array densities that adapt to different algorithms becomes necessary to ensure reconstruction accuracy [7,8]. This requirement imposes substantial data transfer and caching demands, escalating hardware burdens, costs, and limiting system efficiency. Additionally, the use of panel-level illumination in these projection technologies reduces the system's optical efficiency, considering that structured light patterns typically occupy less than 50% of the total projection area. Notably, both DLP and LCD projection systems require multiple optical lens units, or color filters and polarizers, contributing to a small depth of field that restricts the field of view and measure distance tolerance of the projection. This limitation impedes the miniaturization of the system, hindering its adaptability to highly integrated and portable scenarios [9–11].

Micro-electro-mechanical systems (MEMS) laser beam scanners (LBSs) present an alternative approach to structured light 3D imaging methods. Unlike DLP and LCD technologies, MEMS LBSs operate at the pixel level, offering laser-on-demand functionality with an impressive optical efficiency of up to 90% [1,12]. These systems are inherently focal-free, allowing for a wide range of projection image sizes and distances. By generating a scanning trajectory, LBSs enables adjustment of the projection field of view based on the object's position at varying distances. Furthermore, the system typically requires only a single projection lens unit, or none, which facilitates the miniaturization and integration of systems. The application of MEMS LBSs for structured light 3D reconstruction has witnessed several implementations, operating in either single-axial (1D) or bi-axial (2D) scanning mode. The 2D MEMS scanning mode demonstrates superiority in optical system minimization and projection pattern diversity. It eliminates the need for beam expanders required in 1D MEMS scanning to convert the 1D pattern into 2D, simplifies optics and enables generating more free-form patterns. It also adapts better to varying algorithmic demands across different application scenarios involving versatile object feature sizes [4,13,14]. In a typical 2D MEMS scanning configuration, Lissajous MEMS LBSs offers notable advantages such as robust mechanical stability, thanks to its high-frequency bi-axial resonance, making it resistant to external shocks. Additionally, it enables fast global scanning capabilities, eliminating the need for precise sensor-to-projection refresh rate matching, a feat not easily achievable with mirrors operating under raster scanning [15]. These characteristics firmly establish Lissajous scanning as the preferred solution for MEMS 3D imaging systems [16]. However, advancements in both 2D MEMS scanning projections for structured light patterns primarily rely on a frame-by-frame pre-defined pattern image encoding and projection paradigm. This exacerbates the hardware data processing burden and slows down single-frame projection speeds, thereby presenting limitations in scenarios requiring variable and rapid structured light pattern projection, [17] such as moving objects with multi-scale features on a product line or the laser emission module of a LiDAR system [18]. As depicted in Fig. 1, the ability to dynamically configure image pattern density at variable frame rates through simple modulation on MEMS LBSs is preferred, promising to address issues associated with different complex scenes, adapt to various 3D reconstruction algorithms, and simplify system architecture. However, existing studies are still far from optimum to realize this potential.

 

Fig. 1. The concept for different 3D imaging applications based on reconfigurable structured light patterns generated from the proposed modulation of Lissajous MEMS laser scanning.

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This work introduces a novel modulation strategy tailored for Lissajous MEMS projection systems, enabling the creation of reconfigurable optical patterns crucial for structured light 3D imaging. By employing a single bi-axial MEMS scanning mirror, a novel mathematical framework for laser pulse modulation is established to elucidate the electrical control principles that governing MEMS LBSs. The key advantage of this method lies in its capacity to project structured light patterns of varying types and densities by synchronizing the laser pulse with the resonance frequency of the MEMS mirror. This facilitates an adaptability to different 3D imaging algorithms. Consequently, the proposed method eliminates the necessity for multi-frame pattern image encoding, streamlining data caching and simplifying digital logic hardware architecture that generally used in conventional methods. This simplification is particularly beneficial when dealing with intricate object surface measurements requiring multi-type patterns, ultimately enhancing the overall efficiency of the projection system. Moreover, this approach provides the technological prerequisites for lens-free optics with miniaturization, high adaptability to a broad range of projection distances and fields-of-view in structured light 3D reconstruction systems. To validate the technical feasibility, prototypes were developed to showcase 3D imaging using both 1D MEMS and 2D Lissajous mode laser scanning projection. Employing the Fourier transform profilometry (FTP) measurement method, the system successfully extracted the 3D profile information of a polynomial surface object by projecting a single frame of structured light stripe pattern. The proposed modulation method offers a straightforward principle for dynamically adjusting scan line density at variable frame rates, laying the foundation for developing a more compact LiDAR and 3D robotic vision system.

