| Citation: | ZHENG Yi-chen, WU Jin-hui, LIU Ji, ZHANG Bo-yang, YUAN Tao. Micro-displacement measurement based on opposed dual-surface differential conjugate vortex beam interference[J]. Chinese Optics. doi: 10.37188/CO.2026-0097
|
To address the limitations of conventional conjugate vortex beam interference-based micro-displacement measurement methods, including limited rotation-angle variations of interference patterns and insufficient capability for sub-nanometer displacement detection, a micro-displacement measurement method based on opposed dual-surface differential conjugate vortex beam interference is proposed. The proposed method exploits the linear relationship between the rotation angle of the conjugate vortex interference pattern and the phase difference between two interferometric paths, converting micro-displacement into the angular rotation of petal-shaped interference patterns. To overcome the constraints imposed by camera pixel resolution and pattern distortion on tiny rotation-angle extraction, an opposed dual-surface differential optical path is developed, where two conjugate vortex beams interact with opposite surfaces of the same target. Compared with the conventional single-surface reflection configuration, the proposed structure doubles the relative optical path difference, thereby theoretically doubling the interference-pattern rotation angle under identical displacement conditions. Furthermore, an H-Nets model based on circular harmonic convolution is introduced to extract rotation-equivariant features from the rotating interference patterns. Continuous angular variations are encoded as phase shifts in the complex-valued feature space, enabling stable characterization of tiny rotation angles and accurate displacement inversion. Experimental results demonstrate that, within a displacement range of 0–500 nm, the maximum absolute error is below 0.61 nm, with a mean absolute error of 0.37 nm. The proposed method achieves enhanced micro-displacement measurement accuracy and stability through the synergistic integration of differential optical-path amplification and rotation-equivariant feature decoding.
| [1] |
HSIEH H L, LEE J Y, WU W T, et al. Quasi-common-optical-path heterodyne grating interferometer for displacement measurement[J]. Measurement Science and Technology, 2010, 21(11): 115304. doi: 10.1088/0957-0233/21/11/115304
|
| [2] |
CUI C, LI X H. Precision nanometrology: laser interferometer, grating interferometer and time grating sensor[J]. Sensors, 2025, 25(21): 6791. doi: 10.3390/s25216791
|
| [3] |
张智超, 海澜, 张书瑞, 等. 复杂结构光场的多自由度协同调控技术研究进展[J]. 光电工程, 2024, 51(8): 240079. doi: 10.12086/oee.2024.240079
ZHANG ZH CH, HAI L, ZHANG SH R, et al. Advances on the manipulation of structured beams with multiple degrees of freedom[J]. Opto-Electronic Engineering, 2024, 51(8): 240079. (in Chinese). doi: 10.12086/oee.2024.240079
|
| [4] |
赵冬娥, 王思育, 马亚云, 等. 基于涡旋光与球面波干涉的微位移测量研究[J]. 红外与激光工程, 2020, 49(4): 0413005. doi: 10.3788/IRLA202049.0413005
ZHAO D E, WANG S Y, MA Y Y, et al. Measurement of micro-displacement based on the interference of vortex beams and spherical wave[J]. Infrared and Laser Engineering, 2020, 49(4): 0413005. (in Chinese). doi: 10.3788/IRLA202049.0413005
|
| [5] |
MA J B, LI P, GU Y Z. Characteristics of spiral patterns formed by coaxial interference between two vortex beams with different radii of wavefront curvatures[J]. Photonics, 2021, 8(9): 393. doi: 10.3390/photonics8090393
|
| [6] |
XIAO M C, YANG D, XIONG J W. Non-contact measurement for cone angle of axicon lens based on vortex interference[J]. Optics Communications, 2021, 499: 127267. doi: 10.1016/j.optcom.2021.127267
