Research on missing tooth detection of gear-shaped targets based on beam orbital angular momentum scanning
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摘要:
传统基于轨道角动量强度谱的检测方法虽能判断齿轮是否存在缺陷，却因相位信息丢失而无法识别缺齿的具体方位。针对这一局限，本文通过模拟发射不同拓扑荷值的涡旋光束扫描完好及缺陷齿轮，结合理想平面波四步相移处理，构建出包含螺旋相位信息的OAM复数谱，提取了各齿轮的方位角信息，从而实现了缺齿方位及序号的准确判定。本文扩展了非简单扇形目标如齿轮的基圆参数和齿高对缺陷测量影响的研究，发现缺损位置信号与相邻正常齿轮信号相对幅度差距大小与齿轮参数有关，在固定基模束腰半径为6 mm时，其中信号幅度差值随齿高从2 mm逐渐提升到4 mm而提升，随基圆从10 mm逐渐提升到14 mm时而降低。本研究为基于OAM扫描的无接触、高精度齿轮缺陷定位中提供了初步探索和应用途径。
Abstract:Conventional detection methods based on OAM intensity spectra can identify the presence of gear defects but fail to determine the specific azimuthal positions of missing teeth due to the loss of phase information. To address this limitation, this study simulates the scanning of intact and defective gears using vortex beams with varying topological charges. By incorporating a four-step phase-shifting algorithm based on ideal plane waves, we construct an OAM complex spectrum that retains helical phase information. This spectrum extracts the azimuthal characteristics of the gear, enabling the accurate determination of both the position and the index of missing teeth. Furthermore, this study investigates the impact of base circle parameters and tooth height on defect measurements in non-trivial sector targets. The results demonstrate that the relative amplitude difference between defective and adjacent intact gear signals is highly dependent on these geometric parameters. Specifically, when the fundamental mode waist radius is fixed at 6 mm, increasing the tooth height from 2 mm to 4 mm enhances the signal amplitude difference, whereas increasing the base circle radius from 10 mm to 14 mm diminishes it. Ultimately, this research provides preliminary insights and a viable pathway toward high-precision, non-contact gear defect localization based on the OAM scanning.
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图 1 利用相位解调法测量齿轮回波信号OAM强度谱的模拟算法流程图
Figure 1. Flowchart of the simulation algorithm for measuring the OAM intensity spectrum of echo signals of gear using the phase demodulation method
图 2 利用四步相移法测量齿轮缺齿情况的模拟算法流程图
Figure 2. Flowchart of the simulation algorithm for measuring the gear missing-tooth condition using the four-step phase-shifting method
图 3 72°目标所对应OAM相位谱，以及OAM复数谱傅里叶变换的结果
Figure 3. OAM phase spectrum corresponding to the 72° target and OAM complex spectrum Fourier transform result
图 4 基于相位解调法测量拓扑荷为(a)l=0,(b)l=−1的涡旋光束照射八齿齿轮OAM强度谱;(c) 拓扑荷为(c)l=0,(d)l=−1的涡旋光束照射十齿齿轮OAM强度谱
Figure 4. OAM intensity spectra using phase demodulation method of 8-tooth gear illuminated by vortex beams with (a) l = 0 and (b) l = −1; OAM intensity spectra of 10-tooth gear illuminated by vortex beams with topological charges of (c) l = 0 and (d) l = −1.
图 5 基于相位解调法测量拓扑荷为−2的涡旋光束照射，无缺陷(左)，三号齿缺陷(中)，五号齿缺陷(右)十齿齿轮的OAM强度谱
Figure 5. Measurement of the OAM intensity spectrum for a ten-tooth gear with no defect (left), missing tooth #3 (middle), and missing tooth #5 (right) illuminated by a vortex beam with a topological charge of −2 using the phase demodulation method
图 6 不同阶数涡旋光束与平面波叠加态光强分布示意图
Figure 6. Schematic diagram of the intensity distribution of the superposition state of vortex beams of different orders and reference beams
图 7 八齿（上）、十齿（中）与十二齿（下）的完整齿轮被不同拓扑荷涡旋光的扫描的OAM谱以及OAM复数谱傅里叶变换结果
Figure 7. OAM spectra and the OAM complex spectrum Fourier transform for complete gears with eight (top), ten (middle), and twelve (bottom) teeth scanned by vortex beams with different topological charges
图 8 OAM谱特征峰的大小随齿高的变化
Figure 8. Variation of the OAM spectral characteristic peak magnitude with tooth height
图 9 八齿（上）、十齿（中）与十二齿（下）的缺齿齿轮被不同拓扑荷涡旋光的扫描的OAM谱以及OAM复数谱傅里叶变换结果
Figure 9. OAM spectra and the OAM complex spectrum Fourier transform results for missing tooth gears with eight (top), ten (middle), and twelve (bottom) teeth scanned by vortex beams with different topological charges
图 10 二十齿齿轮探测结果，归一化OAM谱（左），以及方位角谱（右）
Figure 10. Detection results of a 20-tooth gear: Normalized OAM spectrum (left) and azimuthal spectrum (right).
图 11 十二齿齿轮缺齿所在方位角的幅度差随齿轮高度（左）和基圆半径（右）变化的曲线
Figure 11. Curve of the amplitude difference corresponding to the azimuthal angle of the missing tooth varying with tooth height (left) and base circle radius (right) for a twelve-tooth gear
图 12 涡旋光叠加态照射齿高为(a)2 mm(b)4 mm齿轮,以及（c）基圆为14 mm齿轮光场振幅图示
Figure 12. Schematic diagram of the optical field amplitude distribution of superimposed vortex beams illuminating gears with tooth heights of (a) 2 mm and (b) 4 mm, and (c) base circle of 14 mm.
图 13 中心偏移(a)0.1(b)0.2个基模束腰半径下测量第9齿缺齿齿轮方位角谱；齿轮总体有(c)3°(b)6°旋转下测量第9齿缺齿齿轮方位角谱
Figure 13. Azimuthal spectra of the 9th missing-tooth gear measured under center offsets of (a) 0.1w0 and (b) 0.2w0, and overall gear rotations of (c) 3° and (d) 6°.
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