2. Experimental and methods

2.1 Modulation principles for reconfigurable structured light patterns generation

The Lissajous scanning pattern is dominated by two sinusoidal signals of bi-axial resonance frequencies, as the control equations shown in Eq. (1):[19]

Here, X and Y denote the position of the laser beam over time t, A is the scanning amplitude, f_x and f_{y are the scanning frequencies of the fast- and slow-axes, φx and φy are the phases of both axes with default 0 degrees. Both axes of the MEMS mirror are simultaneously actuated to produce Lissajous laser trajectories.}

To generate different types of structured light patterns based on the Lissajous scanning, the scanning trajectory can be further analyzed. Considering there exists a greatest common divisor (GCD) G₀ for f_x and f_y:

Here, 1/f_x and 1/f_y represent the periods of fast-axis and slow-axis scanning of the MEMS mirror, respectively. When the MEMS mirror is actuated to generate Lissajous patterns, the scanning trajectory is repeated periodically by times of G₀, which is the frames per second (fps). As shown in Fig. 2(a), the Lissajous scanning trajectory moves in the X-direction from the initial position with a period T_x= 1/n_x, while the movement in Y-direction with a period T_y= 1/n_y. Therefore, a simple laser frequency modulation method for Lissajous scanning can be proposed. Different types of structured light pattern are created by simple frequency matching as follows:

L_M is the laser modulation frequency. If N represents an integer, modulated structured light patterns can be generated, including stripe and dot-matrix patterns in different directions. When N equals to an irrational number, random dot-matrix patterns can be generated. This system possesses inherent focus-free characteristics, which enables adaptability across a broad spectrum of object locations and objective areas, surpassing other methods such as DMD or LCD. Specifically, the scanning area expands proportionately with the increased measuring distance. Consequently, the system can project complex structured light patterns at varying projection distances, constrained only by the acceptable received light intensity and the field-of-view area permitted by the scanning angle. For an instance of stripe structured light pattern, the number of stripes N_f in the H × V of the projection can be calculated by the equation:

 

Fig. 2. (a) Schematic of Lissajous scanning trajectory. (b) Different types of structured light patterns generated by algorithm simulations based on the proposed method.

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In which, x is a positive integer, the algorithm simulation was used to verify the above theory, as shown in Fig. 2(b). f_x and f_y were randomly taken as 12246 Hz and 7182 Hz (referring to the property of MEMS mirror that used in this work), respectively, with G₀ = 6, N = 25 and N = 25/26, respectively. When n is taken as n_x, a structured light pattern in the horizontal orientation is generated, and vertical direction is generated when n is taken as n_y. In terms of the scanning essence of laser pulses, the stripe pattern is essentially dense dots collection, but the laser dots are no longer visually distinguishable from each other, and the edges have overlapped. Therefore, it is possible to control the duty cycle of the laser modulation and increase the H × V of the MEMS mirror to generate dot matrices as well.

2.2 Setup for MEMS laser scanning and device characterization

Figure 3 illustrates the setup of the MEMS laser structured light projection prototype system. It employs a MEMS mirror to guide the modulated laser beam for diverse structured light pattern projection without the need for an additional optical lens unit. This setup creates the technical conditions for a compact structured light 3D reconstruction system. The MEMS mirror operates in an open-loop design, utilizing an external lead zirconate titanate (PZT) piezoelectric ceramic to simultaneous actuate mirror scanning in the horizontal (fast-axis) and vertical (slow-axis) directions. This design allows for relatively large actuation forces and simple device structures. The laser driver module modulates the laser, while the intensity of the laser beam and the mirror resonance are controlled synchronously to generate reconfigurable structured light patterns. The structured light projection is achieved by adjusting the resolution and shape size of the Lissajous scanning pattern, strictly tailored by the fast and slow-axis frequency of the MEMS mirror. For optimal coverage density of the light pattern and meeting specific projection resolution requirements (e.g., QVGA or higher), the dual axis scanning frequency must be matched. To achieve arbitrary control of the Lissajous pattern, the MEMS mirror requires a fast-axis scanning frequency higher than 8 kHz and a slow-axis scanning frequency higher than 4 kHz [20]. The design, process, and characterization of the MEMS mirror used in this work have been thoroughly discussed in our previous publication [21].