|
| [7] |
YANG D, YANG ZH M, ZHAO ZH G, et al. Radius of curvature of spherical wave measurement based on vortex beam interference[J]. Optics and Lasers in Engineering, 2021, 142: 106592. doi: 10.1016/j.optlaseng.2021.106592
|
| [8] |
WANG Y C, SHYU L H, CHANG C P. The comparison of environmental effects on Michelson and Fabry-Perot interferometers utilized for the displacement measurement[J]. Sensors, 2010, 10(4): 2577-2586. doi: 10.3390/s100402577
|
| [9] |
ZHAO N, QIAN G, FU X CH, et al. Integrated optical displacement sensor based on asymmetric Mach–Zehnder interferometer chip[J]. Optical Engineering, 2017, 56(2): 027109. doi: 10.1117/1.OE.56.2.027109
|
| [10] |
SENTHILKUMARAN P, MASAJADA J, SATO S. Interferometry with vortices[J]. International Journal of Optics, 2012, 2012(1): 517591. doi: 10.1155/2012/517591
|
| [11] |
GAO H W, YANG D, HU X N, et al. High-precision micro-displacement measurement in a modified reversal shearing interferometer using vortex beams[J]. Optics Communications, 2023, 537: 129454. doi: 10.1016/j.optcom.2023.129454
|
| [12] |
WEBSTER J, ROSALES-GUZMÁN C, FORBES A. Radially dependent angular acceleration of twisted light[J]. Optics Letters, 2017, 42(4): 675-678. doi: 10.1364/OL.42.000675
|
| [13] |
EMILE O, EMILE J. Naked eye picometer resolution in a Michelson interferometer using conjugated twisted beams[J]. Optics Letters, 2017, 42(2): 354-357. doi: 10.1364/OL.42.000354
|
| [14] |
夏豪杰, 谷容睿, 潘成亮, 等. 涡旋光位移干涉测量方法与信号处理[J]. 光学 精密工程, 2020, 28(9): 1905-1912. doi: 10.37188/OPE.20202809.1905
XIA H J, GU R R, PAN CH L, et al. Signal processing method for displacement measurement interferometry using vortex beams[J]. Optics and Precision Engineering, 2020, 28(9): 1905-1912. (in Chinese). doi: 10.37188/OPE.20202809.1905
|
| [15] |
LU H L, HAO Y Y, GUO CH J, et al. Nano-displacement measurement system using a modified orbital angular momentum interferometer[J]. IEEE Journal of Quantum Electronics, 2022, 58(2): 7500105.
|
| [16] |
YUAN T, LIU J, WU J H, et al. Advanced vortex beam interference system enhanced by CNN for micro-displacement detection[J]. Optics and Lasers in Engineering, 2025, 191: 108987. doi: 10.1016/j.optlaseng.2025.108987
|
| [17] |
杨雪娇, 刘吉, 武锦辉, 等. 深度学习融合模型共轭涡旋光干涉微位移测量[J]. 光学 精密工程, 2025, 33(15): 2331-2341. doi: 10.37188/OPE.20253315.2331
YANG X J, LIU J, WU J H, et al. Conjugate vortex beam interferometry for micro-displacement measurement with deep learning fusion architecture[J]. Optics and Precision Engineering, 2025, 33(15): 2331-2341. (in Chinese). doi: 10.37188/OPE.20253315.2331
|
| [18] |
COHEN T, WELLING M. Group equivariant convolutional networks[C]. Proceedings of the 33rd International Conference on Machine Learning, JMLR. org, 2016: 2990-2999.
|
| [19] |
MARCOS D, VOLPI M, KOMODAKIS N, et al. Rotation equivariant vector field networks[C]. Proceedings of the IEEE International Conference on Computer Vision, IEEE, 2017: 5058-5067.
|
| [20] |
WORRALL D E, GARBIN S J, TURMUKHAMBETOV D, et al. Harmonic networks: deep translation and rotation equivariance[C]. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition, IEEE, 2017: 7168-7177.
|
| [21] |
ZHANG ZH H, ZHAO G B, BAN Y W, et al. High-fold optical subdivision blazed grating interferometer based on Mach-Zehnder interferometer[J]. Measurement, 2025, 242: 116128. doi: 10.1016/j.measurement.2024.116128
|
| [22] |
YE G Y, YUAN T, ZHANG Y L, et al. Recent progress on laser interferometry based on vortex beams: status, challenges, and perspectives[J]. Optics and Lasers in Engineering, 2024, 172: 107871. doi: 10.1016/j.optlaseng.2023.107871
|
Figures(9) / Tables(5)
DownLoad:
