Precise 2D and 3D Hybrid Measurement of Drill Bits with Complex Geometries

Wenqi Wang; Wei Liu; Yang Liu; Yang Zhang; F. Zhenyuan Jia

doi:10.1016/j.eng.2025.03.035

Engineering ›› DOI: 10.1016/j.eng.2025.03.035

Precise 2D and 3D Hybrid Measurement of Drill Bits with Complex Geometries

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Abstract

Drill bits with complex geometries are pivotal role as essential tools widely applied in high-performance manufacturing processes, particularly in aerospace and related industries. However, the precise measurement of the geometries of such cutting tools is quite challenging owing to their complex reflective properties, surface morphology, and numerous parameters within small dimensions. In this paper, we present an investigation of the effects of lighting and processing marks on visual measurement and propose a correlated fusion vision dual-platform with high accuracy and efficiency. First, a comprehensive calibration model and method that considers installation errors for bi-telecentric imaging is proposed. Then, improved methods for robust and precise two-dimensional measurement are presented, including an adaptive illumination method for high-contrast imaging and an interactive measurement algorithm for accurate feature extraction. Furthermore, a novel enhanced focus measure (ITene-Gabor) that incorporates both grayscale gradient and frequency information is proposed for high-quality three-dimensional topography reconstruction. Finally, we detail experiments and accuracy verification performed on two typical complex drill bits with sawtooth features. The experimental results demonstrate that the developed equipment achieves measurement deviations of less than 3 μm for length and 0.5° for angle as compared with a commercial microscope. The measurement efficiency averages 30 s per parameter, confirming the high accuracy, effectiveness, and reliability of the proposed method and system for measuring all drill bit parameters. The correlated fusion vision dual-platform and measurement methods also have the potential to be extended to other complex industrial products and can serve as a basis for developing universal measurement equipment.

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Aircraft manufacturing / Cutting tools / Geometry measurement / Composite vision measurement systems / Machine vision

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Wenqi Wang, Wei Liu, Yang Liu, Yang Zhang, F. Zhenyuan Jia. Precise 2D and 3D Hybrid Measurement of Drill Bits with Complex Geometries. Engineering DOI:10.1016/j.eng.2025.03.035

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1. Introduction

Drill bits represent one of the most critical components in machining processes, exerting pivotal influence across industries such as aerospace, shipbuilding, vehicles, and electronic devices. In recent years, with the widespread use of advanced materials such as carbon fiber-reinforced polymers (CFRPs), an increasing number of drill bits with complex structures have been continuously improved to meet the demand for high-performance manufacturing [1,2]. Reports indicate that the rejection rate of CFRP components because of drilling damages during the manufacturing process is as high as 60%, leading to enormous losses [3]. Recently, the development of novel drill bits designed with microstructures, particularly stepped drill bits with sawtooth features, has exhibited advantages and attracted significant attention [4]. Unlike traditional drill bits, the intricate geometries of these novel drill bits are key to achieving better machining performance and longer tool life. Accurate measurement of key geometric parameters, including length and angle, is a vital prerequisite for precision and high-performance manufacturing [5,6]. Furthermore, knowledge of these geometries is essential to investigate the mechanism of material removal and tool wear [7]. Tens of thousands of these cutting tools are manufactured and utilized annually in industrial production lines. Therefore, precise measurement methods and equipment for geometric parameters are crucial throughout the lifecycle of drill bits.

For measuring the geometry of traditional cutting tools (including lathe cutting tools, milling cutters, and drill bits with simple structures), universal instruments such as optical microscopes [8] and tool presetting machines [9] are the most common tools used in practice. However, the requirement for multiple manual operations leads to poor consistency and low efficiency. In addition, the consecutive measurement range is limited by the finite field depth and fields of view. In recent decades, the progress of automatic optic inspection (AOI) has been increasingly facilitated by advancements in industrial cameras and image processing technology [10,11]. Constantly improving, AOI technology generates new methods, including high-quality image acquisition, image enhancement, and robust feature extraction algorithms, to achieve accurate geometry measurements of traditional cutting tools. However, all the aforementioned methods struggle to guarantee the measurement requirements for drill bits with complex structures. This is mainly because of the sensitivity of visual measurement to environmental lighting and occlusions between microstructures, as well as its inability to measure three-dimensional (3D) parameters (spatial angles and tool wear volume) [12]. While some 3D visual measurement methods have been applied to measure the parameters of cutting tools, the results are often unsatisfactory because balancing measurement accuracy and efficiency is challenging.

Therefore, this study devised robust visual geometric parameter measurement methods that make the results immune to interference from variations in the environment and surface topography. A hybrid vision measurement system that can guarantee efficient and accurate measurement results, while also providing high levels of automation and flexibility, was developed. Research on geometric measurement techniques for drill bits with complex topography provides precise data support for the study of material removal mechanisms and damage analysis in manufacturing processes, thereby facilitating the advancement of difficult-to-machine materials manufacturing. Through high-resolution 3D topography reconstruction and micron-scale wear quantification, the proposed method enables precise correlation between cutting-edge geometry evolution and subsurface damage initiation patterns; this is particularly critical when processing nickel-based superalloys or CFRPs. Concurrently, investigations into universal measurement methods for highly reflective complex components can be extended to defect detection in other mechanical parts and electronic circuit elements, thereby offering valuable references for developing related precision measurement technologies and instrumentation.

The rest of this paper is organized as follows: Section 2 reviews the related works. Section 3 introduces the measurement system, and Section 4 details the vision measurement method. Section 5 presents the measurement results and discussion, and Section 6 presents the conclusions drawn from this study.

2. Related works

The significant requirement for visual measurement of geometric parameters in the industry has sparked numerous research endeavors. In this section, the related works proposed to address the measurement and inspection of geometric parameters for objects with complex morphology have been summarized. The related techniques and their applications in tool geometry measurements are discussed in two parts: two-dimensional (2D) machine vision and 3D vision measurement.

2.1. 2D machine vision

The visual measurement and detection of 2D geometric features of workpieces with complex morphology remains a difficult task—on the one hand, acquiring high-quality images is challenging; on the other hand, stable feature extraction algorithms are required.

Lighting conditions and viewing angles significantly influence the quality of images acquired by 2D machine vision systems. Commonly used off-the-shelf light-emitting diode (LED) light sources, such as ring lights or combinations of bar lights, may provide globally uniform illumination across the system [13]. However, global uniformity across the field of view is not conducive for extracting complex features. When inspecting intricate workpieces, achieving local illumination uniformity and ensuring high contrast between the features and background becomes crucial. To obtain high-contrast images of tool wear, Zhou and Yu [14] proposed a mixed-mode multispectral LED spherical light source that exploits the response properties of the sensor to different wavelengths for improving the visibility of the feature area. Compared with the trial-and-error approach, modeling, analytic solutions, and optimization of the lighting system prove to be more efficient. Gerges and Chen [15] presented a geometric model of multisource lighting and an adaptive illuminance distribution method for visual robotic inspection of curved parts with complex reflectivity. Experimental results demonstrated that the optimal lighting solution could achieve a 95% identification accuracy in defect detection on aeronautical blades. Another proven approach involves multisource information fusion, which coordinates images captured under different lighting conditions to provide complementary visual feature details for the same target [16]. Fu et al. [17] proposed a multilight source fusion image acquisition system that employed four directional strip light sources to illuminate the measured workpiece with a highly reflective surface. Similarly, Yin et al. [18] proposed a multilight fusion mechanism for the automated acquisition of images, which incorporated ring, coaxial, and back-transmitted light sources to enrich the characteristics of micro flaws in optical components. However, such methods typically rely on deep learning architectures to further process a large number of images, and the integration of multiple light sources is not always advantageous.

Several algorithms have been proposed to enhance feature extraction, addressing challenges such as non-uniform illumination and significant noise in image processing. Utilizing the morphological characteristics of tool wear images, Zhu and Yu [19] proposed a single-image super-resolution image reconstruction algorithm [20] and a morphological component analysis-based feature extraction algorithm, yielding more precise results. Zhang et al. [21] ingeniously combined the robustness of deep learning with the precision of traditional edge detection operators, proposing a fusion-vision method for evaluating tool wear. This method effectively overcame the issue of inaccurate edge recognition caused by lighting effects.

2.2. 3D vision measurement

In recent years, 3D vision measurement technology has revolutionized geometric measurement for industrial components. In contrast to traditional 2D measurement techniques, 3D measurement can provide more comprehensive information, particularly when applied to cutting tools, enabling a more precise evaluation of tool performance. In general, 3D vision measurement methods can be divided into macroscopic and microscopic approaches. For macroscopic methods, active-vision-based techniques such as laser and fringe projection profilometry offer relatively fast speed, high precision, and ease of implementation. Yang et al. [22] proposed a novel dual-platform scanner coupled with a hybrid calibration method, facilitating the high-precision 3D reconstruction of irregular objects exemplified by dental pieces. Nevertheless, highly reflective surfaces may result in a lack of point cloud data, which fails to meet the requirements for measuring cutting tools. Li et al. [23] utilized a galvanometer scanner to acquire 3D information of a triangular turning tool. However, this measurement system is susceptible to environmental interference and requires significant maintenance costs. Another macroscopic method employed 2D images and precise relative motion [24]. Although this method could achieve online measurement, it required accurate calibration of the spindle position and was only suitable for simple rotary parts [25]. The primary limitation of macroscopic 3D vision lies in the inherent tradeoff between lateral resolution and depth of focus, which makes it suboptimal for tool measurement.

Many scholars have attempted to use 3D microscopy technologies such as atomic force microscopy [26], laser scanning confocal microscopy [27], and white light interferometry for the metrology of cutting tools [28]. Although these devices offer high precision and the ability to evaluate surface topography parameters, the process of sampling and analysis is time consuming. In contrast, focus variation-based 3D microscopy technology is a more promising approach owing to its rapid speed, simple structure, and low cost [29]. Lin et al. [30] developed a shape from focus system and improved the search strategy of the focus function to measure the parameters of round-nosed cutting tools. However, the aforementioned methods are not feasible for the 3D reconstruction of drill bits, often resulting in incomplete and inefficient acquisition of the 3D point cloud because of the large slope and highly reflective surfaces.

2.3. Discussion

Fig. 1 illustrates the geometry of a typical complex drill bit, specifically a stepped drill bit with sawtooth features. The parameters are summarized in Table 1. Evidently, the various parameters, characterized by small dimensions, multiple categories, and complex structures with large slopes, present a formidable challenge for accurate and efficient measurement. Additionally, apart from 2D parameters like the chisel edge length b, drill bits also require the measurement of spatial parameters such as the cutting edge rake angle γ_o. Based on the preceding analysis, existing methods offer good support for simple workpieces and have inspired the current work. However, when applied to drill bits with complex structures, their measurement capabilities exhibit certain limitations. Relying solely on either 2D or 3D vision proves challenging when attempting to comprehensively measure all of these geometric parameters. A single 2D vision measurement technology cannot meet the requirements because of the spatial angle parameters, as depicted in Fig. 1. On the other hand, 3D measurement also encounters challenges such as low efficiency and variations in parameter scales. Furthermore, current methods are unable to address the impact of the complex morphology and high reflectivity of drill bits on measurement accuracy.

Thus, leveraging both 2D machine vision and 3D shape-from-focus techniques, a correlated fusion vision dual-platform for drill bits is proposed herein that can quickly and accurately acquire information of geometric parameters and 3D morphology. While composite vision measurement systems have been reported in the literature [17,31], the innovation of this study lies in the integration of multidimensional visual imaging systems, and its first application to the measurement of geometric parameters for complex tools. Moreover, this study investigated several key issues, including an adaptive illumination-based imaging method to avoid the influence of local highlights on images, an interactive feature detection algorithm for more reliable and automatic measurement, and a novel focus measure that combines the focus features in both spatial and frequency domains for high-quality 3D topography reconstruction. Furthermore, the effectiveness of the system and method was validated through a series of measurement experiments.

3. System

A correlated fusion vision measurement dual-platform for drill bits with complex geometries is designed to obtain feature images under the two imaging models and achieve flexible and precise automatic measurement of the drill bit geometry. The design of the measurement system is described in this section.

3.1. Overall structure of the correlated fusion vision measurement system

For measuring the profile parameters of drill bits, 2D machine vision undoubtedly presents the optimal solution. The extraction of profile features is easier and faster as compared with acquiring 3D point clouds. In 2D machine vision measurement systems, bi-telecentric imaging lenses are commonly utilized in high-precision measurement scenarios because the parallelism of incident light rays reduces errors caused by variations in measurement distance. As shown in Fig. 1, the axial parameters of the drill bit are independent and non-interfering, which enables the reflected light to enter the telecentric vision measurement system and be used for imaging via bright field illumination. In contrast, the circumferential contour features are distinct. Capturing these features requires dark field illumination under transmitted light, thus achieving higher precision. However, the telecentric measurement system cannot achieve 3D morphology reconstruction, making it difficult to meet the measurement requirements for the spatial angles of drill bits. Based on the analysis in Section 2, the shape from focus with wide-field microscopy can be considered to be the most suitable approach for the 3D morphology measurement of small industrial components, as it achieves a better balance between measurement efficiency and precision. To measure the spatial angles of drill bits, scanning is required from both the circumferential and axial directions. Subsequently, point cloud registration and stitching should be performed based on their spatial relationships to create a complete 3D point cloud. Finally, these specific spatial angles are obtained by calculating the normal vectors.

To achieve rapid and accurate measurement, a correlated fusion vision dual-platform was developed in this study. Fig. 2(a) shows the schematic of the designed system, which is constructed from two perpendicular vision measurement modules. The first module, situated on the Z-axis, employs 2D image-based measurements and includes a Z-axis motion platform, an industrial camera, a bi-telecentric lens, a backlighting device, and an adaptive front light source. By adjusting the illumination strategy, feature images of the geometric parameters can be captured, and 2D parameters on the projection plane can be measured via image processing. The second module, a 3D measurement system based on shape from focus, is situated along the X-axis. An image sequence is generated by scanning along the X-axis, and the depth of each point in the image is calculated using the focus measure. The systems of both axes are mutually constrained, with a full-focus image obtained through the X-axis providing a positional reference for measurements undertaken on the vertical axis.