 

Fig. 3. (a) SEM observation of MEMS mirror used in this work that has been demonstrated in our previous work [21]. (b) The schematic setup for MEMS laser scanning system to generate structured light.

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2.3 Concept and prototype system for structured light 3D imaging

Figure 4 illustrates the flowchart of the 3D imaging process and the prototype system developed in this work based on Lissajous MEMS laser scanning projection. Utilizing a bi-axial MEMS laser beam scanner, the prototype system employs a straightforward hardware setup and fewer or no additional back-end projection lenses to project structured light patterns. This configuration significantly reduces costs and facilitates miniaturization. Unlike the system based on single-axis MEMS laser scanning, the laser beam is directly spatially modulated by the bi-axial MEMS scanner to generate 2D structured light patterns. Both the laser modulation signals and the drive signals for the MEMS mirror are generated by arbitrary function signal generators, ensuring synchronous modulation of laser intensity and MEMS scanner to produce the structured light patterns.

 

Fig. 4. (a) Flowchart of the 3D imaging process in this work based on (b) the prototype system of Lissajous scanning projection with reconfigurable structured light generation.

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3. Results and discussions

3.1 MEMS mirror characterization and validation of structured light projection

Figure 5 indicates a relationship between the scanning frequency shift of the MEMS mirror and Lissajous scanning trajectory. The fast-axis was driven at f_x= 12246 Hz with V_f =58.4 V and the slow-axis was driven at f_y= 7182 Hz with V_s= 25.0 V. The optical scanning angle of the MEMS mirror in two dimensions (H × V) was 25.02°×14.95°, as shown in Fig. 5(a). Meanwhile, remaining the driving voltage, the maximum H × V changed to 26.70°×16.00° after manually adjusting the bi-axial resonance of MEMS mirror to f_x= 12236 Hz and f_y= 7176 Hz, as shown in Fig. 5(b). In addition, the Lissajous pattern was built on a strict mathematical relationship between the scanning frequencies of the MEMS mirror. The density of the Lissajous pattern is directly determined by the greatest common divisor (GCD) of the scanning frequencies. Decreasing the GCD of the scanning frequencies results in an increase on the density of the pattern. The tunability of the scan line density and the size of the Lissajous pattern shape lays the technical foundation for projecting reconfigurable structured light patterns, which will be discussed later.

 

Fig. 5. The relationship between the scanning frequencies of the MEMS mirror and the projected Lissajous patterns. Note that f_x and f_y infer the resonant frequency of the fast-axis and the slow-axis of MEMS mirror, respectively. (a) f_x =12246 Hz, f_y =7182 Hz, GCD = 6, H × V = 25.02°×14.95°. (b) f_x =12236 Hz, f_y =7176 Hz, GCD = 92, H × V = 26.70°×16.00°.

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According to the laser modulation method proposed in Eq. (5), the MEMS mirror's fast and slow axes were simultaneously actuated, respectively. Diverse structured light patterns were projected under varying combinations of scanning frequencies and N value. Figure 6 shows the comparisons through algorithmic simulations and experimental results. Four experimental groups with different G₀ settings were designed to facilitate MEMS laser scanning projection of stripe-type patterns with different orientations and densities. Additional frequency sets were also designed for MEMS laser scanning projection of different dot-matrix pattern densities.

To better observation, the laser modulation was maintained at 20% duty cycle. Tailoring the pattern orientation and line density were realized as shown in Fig. 6(a1) and (a2), featured with f_x =12240 Hz, f_y =7185 Hz, G₀ = 15, H × V = 27.73°×10.00°, while (a3) and (a4) of f_x = 12240 Hz, f_y =7180 Hz, G₀ = 20, H × V = 26.00°×15.39°, respectively. The H × V dimension is governed by both fast- and slow-axis scanning frequencies. The experimental observations of MEMS laser scanning projection patterns aligned well with simulation results. It is noting that the dynamic modulation of scan line density at different frame rates laid the groundwork for MEMS application in LiDAR. In the Fig. 6(b), types of light pattern projection were also configured with four sets of scanning frequency combinations, corresponding structured light patterns of lines, regular dots and quasi-random dots were obtained through both algorithm simulations and actual MEMS laser scanning projection: (b1) f_x = 12246 Hz, f_y = 7182 Hz, G₀= 10, H × V = 25.02°×14.95°; (b2) f_x = 12240 Hz, f_y = 7185 Hz, G₀ = 15, H × V = 27.73°×10.00°; (b3) f_x =12236 Hz, f_y =7182 Hz, G₀ = 266, H × V = 27.10°×11.60°; (b4) f_x =12240 Hz, f_y= 7180 Hz, G₀= 20, H × V = 26.00°×15.39°. Slight differences between experimental and theoretical simulation results of MEMS scanning projection dot-matrix structured light patterns were observed, more pronounced due to the phase delay of the actual operation in MEMS mirror.

 

Fig. 6. Modulation of different types of structured light patterns generated by simulations and experiments. (a) Line orientations and densities control. (a1) f_x =12240 Hz, f_y =7185 Hz, G₀ = 15, H × V = 27.73°×10.00°; (a2) f_x =12240 Hz, f_y= 7180 Hz, G₀ = 20, H × V = 26.00°×15.39°. (b) Pattern type control with line stripes, periodical and quasi-random dots, interlaced trajectories.

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3.2 Fourier transform profilometry and filter design to extract frequency components

For a typical structured light 3D reconstruction, such as line stripe pattern projection system, the necessary process to extract the wrapped phase from the structured light pattern involves using Fourier transform, filtering, and inverse Fourier transform [22–24]. Fig. 7(a) illustrates the optical path of a structured light 3D imaging system employing MEMS laser scanning projection, with M and C representing the projection module and camera, respectively. In the prototype system for 1D laser scanning projection, M comprises the laser, MEMS mirror, and beam expander. In the Lissajous laser scanning prototype system, M consists of the laser and MEMS mirror. B denotes the measured point, d is the vertical distance from M to the datum plane, and L is the distance from M to C.

 

Fig. 7. (a) The diagram of optical path of structured light 3D imaging system with MEMS laser scanning projection. (b) Flow chart of filter window design for extracting the frequency components. (c) Spectrum pattern obtained by Fourier transform of the structured light pattern.

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The relation between the period T(x) of stripe pattern, height h and Δ$\phi $ of point-B can be expressed as:

Further, the stripe pattern on the datum plane with the MEMS laser scanning projection can be expressed as:

Here, I₀(x, y) refers to the intensity of point (x, y) of the stripe pattern, a(x, y) is the average intensity, b(x, y) is the background modulation intensity, and φ(x, y) denotes the phase to be solved. Fourier transform is performed to analyze the frequency domain information of the stripe pattern. Since accurate selection of these components significantly influences the imaging accuracy of FTP, a suitable filter window is then designed to select one of the complex frequency components in the spatial frequency domain. A fast and simple filter window design method can be obtained as depicted in the principle of Fig. 7(b), and the spectrum pattern of a typical stripes pattern after Fourier transform is presented in Fig. 7(c). By using a traversal algorithm, the coordinates (f₀, A₀) corresponding to the maximum amplitude A₀ of the spectrum pattern are determined. Taking the example of extracting the right side-peak frequency component, the traversal continues from (f₀, A₀) to the right, obtaining the coordinates (f₁, A₁) corresponding to the maximum amplitude A₀, which serves as the location coordinates of the filter window. Further traversal within the frequency range f₀ - f₁ identifies the coordinate value (f₁ min, A₂) corresponding to the minimum amplitude A₂. Since frequency components are usually symmetric about f₁, the frequency intervals or width of the filter window can be determined as [f₁ min, 2f₁-f_min]. This filter window design method enables the accurate and quick extraction of the required frequency components for imaging.