In this study, a prototype measurement equipment was developed, as shown in Fig. 2(b). An industrial camera (EoSens 25CXP), manufactured by Mikrotron (Germany), with a data transfer rate of 6.25 Gbits·s^–1, resolution of 5120 pixels × 5120 pixels, and pixel size of 4.5 μm was used. This camera can rapidly capture grayscale images, thereby providing indispensable support for high-precision measurement. The bi-telecentric lens (TC4M009-F) used for 2D imaging was made by OPTO (Germany) and had a magnification of 2X. The microscope lens used for focus variation was RK-AP200 (Resking Vision Technology, China), with a magnification of 5X and a depth of field of 14 μm. The motion platforms and controller were provided by the Nengji company (China). The motion space of the Z-axis was 300 mm, and that of the X-axis was 60 mm. The localization accuracy was verified to be within ±0.01 mm and ±0.1 μm, respectively. This design scheme, featuring two cross-scale axis visual systems, presents the advantages of compact size and high flexibility. The two modules were tightly and effectively connected through the parameter transmission process for rapid and accurate measurement of complex and multiscale geometric parameters.

3.2. Calibration of the bi-telecentric imaging system

Based on the designed system, further evaluation is required regarding the input axis misalignment of the dual-platform system. In this case, the precision of the 3D system along the X-axis is not affected by the installation position owing to the inherent geometric constraints present in the features of the object being measured. However, for the 2D visual measurement system, ensuring verticality to the X–Y plane is crucial to guarantee measurement accuracy. As depicted in Fig. 3, a measurement error arises owing to the unavoidable deviation between the optical axis and the normal of the object plane, caused by installation inaccuracies. Hence, introducing internal parameter deviation angles φ and λ into the calibration model is necessary to eliminate errors, where φ is the vertical deviation angle and λ is the horizontal deviation angle. Considering the impact of installation angle errors, this study devised a novel calibration model for bi-telecentric lenses. Based on the pose constraint and the imaging model of bi-telecentric lenses, an imaging calibration model with an error installation angle matrix is established as follows:(1)

\begin{matrix} [\begin{matrix} u \\ v \\ 1 \end{matrix}] = [\begin{matrix} α & γ & u_{0}^{'} \\ 0 & β & v_{0}^{'} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & φ \\ 0 & 1 & - λ \\ - φ & λ & 1 \end{matrix}] [\begin{matrix} cos ε & - sin ε & t_{x} \\ sin ε & cos ε & t_{y} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x_{w} \\ y_{w} \\ 1 \end{matrix}] \\ α = \frac{m}{d_{u}}, β = \frac{m}{d_{v} sin θ}, γ = \frac{cos θ}{d_{u}}, u_{0}^{'} = \frac{u_{0} - v_{0} cot θ}{d_{u}}, v_{0}^{'} = \frac{v_{0}}{d_{v} sin θ} \end{matrix}

\begin{matrix} [\begin{matrix} u \\ v \\ 1 \end{matrix}] = [\begin{matrix} α & γ & u_{0}^{'} \\ 0 & β & v_{0}^{'} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} 1 & 0 & φ \\ 0 & 1 & - λ \\ - φ & λ & 1 \end{matrix}] [\begin{matrix} cos ε & - sin ε & t_{x} \\ sin ε & cos ε & t_{y} \\ 0 & 0 & 1 \end{matrix}] [\begin{matrix} x_{w} \\ y_{w} \\ 1 \end{matrix}] \\ α = \frac{m}{d_{u}}, β = \frac{m}{d_{v} sin θ}, γ = \frac{cos θ}{d_{u}}, u_{0}^{'} = \frac{u_{0} - v_{0} cot θ}{d_{u}}, v_{0}^{'} = \frac{v_{0}}{d_{v} sin θ} \end{matrix}

Here, (u, v) are the coordinates of the target point in the image pixel system, m is the equivalent magnification of the telecentric lens, d_u and d_v are scale factors from the pixel coordinate system to the image coordinate system, and θ is the angle between the horizontal and vertical directions of the complementary metal oxide semiconductor array pixels. (u₀′, v₀′) represent the real projection center coordinates, while (u₀, v₀) denote the ideal projection center coordinates. ε is a parameter of the rotation matrix, t_x and t_y are translation parameters, and (x_w, y_w) are the coordinates of the target point in the world coordinate system. Furthermore, let M_2×2 = [α, γ; 0, β], V_2×1 = [u₀ ′, v₀′]^T,

ϕ

ϕ

_2×1 = [λ, −

φ

φ

]^T, R_2×2 be the rotation submatrix of Eq. (1), and T_2×1 be the translation vector of Eq. (1). Then, the calibration model can be expressed as follows according to the block matrix:(2)

[\begin{matrix} u \\ v \\ 1 \end{matrix}] = [\begin{matrix} M_{2 \times 2} & V_{2 \times 1} \\ 0 & 1 \end{matrix}] [\begin{matrix} E_{2 \times 2} & ϕ_{2 \times 1} \\ - {ϕ_{2 \times 1}}^{T} & 1 \end{matrix}] [\begin{matrix} R_{2 \times 2} & T_{2 \times 1} \\ 0 & 1 \end{matrix}] [\begin{matrix} x_{w} \\ y_{w} \\ 1 \end{matrix}] = H_{3 \times 3} [\begin{matrix} x_{w} \\ y_{w} \\ 1 \end{matrix}]

[\begin{matrix} u \\ v \\ 1 \end{matrix}] = [\begin{matrix} M_{2 \times 2} & V_{2 \times 1} \\ 0 & 1 \end{matrix}] [\begin{matrix} E_{2 \times 2} & ϕ_{2 \times 1} \\ - {ϕ_{2 \times 1}}^{T} & 1 \end{matrix}] [\begin{matrix} R_{2 \times 2} & T_{2 \times 1} \\ 0 & 1 \end{matrix}] [\begin{matrix} x_{w} \\ y_{w} \\ 1 \end{matrix}] = H_{3 \times 3} [\begin{matrix} x_{w} \\ y_{w} \\ 1 \end{matrix}]

where E is a second-order unit matrix. Moreover, by establishing the relationship between the product of block matrices and the homography matrix H_3×3 (h₁₁∼h₃₃)_, the calibration parameters can be derived.(3)

\begin{matrix} H_{3 \times 3} = [\begin{matrix} \begin{matrix} h_{11} & h_{12} h_{13} \\ h_{21} & h_{22} h_{23} \end{matrix} \\ h_{31} h_{32} h_{33} \end{matrix}] \\ \{\begin{matrix} (M - V ϕ^{T}) R = [\begin{matrix} h_{11} & h_{12} \\ h_{21} & h_{22} \end{matrix}] \\ - ϕ^{T} R = [h_{31}, h_{32}] \end{matrix} \end{matrix}

\begin{matrix} H_{3 \times 3} = [\begin{matrix} \begin{matrix} h_{11} & h_{12} h_{13} \\ h_{21} & h_{22} h_{23} \end{matrix} \\ h_{31} h_{32} h_{33} \end{matrix}] \\ \{\begin{matrix} (M - V ϕ^{T}) R = [\begin{matrix} h_{11} & h_{12} \\ h_{21} & h_{22} \end{matrix}] \\ - ϕ^{T} R = [h_{31}, h_{32}] \end{matrix} \end{matrix}

In the above calibration model, because of the large number of internal parameters, conventional calibration methods require a significant amount of calibration images. Therefore, this study developed a calibration method that optimizes the solution for intrinsic parameters by maintaining the invariance of the extrinsic rotation matrix, thereby streamlining the complex calibration process. As shown in Fig. 4(a), a calibration board image is first captured at the left edge of the field of view. Subsequently, using a high-precision displacement platform, the calibration board is moved horizontally and vertically by distances Δt_x and Δt_y, respectively, and corresponding calibration board images are captured at the two positions. Then, the homography matrix corresponding to the calibration images is solved using a nonlinear iterative method as H¹, H², H³. Through Eq. (3), the relationship between the error angle and external rotation matrix can be determined:

\{\begin{matrix} \begin{matrix} φ^{2} + λ^{2} = h_{31}^{2} + h_{32}^{2} \\ \cos ε = \frac{λ h_{32} - φ h_{31}}{h_{33}^{2} + h_{32}^{2}} \end{matrix} \\ \sin ε = \frac{λ h_{31} + φ h_{32}}{h_{33}^{2} + h_{32}^{2}} \end{matrix}

\{\begin{matrix} \begin{matrix} φ^{2} + λ^{2} = h_{31}^{2} + h_{32}^{2} \\ \cos ε = \frac{λ h_{32} - φ h_{31}}{h_{33}^{2} + h_{32}^{2}} \end{matrix} \\ \sin ε = \frac{λ h_{31} + φ h_{32}}{h_{33}^{2} + h_{32}^{2}} \end{matrix}

Next, the parameter of rotation matrix ε and the installation error angles λ and φ are solved based on the orthogonality constraint of the rotation matrix. Then, the intrinsic parameters are calculated using the known translation matrix:(5)

\{\begin{matrix} [\begin{matrix} 0 & (M - V ϕ^{T}) Δ t_{x} \\ 0 & - ϕ^{T} Δ t_{x} \end{matrix}] = H^{2} - H^{1} \\ [\begin{matrix} 0 & (M - V ϕ^{T}) Δ t_{y} \\ 0 & - ϕ^{T} Δ t_{y} \end{matrix}] = H^{3} - H^{2} \end{matrix}

\{\begin{matrix} [\begin{matrix} 0 & (M - V ϕ^{T}) Δ t_{x} \\ 0 & - ϕ^{T} Δ t_{x} \end{matrix}] = H^{2} - H^{1} \\ [\begin{matrix} 0 & (M - V ϕ^{T}) Δ t_{y} \\ 0 & - ϕ^{T} Δ t_{y} \end{matrix}] = H^{3} - H^{2} \end{matrix}

Furthermore, utilizing the properties of the homography matrix, it can be determined that(6)

\{\begin{matrix} α = \frac{Δ h_{13}^{21}}{Δ t_{x}}, β = \frac{Δ h_{23}^{32}}{Δ t_{y}}, γ = \frac{Δ h_{13}^{32}}{Δ t_{y}}, θ = \arctan (\frac{α β}{γ}) \\ u_{0}^{'} = \frac{α \cos ε + γ \sin ε - h_{11}}{h_{31}}, v_{0}^{'} = \frac{β \sin ε - h_{21}}{h_{32}} \end{matrix}

\{\begin{matrix} α = \frac{Δ h_{13}^{21}}{Δ t_{x}}, β = \frac{Δ h_{23}^{32}}{Δ t_{y}}, γ = \frac{Δ h_{13}^{32}}{Δ t_{y}}, θ = \arctan (\frac{α β}{γ}) \\ u_{0}^{'} = \frac{α \cos ε + γ \sin ε - h_{11}}{h_{31}}, v_{0}^{'} = \frac{β \sin ε - h_{21}}{h_{32}} \end{matrix}

where

Δ h_{13}^{21}

Δ h_{13}^{21}

= h₂₁- h₁₃, and

Δ h_{23}^{32}

Δ h_{23}^{32}

and

Δ h_{13}^{32}

Δ h_{13}^{32}

are defined in the same manner.

Since the bi-telecentric lens has minimal distortion, it is sufficient to calculate the first- and second-order distortion parameters. Finally, the following optimization function is established:(7)

\{\begin{matrix} X = {[m, φ, λ, k_{1}, k_{2}, p_{1}, p_{2}, s_{1}, s_{2}]}^{T} \\ \hat{X} = \underset{X \in R^{9}}{argmin} \sum_{i =1}^{col} \sum_{j =1}^{row} {‖ p_{i,j} - \tilde{p} (X) ‖}^{2} \end{matrix}

\{\begin{matrix} X = {[m, φ, λ, k_{1}, k_{2}, p_{1}, p_{2}, s_{1}, s_{2}]}^{T} \\ \hat{X} = \underset{X \in R^{9}}{argmin} \sum_{i =1}^{col} \sum_{j =1}^{row} {‖ p_{i,j} - \tilde{p} (X) ‖}^{2} \end{matrix}

where col is the feature number in a column of the calibration board, row is the feature number in a row of the calibration board, k₁ and k₂ are radial distortion parameters, p₁ and p₂ are tangential distortion parameters, s₁ and s₂ are prism distortion parameters, and

\tilde{p} (X)

\tilde{p} (X)

is the calculated coordinate of the projection point. p_{i, j} represents the coordinate of a feature on the calibration board, and the Levenberg–Marquardt optimization algorithm is used to determine the distortion coefficient and optimized internal parameters. Therefore, only three images are required to calibrate the 2D measurement system, making the method simple and easy to use. In this study, a circular calibration board ASD-4-D0.2-T1.6 (Jiangtu Vision, China) and the high-precision motion platform UMS130-60X (Nengji company, China) were utilized to calibrate the bi-telecentric system, as illustrated in Fig. 4(a). The calibration results show that the re-projection error of the proposed calibration method is 0.05 pixels, which is superior to the HALCON calibration method (0.08 pixels) [32], as displayed in Figs. 4(b) and (c). This approach mitigates the impact of installation errors on the measurement accuracy of the dual-axis vision system, ensuring precision in the measurement of the geometric parameters of drill bits. Additionally, an optical precision linear scale (as depicted in Fig. 4(d)) was used to verify the accuracy of the 2D visual measurement system. Measurement experiments were conducted at 20 selected transverse and longitudinal positions with a nominal distance of 1 mm by using both HALCON’s calibration method and the proposed method, with the results shown in Fig. 4(e). The average measurement error based on the HALCON calibration model is 2.8 μm, while the proposed method yields an average error of 0.8 μm, with more stable measurement results surpassing those obtained from the HALCON calibration model.

4. Methodologies

4.1. Adaptive illumination method for 2D imaging

High-quality imaging helps facilitate algorithm design and improve measurement stability. When measuring the geometry of drill bits, feature images with high discrimination between the features and background, as well as sharp edges were preferred. Owing to the wide topographic variation of drill bits, obtaining a proper image using off-the-shelf light sources such as ring lights and bar lights is difficult. Inspired by the flexibility of LEDs, in this study, an adaptive bright light source was fabricated for measuring the axial parameters. As illustrated in Figs. 5(a) and (b), a dome-shaped LED array was designed with 12 LEDs embedded on substrates at 30°, 60°, and 90° intervals in four partitions. A 3D-printed shell with a diffuse reflectance coating insert was fabricated to realize this structure. This particular design serves a dual purpose. First, when all LED elements emit light with the same intensity, the light source creates an effect equivalent to a domed light source, ensuring uniform illumination across the field of view. Second, by controlling the parameters of the LED L_i, including the position p_i (x_i, y_i, z_i), illumination angle α_i, and intensity P_i in various combinations, different illumination patterns can be achieved, thus attaining high-contrast illumination. Based on the previous study [33], the luminance E_n of each LED chip can be calculated using the following equation:(8)

E_{n} (x, y, z)= \frac{{(z \cos (α_{i}) - x (\sin (α_{i}))}^{m_{h}} P_{i}}{{({(x \cos (α_{i}) + z \sin (α_{i}) - x_{i})}^{2} + {(y - y_{i})}^{2} + {(z \cos (α_{i}) - x \sin (α_{i}))}^{2})}^{m_{h} +3/2}}

E_{n} (x, y, z)= \frac{{(z \cos (α_{i}) - x (\sin (α_{i}))}^{m_{h}} P_{i}}{{({(x \cos (α_{i}) + z \sin (α_{i}) - x_{i})}^{2} + {(y - y_{i})}^{2} + {(z \cos (α_{i}) - x \sin (α_{i}))}^{2})}^{m_{h} +3/2}}

where n is the number of LEDs and m_h is a factor related to the half-angle of the LED. (x, y, z) are the coordinates of the measured point for luminance. To achieve better directionality and distinguishability of adjacent beads, straw-hat LEDs with a half-angle of 30° and a diameter of 5 mm were selected. The radiation characteristics of the LED are shown in Fig. 5(c). To rationally design the dimensions of the light source, the illuminance distribution of two symmetrically distributed LED beads was calculated using Eq. (5). The results indicate that the proposed light source with a diameter of R_L = 100 mm and a height of H_L = 35 mm can achieve a balance between uniformity and distinctiveness based on the designed distribution. The simulated calculation results are shown in Fig. 5(d), illustrating the differentiation in the peak positions of the distribution. Additionally, to achieve automated measurement, a method of adaptive illumination based on the aforementioned light source was proposed, enabling the acquisition of high-quality images through simple interactive operations as depicted in Fig. 5(e). First, when all the LEDs, parameterized as L_i(x_i, y_i, z_i, α_i, P_i), are illuminated with the same luminous intensity, the proposed light source approximates a dome light source that can provide uniform illumination of the entire field. The initial illumination pattern (

E_{I n i t i a l}

E_{I n i t i a l}

) can be expressed as(9)

\begin{matrix} E_{Initial} = \sum_{n = 1}^{12} E_{n} (L_{i} (x_{i}, y_{i}, z_{i}, α_{i}, P_{i})) \\ s . t . \{\begin{matrix} x_{i}^{2} + y_{i}^{2} < R_{L}^{2}, z_{i} \in [0, H_{L}] \\ α_{i} \in \{30 °, 60 °, 90 °\} \\ P_{i} \in \{1, 0\} \end{matrix} \end{matrix}

\begin{matrix} E_{Initial} = \sum_{n = 1}^{12} E_{n} (L_{i} (x_{i}, y_{i}, z_{i}, α_{i}, P_{i})) \\ s . t . \{\begin{matrix} x_{i}^{2} + y_{i}^{2} < R_{L}^{2}, z_{i} \in [0, H_{L}] \\ α_{i} \in \{30 °, 60 °, 90 °\} \\ P_{i} \in \{1, 0\} \end{matrix} \end{matrix}

Thus, this uniform illumination pattern can be used to obtain a focused and globally illuminated image I_G. Second, a rectangular focus area I_GF can be extracted by a focused region detection algorithm based on grayscale gradients. Then, as displayed in Fig. 5(e), the target feature areas (red arrows) and background areas (blue arrows) within the focus area are simply labeled with scribbles on the I_GF to generate an image with sparse constraints. The preliminary relative positional information of the target area and background area can be obtained through an image matting algorithm based on the closed form solution [34]. Once the transparency solution is obtained, binarizing the transparency matrix yields the distribution of the target and background areas. Furthermore, based on the previously derived relationship between the position and illumination intensity of the light source, the optimal solution for measuring the feature parameters of the illumination can be obtained. Subsequently, the selection and combination of LED parameters can be modified by calculating the contrast and uniformity. Finally, high-contrast lighting is achieved by a light source controller. The results shown in Fig. 5 also demonstrate that the proposed adaptive lighting system and strategy are capable of enhancing image features. For the backlight source, the parallelism of the emitted light rays and the area of the light source are key to reducing edge scattering. Therefore, the luminous area of the backlight source was designed to be the same as the cross-sectional size of the drill bits and the parallelism of the light source was ensured using a shading panel to obtain clear contour images of the boundaries.

4.2. Automatic feature identification and measurement method for 2D parameters

Most existing geometric parameter measurement methods based on image processing require manual selection of key points and simple image processing algorithms for identification, leading to significant errors and poor stability. To avoid measurement errors caused by subjective judgments and improve the stability of feature extraction, this study devised an automatic feature identification and parameter measurement method based on the accurate extraction of quantitative subpixel information. Fig. 6(a) illustrates the automatic image processing flowchart for parameter measurement, while Fig. 6(b) displays an example of the process for the chisel edge. After acquiring high-contrast feature images, the initial step involves delineating the region of interest (ROI) in the image through box selection. Further refinement involves subpixel feature extraction within the selected ROI. Given that cutting tool edges conform to curve generation rules, subpixel edge extraction algorithms based on fitting methods can more accurately extract actual edges. Therefore, a subpixel edge extraction algorithm based on local grayscale area effects [35] was employed. Specifically, based on ideal linear and curve equations, the grayscale area around the edge is calculated through integration within a computational window. By utilizing this area calculation, fitting edge coefficients are obtained, ultimately determining the position and gradient direction of subpixel edges. After acquiring subpixel edge features, accurate identification and localization of edge corners are necessary to automate parameter measurements, enabling subsequent feature fitting and measurement. To improve the robustness of corner detection to small-scale noise, the gray gradient direction angle is introduced as a criterion to enhance the K-cosine corner recognition algorithm. This enhanced algorithm is suitable for detecting corners (formed by lines and lines, lines and curves, and tangent points of curves and lines) in tool images. Based on the edge gradient direction information extracted from subpixel edges, the discerning criteria for corner points are proposed as follows:(10)