With an inverse Fourier transform on this frequency component, the wrapped phase of the datum plane can be obtained by Eq. (8). Where Im(I'₀(x, y)) and Re(I'₀(x, y)) denote the imaginary and real parts of I'₀(x, y), respectively. The wrapped phase of the stripe pattern by object modulation can be calculated as φ(x, y). The distribution of the wrapped phase information of the object and the phase unfolding can then be expressed as:

Here, Fun is phase unfolding algorithm function [25]. The system position parameters determination that necessary for obtaining height information will be discussed later.

3.3 MEMS laser scanning projection for structured light 3D imaging

A prototype optical system for 3D imaging with structured light is depicted in Fig. 8. It utilizes a MEMS mirror with 1D (mode-1) and (mode-2) Lissajous scanning to project stripe laser patterns. The MEMS mirror operates at fast- and slow-axis resonant frequencies of 12240 Hz and 7180 Hz, respectively. Figure 8(a) shows the spatial modulation of laser beam (wavelength: 650 nm, power: 20 mW, beam-spot diameter: 1 mm) with only fast-axis mirror actuation. The reflected beam passes through a beam expander (plano-convex cylindrical with a focal length of 6 mm) to create arrayed stripe pattern, subsequently be projected on screen, and captured by camera for 3D imaging. Figure 8(b) demonstrates the direct reflection of the laser beam by driving the bi-axial Lissajous scanning of mirror, directly forms stripe arrays.

 

Fig. 8. The schematic of the structured light 3D imaging prototype system architecture with (a) 1D scanning mode and (b) Lissajous scanning mode. The photographs correspond to the actual structured light patterns generated from (a) and (b).

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In the mode-1, the MEMS mirror operates at f_m= 12240 Hz, and the laser modulates at L_m1= 1224 kHz. Mode-2 involves light pattern projection by Lissajous laser scanning, with the fast and slow axes of the MEMS mirror simultaneously driven at f_x= 12240 Hz and f_y= 7180 Hz, and laser modulation frequency of L_m2= 1224 kHz. The Lissajous scanning speed exhibits a characteristic of being fast in the middle and slow on the sides, resulting in a non-uniform structured light pattern with sparse density in the middle and denser density on the sides. This paper focuses on the region with a relatively uniform structured light stripe pattern in the middle for experiments and analysis.

Figure 9 showcases the captured structured light stripe patterns, intensity distribution curve, and the spectrum after Fourier transform. The grayscale level of the structured light stripe pattern changes sinusoidally, and the spectrum pattern closely resembles a standard sinusoidal-like function. It is noteworthy that the distortion observed in projection images can be ascribed to the misalignment between the incidence of the laser beam and the normal plane of the MEMS mirrors, leading to variations in stereo angle during bi-axial scanning rotation. A strategy to optimize the relative positions of the laser and MEMS components may effectively mitigate this issue. Additionally, concerning image distortion itself, its impact on measurement accuracy varies depending on the type of projection pattern employed. In the case of measurement based on structured light patterns of horizontal stripes, alterations in stripe spacing predominantly influence measurements. Techniques such as reverse compensation of driving voltage [26] present potential remedies to address this issue. Conversely, in measurements relying on longitudinal stripes in this experiment, distortion primarily affects patterns in the peripheral areas of the projection, with minimal impact on key features such as stripe spacing and sinusoidal properties in the central part of the stripes. Hence, focusing on the central region of interest for longitudinal stripes may facilitate more precise measurements.

 

Fig. 9. Structured light tripe patterns captured by camera. (a) and (b) are structured light stripe patterns generated by the 1D laser scanning and Lissajous scanning, respectively. (a1) and (a2) are the intensity distribution and the spectrum curve after Fourier transform of A-A’. (b1) and (b2) are the intensity distribution and the spectrum curve after Fourier transform of B-B’, respectively.

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Based on Eq. (6)∼(10), method for calibration of system position parameters based on FTP method can be obtained. As shown in Fig. 10, the same stripe pattern is projected by MEMS laser scanning onto multiple planes of known height with the same interval Δmm between each plane, and the stripe patterns modulated by each plane are captured by camera. The Δϕ(x, y) in each plane is solved, and finally the system position parameter a(x, y) is obtained with the known height h(x, y) [27]. Solving the position parameters pixel-by-pixel improves the geometric constraints between the camera and the MEMS projection module, as well as the imaging range. The height information distribution of the object to be measured is known, and the camera calibrated by the method [28] enables the 3D profile information of the object to be measured. In Fig. 10(b), a whiteboard is affixed to the precise displacement platform to obtain planes at different heights. The initial position of the platform, h₁= 0 mm, serves as the reference plane. The platform is then adjusted at 5 mm intervals (Δ=5 mm) to acquire totally 11 planes.