\{\begin{matrix} β_{i} = \frac{\partial I(x_{ei}, y_{ei})}{\partial y_{e i}} / \frac{\partial I(x_{ei}, y_{ei})}{\partial x_{e i}} \\ |β_{i +1} - β_{i}| \geq T_{1}, |β_{i +2} - β_{i}| \geq |β_{i +1} - β_{i}| + T_{1} \end{matrix}

\{\begin{matrix} β_{i} = \frac{\partial I(x_{ei}, y_{ei})}{\partial y_{e i}} / \frac{\partial I(x_{ei}, y_{ei})}{\partial x_{e i}} \\ |β_{i +1} - β_{i}| \geq T_{1}, |β_{i +2} - β_{i}| \geq |β_{i +1} - β_{i}| + T_{1} \end{matrix}

where β_i is the gray gradient direction angle of the subpixel edge point (x_ei, y_ei), T₁ is an experience threshold value, and I (x_ei_, y_ei) is the gray value of point (x_ei, y_ei). In this study, T₁ = 0.028π. As depicted in Fig. 5(b), the gradient direction angle for each subpixel edge point is first computed, followed by individual verification of whether the angles of adjacent points satisfy Eq. (7). If they do, the point is then designated as a distinctive corner point. Fig. 6(c) illustrates the proposed corner detection method and the comparative results of corner point detection between the proposed method and the traditional method. Evidently, the proposed algorithm can robustly detect corners with subtle feature variations in the tool image, providing a solid basis for subsequent tool contour fitting and parameter measurement.

4.3. 3D reconstruction for complex drill bits

Shape from focus is a commonly used method for measuring the 3D topography of small components. It employs a high-precision linear motor to drive the stage, and image sequences are captured with a microscopic imaging system. Notably, owing to the presence of machining marks, the surface of drill bits is not completely smooth; small grooves were discernible. Additionally, the inherent high reflectivity of the metal material used for drill bits can lead to localized areas of high reflection in the acquired image sequences, which in turn affects the integrity and accuracy of 3D measurements. For a shape-from-focus 3D microscopic imaging system, capturing images with excellent edge contrast and overall uniformity is essential to ensure that the focus evaluation function calculates features more accurately. Notably, using a single point light source with coaxial lighting may weaken edge information in the resulting image. To overcome this limitation, in this study, an additional dome light source with a wavelength of 458 nm was utilized to ensure uniform illumination and clear edge information in the feature images. As displayed in Fig. 7, the effectiveness of using the dome light source was validated through both simulations (Fig. 7(a)) and experiments (Fig. 7(b)), determining the optimal illumination area and distance.

As shown in Fig. 8, the system first acquires a sequence of images of the drill bits and then calculates the focus value for each pixel across these sequential images using a focus evaluation function. Interpolation is used to determine the precise position of each pixel corresponding to its peak focus value, enabling the accurate calculation of the relative height of each pixel. The relative height h of a pixel can be calculated using(11)

\begin{matrix} h = \frac{({ln F}_{i} - {ln F}_{i +1}) (d_{i}^{2} - d_{i -1}^{2}) - ({ln F}_{i} - {ln F}_{i -1}) (d_{i}^{2} - d_{i +1}^{2})}{2 Δ d \{({ln F}_{i} - {ln F}_{i -1}) + ({ln F}_{i} - {ln F}_{i +1})\}} # \end{matrix}

\begin{matrix} h = \frac{({ln F}_{i} - {ln F}_{i +1}) (d_{i}^{2} - d_{i -1}^{2}) - ({ln F}_{i} - {ln F}_{i -1}) (d_{i}^{2} - d_{i +1}^{2})}{2 Δ d \{({ln F}_{i} - {ln F}_{i -1}) + ({ln F}_{i} - {ln F}_{i +1})\}} # \end{matrix}

where F_i is the focus value at the maximum point d_i, and

Δ d

Δ d

is the scanning step. After reconstructing the surface topography, the parameters of the cutting tools can be further determined. As is evident from the preceding analysis, the focus measure is the key to ensuring the accuracy and quality of 3D reconstruction. Conventional focus measures often fail to meet the needs of depth calculation for tool image sequences, resulting in poor quality of 3D reconstructed point cloud and increased noise. As depicted in Fig. 8, this study devised an improved focus measure that enhances focusing features in both the spatial and frequency domains (ITene–Gabor). Specifically, the proposed method leverages the strengths of both domains to enhance the accuracy and robustness of the focus evaluation process. In the spatial domain, the Tenengrad function is an efficient algorithm for calculating the gray gradient of an image[36]. However, this function is susceptible to noise. Hence, we first introduce an improvement to the Sobel operators:(12)

G_{x} = [\begin{matrix} 2 \sqrt{2} & 0 & - 2 \sqrt{2} \\ 4 & 0 & - 4 \\ 2 \sqrt{2} & 0 & - 2 \sqrt{2} \end{matrix}], G_{y} = [\begin{matrix} 2 \sqrt{2} & 4 & 2 \sqrt{2} \\ 0 & 0 & 0 \\ - 2 \sqrt{2} & - 4 & - 2 \sqrt{2} \end{matrix}]

G_{x} = [\begin{matrix} 2 \sqrt{2} & 0 & - 2 \sqrt{2} \\ 4 & 0 & - 4 \\ 2 \sqrt{2} & 0 & - 2 \sqrt{2} \end{matrix}], G_{y} = [\begin{matrix} 2 \sqrt{2} & 4 & 2 \sqrt{2} \\ 0 & 0 & 0 \\ - 2 \sqrt{2} & - 4 & - 2 \sqrt{2} \end{matrix}]

where G_x and G_y represent the horizontal and vertical operators, respectively. The improved operator compensates for calculating the greater distance from diagonal points to the center point by applying a weighting coefficient, and simultaneously enhances more edge details. To further reduce noise, an edge gradient angle α_g is introduced as follows:(13)

\begin{matrix} α_{g} = arctan \frac{G_{x}}{G_{y}} # \end{matrix}

\begin{matrix} α_{g} = arctan \frac{G_{x}}{G_{y}} # \end{matrix}

Then, the final operator can be written as(14)

\begin{matrix} G (x, y) = \sqrt{{(G_{x} cos α_{g})}^{2} + {(G_{y} sin α_{g})}^{2}} # \end{matrix}

\begin{matrix} G (x, y) = \sqrt{{(G_{x} cos α_{g})}^{2} + {(G_{y} sin α_{g})}^{2}} # \end{matrix}

Therefore, the improved Tenengrad function (

F_{(x,y)}^{1}

F_{(x,y)}^{1}

) can be expressed as(15)

\begin{matrix} F_{(x,y)}^{1} = \sum_{x - \frac{w - 1}{2}}^{x+ \frac{w - 1}{2}} \sum_{y - \frac{w - 1}{2}}^{y+ \frac{w - 1}{2}} {[G (x, y) - \bar{G}]}^{2} (T_{min} < F_{(x,y)}^{1} < T_{max}) # \end{matrix}

\begin{matrix} F_{(x,y)}^{1} = \sum_{x - \frac{w - 1}{2}}^{x+ \frac{w - 1}{2}} \sum_{y - \frac{w - 1}{2}}^{y+ \frac{w - 1}{2}} {[G (x, y) - \bar{G}]}^{2} (T_{min} < F_{(x,y)}^{1} < T_{max}) # \end{matrix}

where

w

w

is the size of the calculation window; here

w = 3.

w = 3.