 

Fig. 10. Diagram of the system position parameters calibration.

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In Fig. 11, 3D imaging of MEMS laser scanning projection was firstly evaluated using standard measuring blocks. A vernier caliper with a precision of 0.02 mm was utilized to perform five measurements for each dimension of the blocks. The resultant average value from these measurements is anticipated to furnish the actual size regarding the measuring blocks. Figure 11(a) displays the 3D imaging of a measuring block with thickness of t₀ = 8.98 mm, width of w₀= 34.96 mm, length of L₀= 50.02 mm, based on the structured light stripe pattern projected by MEMS 1D laser scanning (mode-1). 3D profile of the measuring block is shown in Fig. 11(a3). The calculated height of t₀’=9.56 mm, Δw₀’=33.20 mm, L₀’=48.38 mm, which close to the actual geometries of the block, with measurement error of Δ=6.5%, 5.0% and 3.3%, respectively.

 

Fig. 11. Evaluation of structured light 3D imaging based on (a) 1D MEMS scanning projection and (b) Lissajous scanning method proposed in this work. (a1) and (b1) are structured light pattern projected on measuring standard block captured by a camera. (a2), (b2) are photographs of the standard measuring blocks. (a3) and (b3) demonstrate the extracted 3D profiles.

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In the mode-2, measurement of three standard measuring blocks with ladder-type height difference were performed based on Lissajous scanning projection of stripe pattern that proposed in this paper. The ladder was formed by stacking blocks of different thicknesses: t₁ = 6.02 mm, t₂ = 4.02 mm, and t₃ = 3.02 mm, while the 3D profile of ladder blocks is reconstructed in Fig. 11(b3). By fitting the surface data of the spatial dot clouds, the geometrical feature size of each block was extracted from the reconstructed 3D profile, as displayed in Table 1. The calculated thicknesses of block-1, block-2, and block-3 are t₁^’= 6.41 mm, t₂^’= 4.23 mm and t₃^’=3.16 mm, respectively. The absolute accuracy errors for Blk-1 are as follows: 0.39 mm for thickness, 1.71 mm for length, and 0.49 mm for width. For Blk-2, the absolute errors are 0.21 mm for thickness, 1.65 mm for length, and 0.77 mm for width. Blk-3 demonstrates absolute errors of 0.14 mm, 1.93 mm, and 0.49 mm for thickness, length, and width, respectively. The average errors for thickness, length, and width across all measured blocks were Δt = 5.4%, ΔL = 5.8%, and Δw = 6.5%, respectively. In terms of the comprehensive geometric measurement, an average measurement error can be obtained at Δ_tot= 5.9%.

Table 1. 3D imaging results of the standard measuring blocks based on Lissajous scanning projection.

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To further assess 3D imaging performance of the proposed method, experiments were conducted with various target objects of polynomial curve surface. In Fig. 12, both mode-1 and mode-2 illustrate the reconstructed 3D profiles for a plaster face model, with a clear observation of the polynomial facial surface, such as nose tip, despite discontinuous data jumping and information gaps at the sharp edge that attributed to a relatively low stripe contrast. The feature size and the measurement accuracy were denoted in Table 2. The actual sizes of items were also determined through five measurements using a vernier caliper with a precision of 0.02 mm. The average values derived from these measurements were then recorded in the table. For a plaster model width of 62.96 mm, the absolute errors for Mode-1 and Mode-2 are 5.21 mm and 4.15 mm, respectively. Similarly, for a nose width of 15.12 mm, the absolute errors are 0.83 mm and 1.15 mm, respectively. Regarding the tip-to-base distance of 25.51 mm, the absolute errors for both modes are 1.45 mm and 1.97 mm, respectively. An average measurement error of Δ=7.3% can be obtained at a projection distance around 0.46 m. Finally, the above experiments demonstrated the proposed Lissajous laser scanning projection are potentially applicable to structured light 3D imaging with an overall average measurement error of Δ=6.6% for a typical target body size range from 3.0 mm to 65.0 mm level and implies a comparable performance to that 1D laser scanning counterparts.

 

Fig. 12. Reconstructed 3D profile of a plaster face model based on (a) mode-1: single-axis laser scanning and (b) mode-2: modulated Lissajous laser scanning projection proposed in this work.

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Table 2. Feature size and measurement error of 3D imaging based on two scanning modes in Figure 12.

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It is worth noting that the FTP measurement method tends to exhibit instability in areas where object height changes drastically, leading to some jumps in the reconstructed object with sharp edge [23]. The slight phase delay coupled with the deconcentrated energy laser power during MEMS mirror scanning, lead to a weak and unstable pattern projection, affecting the contrast of the projected structured light pattern. Despite that, the Lissajous scanning projection for structured light 3D imaging offers a simpler system architecture, enabling a cost-effective, miniaturized system. More importantly, it allows dynamic adjustment of scanning projection structured light patterns by simply aligning laser frequency with MEMS resonance, offering more flexibility in structured light 3D imaging technology.

Table 3 illustrates a comprehensive comparison among various projection systems. Noteworthy is the superior projection frame rate of up to 266 Hz achieved by this proposed system, specifically tailored to address the demands of 3D object imaging, particularly in measuring moving objects. Furthermore, this system eliminates the necessity for an optical lens group, thereby reducing the overall system footprint. Through the utilization of frequency matching to generate structured-light patterns, this approach eliminates the need for pre-defined multi-frame pattern image encoding, streamline data caching and simplifies the digital logic hardware architecture commonly employed in conventional methods. This innovative concept enables the projection of diverse structured light patterns, including stripes, lines, dot matrices, and random dot clouds, which can dynamically adapt to the requirements of various 3D imaging algorithms. This adaptability is particularly advantageous for addressing the multi-scale features of object surface measurements that necessitate multiple pattern types and rapid projection, ultimately enhancing the overall efficiency of the projection system. Additionally, as a focus-free system, it offers high adaptability to a broad range of projection distances and fields-of-view. Although this study exhibits a larger relative error compared to conventional methods such as DMD and LCD, it is important to note the extended measuring distance in this work. This expanded distance offers adaptability to a wider operational space, beneficial for practical applications like robotic arms in product lines. However, as a trade-off, longer distance results in some degradation of image pattern brightness and contrast, thus a decay on measurement accuracy. Moreover, the accuracy of the system can be further enhanced by implementing more sophisticated image filtering algorithms to extract features with greater precision. This avenue for improvement is a focus of our future research efforts.

Table 3. Comparisons of structured light generation for different projection systems.

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4. Conclusion

This paper introduces a prototype for an advanced structured light 3D imaging system, integrating a highly efficient and compact spatial structured light pattern projection technology. The innovation lies in a tailored modulation method designed for Lissajous MEMS laser beam scanning, introducing reconfigurable optical patterns to enhance 3D imaging capabilities. Leveraging the Lissajous scanning technique, a mathematical model has been developed for laser pulse frequency modulation and the electrical control principles of MEMS LBSs. This model enables seamless projection of structured light patterns with various types and array densities by simply aligning the laser pulse frequency with the bi-axial MEMS mirror scanning frequency. This approach significantly reduces the hardware burden associated with frame-by-frame pre-defined pattern images encoding and projection that often used in conventional systems, leading to simplified streamline digital logic hardware and improved system efficiency. To validate feasibility, a prototype system was established and successfully demonstrated structured light 3D imaging in both 1D and 2D MEMS laser scanning projection modes. Utilizing the Fourier transform profilometry method, the system accurately obtained 3D profile by projecting a single frame of stripe pattern through Lissajous MEMS laser scanning. With a projection distance of 0.46 m, an average measurement error of 6.6% can be obtained for both block and polynomial surface at feature sizes ranging from 3 mm to 65 mm level. The proposed modulation method fosters a platform towards an efficient, reconfigurable spatial structured light pattern projector. By offering a simple control principle for dynamic modulation of pattern type, array density at variable frame rates, it lays the technical foundation for integrated, and patterns-to-algorithms adaptation structured light 3D reconstruction systems for complex 3D vision scenarios, such as advanced LiDAR systems.