\bar{G}

\bar{G}

is the average of

G (x, y)

G (x, y)

in the window. Additionally, a threshold interval [T_min, T_max] is specified to prevent noise interference. In the frequency domain, the focus area typically contains high-frequency information. By introducing a filter, more texture information can be captured, and the interference of illumination changes on the focus measure can be further eliminated. In this study, a Gabor filter was introduced to construct the function in frequency (

H (x_{i}, y_{i})

H (x_{i}, y_{i})

) for an image I:(16)

\begin{matrix} H (x_{i}, y_{i}) = I \sum_{x_{i} - (\frac{w - 1}{2})}^{x_{i} + (\frac{w - 1}{2})} g (x, y) # \end{matrix}

\begin{matrix} H (x_{i}, y_{i}) = I \sum_{x_{i} - (\frac{w - 1}{2})}^{x_{i} + (\frac{w - 1}{2})} g (x, y) # \end{matrix}

where

I

I

g (x, y) is the Gabor filter. Because the result is a complex number, the evaluation function (

F_{(x, y)}^{2}

F_{(x, y)}^{2}

) can be described as follows:(17)

\begin{matrix} F_{(x, y)}^{2} = H (x, y) \bar{H} (x, y) # \end{matrix}

\begin{matrix} F_{(x, y)}^{2} = H (x, y) \bar{H} (x, y) # \end{matrix}

Here,

\bar{H} (x, y)

\bar{H} (x, y)

is the conjugate complex number of H (x, y). Specifically, the weighting factor is defined as the ratio of the gray level of the central pixel to the average gray level within the calculation window. The final focus measure can be written as follows:(18)

\begin{matrix} F (x, y) = F_{(x, y)}^{1} F_{(x, y)}^{2} # \end{matrix}

\begin{matrix} F (x, y) = F_{(x, y)}^{1} F_{(x, y)}^{2} # \end{matrix}

By constructing this focus measure, which enhances both grayscale gradients and high-frequency information, the calculation of the optimal focus position for the cutting tools in the image sequence becomes more accurate. This approach significantly reduces noise in 3D reconstruction caused by inaccurate focus evaluation, thereby enhancing the precision of 3D measurements.

5. Measurement experiments and discussion

5.1. Comparison of 2D measurements with the method using dome lighting imaging

To demonstrate the effectiveness of the proposed adaptive lighting approach and highlight the limitations of uniform illumination, a comparison of 2D measurements using dome lighting imaging was conducted. The same imaging system was used to measure the 2D geometric parameters of complex drill bits under both illumination conditions. The left side of Fig. 9 illustrates the end-face morphology of the two drill bits to be measured, along with the representation of their geometric parameters, revealing significant variations in profile slope and the presence of numerous microstructures. To measure the end-face parameters (b, d_c, and c), images characterizing these feature parameters under the two lighting conditions were acquired at different focusing positions, as displayed in Fig. 9. Evidently, the imaging results with adaptive lighting exhibit better contrast. Conversely, the grayscale of the 2D images obtained under dome lighting is uneven, making it challenging to accurately extract key feature points for measurement, and the measurement results are unstable. For instance, when measuring the length of the chisel edge b, uniform lighting leads to consistent grayscale across the two flanks of the drill bits, causing difficulty in distinguishing the features of the chisel edge. In comparison, adaptive lighting illuminates only one flank, enhancing the contrast between the chisel edge features and the background information, thus facilitating subsequent feature extraction and measurements. Similarly, adaptive lighting is highly effective on the edges of flat and curved surfaces, as well as intricate microstructures.

5.2. Effectiveness verification of 3D reconstruction based on shape from focus

To quantify the accuracy of the 3D visual measurement system, a standard metal groove block with a depth of 1.22 ± 0.001 mm was utilized. Using the system and proposed methods, 3D reconstruction and depth measurement of the block were performed. Feature images of the sample were captured with a step distance of 0.0015 mm, which is the same step distance used in our drill bit measurement experiments. The full-focus images (Fig. 10(a)), 3D reconstruction results (Fig. 10(b)), and cross-sectional measurement results (Fig. 10(c)) of the block were obtained. The results indicate that the average measurement error for depth is 1 μm.

To validate the effectiveness of the proposed focus measure for 3D measurement of drill bits, we compared it with six typical focus measures: Gaussian derivative (GRA1), Tenengrad (GRA6), Energy of Laplacian (LAP1), sum of wavelet coefficients (WAV1), gray-level variance (STA3), and Brenner’s measure (MIS2). Figs. 11(a) and (b) show the normalized focus values of a point on the chisel edge P₁ and cutting edge P₂. The results demonstrate that the proposed focus measure exhibits higher sensitivity, better noise resistance, and unimodality compared to the other measures. These same characteristics are also evident in the global focus sequence images of both the end and side faces of the drill bits, as illustrated in Figs. 11(c) and (d). Therefore, the proposed focus measure is more appropriate for 3D topography reconstruction, as it leads to higher measurement accuracy.

Furthermore, 3D reconstruction of the drill bit was conducted. Owing to the occlusion of the end face, obtaining a complete point cloud from a single view is impossible. Thus, image sequences of the end face (245 images) and side face (70 images) were collected with a scanning step of 15 μm. By applying Eq. (6) and the focus measure proposed herein (ITene-Gabor), the initial point cloud and full-focus images of the drill bit were obtained. Subsequently, the statistical outlier removal point cloud filtering method was used to acquire the 3D topography of the cutting tool, as depicted in Figs. 12(a) and (b). To realize a complete 3D topography, the two parts of the point cloud needed to be fused. During the measurement process from the end face to the lateral face, the position change was achieved using a high-precision fixture turntable. Thus, the rotation and translation matrices are known and can be used to unify the coordinates of the two parts of the point cloud, enabling point cloud fusion and the creation of a complete surface morphology of the drill bit. The fused point cloud of the drill bit is displayed in Fig. 12(c). Moreover, the 3D parameters of the cutting tools can be measured using either vector calculation or projection methods. To further demonstrate the enhanced 3D reconstruction effect achieved by the proposed method, 3D reconstruction was also conducted based on traditional focus measures applied to the same acquired feature images, as shown in Fig. 12(d). The proposed method yields a higher quality point cloud reconstruction for the drill bit with a complex structure. Quality evaluation was performed based on the number of points N_p, surface roughness

S_{q}

S_{q}

, and point cloud surface density ρ within a neighborhood radius R (R = 0.05 mm), as well as the root mean square error (RMSE). A commercially available infinite focus microscope (InfiniteFocusG5, Alicona, Austria) was used to acquire the actual depth map, which had an accuracy of 1 μm for length measurements and 0.15° for angle measurements. The 3D point clouds of the drill bits obtained in this study were compared with those generated using the traditional focus measure (Tenengrad), and the results are listed in Table 2. As indicated, the quality of the 3D points derived in this study is superior to that produced using the traditional focus measure.

5.3. Geometric parameter measurement for drill bits with sawtooth features

Leveraging the proposed correlated fusion vision dual-platform and methodology, measurements were conducted on 15 parameters following the measurement process illustrated in Fig. 13. The steps and parameter transmission of the 2D and 3D imaging systems are described in detail as follows:

Step 1. The fixture is adjusted to ensure that the end face of the drill bit is perpendicular to the X–Z plane. Then, image sequences are obtained by scanning the end face with the 3D measurement system. The 3D positions are calculated to acquire the 3D point clouds of the end face based on various focus levels. Simultaneously, full-focus images are obtained.

Step 2. After a full-focus image is obtained in Step 1, the angle between the main cutting edge and the X-axis is calculated. Based on this calculated angle, the cutting tool rotation is adjusted to effectively position structures such as microteeth within the field of view of the 2D imaging system.

Step 3. The backlight source is controlled, and the position of the Z-axis system is adjusted to achieve focus. The parameters l₁, l₂, d, d₁, φ₁, and φ₂ are then measured based on transmitted light. Subsequently, the backlight source is turned on and the adaptive illumination system is used to measure the parameters f and β based on reflected light at the same position.

Step 4. In Step 1, the spatial positions of features such as the chisel edge and the drill center are obtained from the 3D point cloud. In Step 3, the total length of the drill bit is acquired by detecting the tool tip and the tool shank using the 2D camera. Based on these results, the X-direction movement of the fixture and the Z-direction movement of the camera are automatically calculated. This ensures that the features measured in Step 4 can be perfectly positioned and focused within the view of the 2D camera after rotation around the Y-axis. Then, the adaptive light source illumination can be used to acquire feature images and measure the parameters b, c, and d_c.

Step 5. After the parameters such as the thickness of the drill center are determined in Step 4, the setting of start and end points for 3D reconstruction is automatically adjusted accordingly, enabling faster acquisition of the 3D point cloud. Additionally, based on the total length of the tool obtained in Step 3, the required movement of the fixture device is automatically calculated to achieve automatic alignment of the tool tip within the field of view of the 3D camera after rotation. Subsequently, image sequences of the side face are acquired and the 3D topography of the side surface is then reconstructed.

Step 6. The 3D point clouds obtained in Steps 1 and 5 are fused to acquire a complete 3D topography of the measured drill bit. Then, the parameters γ_oψ, α_oψ, γ_o, and α_o are measured using vector calculation or projection methods.

Geometric parameter measurements were conducted on two typical drill bits with complex structures, as shown in Fig. 14(a). The measurement results of the 2D parameters are displayed in Fig. 14(b). All these results were obtained using the integrated, convenient, instant One-Key measurement software. After image acquisition, the position is box-selected and the type of measurement parameter is input. The feature edge fitting and measurement results are then automatically generated. Fig. 14(c) depicts the 3D topography reconstruction results of the two drill bits. Measurements of the 3D parameters were directly obtained from the acquired point cloud data using the designed automated measuring software. Finally, the measurement results of the geometric parameters of the drill bits are summarized in Table 3. Each parameter was measured five times and compared to the results obtained by the commercial microscope (InfiniteFocus G5, Alicona, Austria) with a 10X objective lens. The results indicate that the length and angle measurement deviations are less than 3 μm and 0.5°, respectively, which meet the requirements. Furthermore, the rationality of the measurement process ensures the efficiency of tool measurement, with an average measurement time of 30 s per parameter.

6. Conclusions

Motivated by the demands for geometric parameter measurement of drill bits with complex structures considering both measurement accuracy and efficiency, this study developed a correlated fusion vision dual-platform and a series of visual measurement methods. Initially, a prototype integrating the correlated fusion visual measurement system was designed, and a novel telecentric lens calibration model and method were proposed to mitigate measurement errors stemming from installation inaccuracies in the correlated dual-platform. Then, an adaptive illumination method was proposed to obtain high-quality images for measuring 2D parameters, and an automatic parameter measurement method based on an improved feature extraction and identification algorithm was investigated. For accurate 3D parameter measurement, a novel and universal focus measure was proposed to enhance the accuracy and robustness of the focus evaluation. Analyses and verification experiments were conducted on the aforementioned methods. First, the superiority of adaptive lighting over uniform illumination was demonstrated for 2D measurements. Second, a comparative analysis was performed on the advantages of the proposed focus measure in 3D reconstruction compared to other measures. Finally, geometric parameter measurements were carried out on two typical drill bits with complex structures. The developed equipment showed a deviation of less than 3 μm for length and less than 0.5° for angle compared to a commercial microscope, achieving a measurement efficiency of 30 s per parameter. This demonstrates the effectiveness of the proposed method. Moreover, it also establishes that the proposed method and system are also suitable for the detection and parameter measurement of other complex industrial parts and have high commercialization potential.

CRediT authorship contribution statement

Wenqi Wang: Writing – review & editing, Writing – original draft, Visualization, Validation, Supervision, Software, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Wei Liu: Writing – review & editing, Supervision, Resources, Funding acquisition, Conceptualization. Yang Liu: Visualization, Validation, Supervision, Software, Resources. Yang Zhang: Writing – review & editing, Resources, Funding acquisition. F. Zhenyuan Jia: Writing – review & editing, Resources, Funding acquisition.

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.

Acknowledgements

This work was supported by the National Natural Science Foundation of China (52125504 and 2023RG001)

Compliance with ethics guidelines

Wenqi Wang, Wei Liu, Yang Liu, Yang Zhang and Zhenyuan Jia declare that they have no conflicts of interest or financial conflicts to disclose.

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1. Introduction

2. Related works

2.1. 2D machine vision

2.2. 3D vision measurement

2.3. Discussion

3. System

3.1. Overall structure of the correlated fusion vision measurement system

3.2. Calibration of the bi-telecentric imaging system

4. Methodologies

4.1. Adaptive illumination method for 2D imaging

4.2. Automatic feature identification and measurement method for 2D parameters

4.3. 3D reconstruction for complex drill bits

5. Measurement experiments and discussion

5.1. Comparison of 2D measurements with the method using dome lighting imaging

5.2. Effectiveness verification of 3D reconstruction based on shape from focus

5.3. Geometric parameter measurement for drill bits with sawtooth features

6. Conclusions

CRediT authorship contribution statement

Declaration of competing interest

Acknowledgements

Compliance with ethics guidelines

References