Absolute Distance Measurement Based on SelfMixing Interferometry Using Compressed Sensing
Abstract
:1. Introduction
2. Theoretical Analysis
2.1. SelfMixing Interferometry
2.2. Compressed Sensing
2.3. SMI Distance Measurement Using CS
 Acceleration
 Robustness
Algorithm 1 The steps of improved OMP 
Input: Sensing matrix Θ ∈ ℝ^{M}^{×N}; Sampling vector y; Maximum number of iterations m. Initialization: Number of iterations t = 0; Residual vector r_{0} = y; Selected atom matrix Ω_{0} = ∅; Selected index matrix Λ_{0} = ∅. 
Iteration:

$\mathbf{Output}:\widehat{S}\left({\Lambda}_{t+1}\right)={S}_{t+1}.$ 
3. Experimental Results
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Conflicts of Interest
References
 Zhao, Y.; Fan, X.; Wang, C.; Lu, L. An Improved Intersection Feedback MicroRadian AngleMeasurement System Based on the Laser SelfMixing Interferometry. Opt. Lasers Eng. 2020, 126, 105866. [Google Scholar] [CrossRef]
 Kou, K.; Wang, C.; Liu, Y. AllPhase FFT Based Distance Measurement in Laser SelfMixing Interferometry. Opt. Lasers Eng. 2021, 142, 106611. [Google Scholar] [CrossRef]
 Donati, S.; Norgia, M. Overview of SelfMixing Interferometer Applications to Mechanical Engineering. Opt. Eng. 2018, 57, 051506. [Google Scholar] [CrossRef]
 Barland, S.; Gustave, F. Convolutional Neural Network for SelfMixing Interferometric Displacement Sensing. Opt. Express 2021, 29, 11433. [Google Scholar] [CrossRef] [PubMed]
 Zhao, Y.; Xu, G.; Zhang, C.; Liu, K.; Lu, L. Vibration Displacement Immunization Model for Measuring the Free Spectral Range by Means of a Laser SelfMixing Velocimeter. Appl. Opt. 2019, 58, 5540. [Google Scholar] [CrossRef]
 Li, D.; Zhang, Z.; Huang, Z.; Wang, X.; Zhang, Z.; Huang, Z. SelfMixing Interference Vibration Measurement Based on Even Equivalent Wavelength Fourier Transform Algorithm under Weak Feedback Regime. Opt. Eng. 2020, 59, 074101. [Google Scholar] [CrossRef]
 Cui, X.; Li, C.; Geng, Y.; Ge, W.; Kan, L.; Zhang, Z. Secondary Envelope Extraction Based on Multiple Hilbert Transforms for Laser SelfMixing MicroVibration Measurement. Appl. Opt. 2019, 58, 9392. [Google Scholar] [CrossRef]
 Xiang, R.; Wang, C.; Lu, L. Laser Doppler Velocimeter Using the SelfMixing Effect of a Fiber Ring Laser with UltraNarrow Linewidth. J. Opt. 2019, 48, 384–392. [Google Scholar] [CrossRef]
 Lin, H.; Chen, J.; Xia, W.; Hao, H.; Guo, D.; Wang, M. Enhanced SelfMixing Doppler Velocimetry by Fiber Bragg Grating. Opt. Eng. 2018, 57, 051504. [Google Scholar] [CrossRef]
 Li, L.; Li, X.F.; Kou, K.; Wu, T.F. Approach of SelfMixing Interferometry Based on Particle Swarm Optimization for Absolute Distance Estimation. J. Opt. Soc. Korea 2015, 19, 95–101. [Google Scholar] [CrossRef] [Green Version]
 Donati, S.; Giuliani, G.; Merlo, S. Laser Diode Feedback Interferometer for Measurement of Displacements without Ambiguity. IEEE J. Quantum Electron. 1995, 31, 113–119. [Google Scholar] [CrossRef]
 Sun, W.; Gui, H.; Zhang, P.; Wu, S.; Li, Z.; Zhang, K. Measuring MillimeterScale Distances in a Laser SelfMixing Velocimeter with LowSpeed Wavelength Modulation. Opt. Commun. 2018, 427, 107–111. [Google Scholar] [CrossRef]
 Norgia, M.; Magnani, A.; Pesatori, A. High Resolution SelfMixing Laser Rangefinder. Rev. Sci. Instrum. 2012, 83, 045113. [Google Scholar] [CrossRef] [PubMed]
 Zhao, Y.; Zhang, B.; Han, L. Laser SelfMixing Interference Displacement Measurement Based on VMD and Phase Unwrapping. Opt. Commun. 2020, 456, 124588. [Google Scholar] [CrossRef]
 Liu, J.; Huang, K.; Yao, X. CommonInnovation Subspace Pursuit for Distributed Compressed Sensing in Wireless Sensor Networks. IEEE Sens. J. 2019, 19, 1091–1103. [Google Scholar] [CrossRef]
 Vinay, A.; Natarajan, S. Satellite Image Compression Using ROI Based EZW Algorithm. Indones. J. Electr. Eng. Informatics 2017, 5, 369–371. [Google Scholar] [CrossRef]
 Zheng, T.; Dai, Y.; Xue, C.; Zhou, L. Recursive Least Squares for NearLossless Hyperspectral Data Compression. Appl. Sci. 2022, 12, 7172. [Google Scholar] [CrossRef]
 Jiang, B.; Huang, G.; Li, F.; Zhang, S. Compressed Sensing with Dynamic Retransmission Algorithm in Lossy Wireless IoT. IEEE Access 2020, 8, 133827–133842. [Google Scholar] [CrossRef]
 Zhou, F.; Zhao, L.; Li, L.; Hu, Y.; Jiang, X.; Yu, J.; Liang, G. GNSS Signal Acquisition Algorithm Based on TwoStage Compression of CodeFrequency Domain. Appl. Sci. 2022, 12, 6255. [Google Scholar] [CrossRef]
 Schoukens, J.; Pintelon, R.; Van Hamme, H. The Interpolated Fast Fourier Transform: A Comparative Study. IEEE Trans. Instrum. Meas. 1992, 41, 226–232. [Google Scholar] [CrossRef]
 Kou, K.; Li, X.; Li, L.; Li, H.; Wu, T. Absolute Distance Estimation with Improved Genetic Algorithm in Laser SelfMixing Scheme. Opt. Laser Technol. 2015, 68, 113–119. [Google Scholar] [CrossRef]
 Zhang, C.; Zhang, R.; Zhu, Y.; Yang, H.; Shen, C.; Wei, S. SingleShot Compressed Imaging via Random Phase Modulation. Appl. Sci. 2022, 12, 4536. [Google Scholar] [CrossRef]
 Nouasria, H.; Ettolba, M. A Fast GradientBased Sensing Matrix Optimization Approach for Compressive Sensing. Signal Image Video Process. 2022. [Google Scholar] [CrossRef]
 Candès, E.J.; Romberg, J.; Tao, T. Robust Uncertainty Principles: Exact Signal Reconstruction from Highly Incomplete Frequency Information. IEEE Trans. Inf. Theory 2006, 52, 489–509. [Google Scholar] [CrossRef]
 Tropp, J.A.; Gilbert, A.C. Signal Recovery from Random Measurements via Orthogonal Matching Pursuit. IEEE Trans. Inf. Theory 2007, 53, 4655–4666. [Google Scholar] [CrossRef]
 Tropp, J.A.; Laska, J.N.; Duarte, M.F.; Romberg, J.K.; Baraniuk, R.G. Beyond Nyquist: Efficient Sampling of Sparse Bandlimited Signals. IEEE Trans. Inf. Theory 2010, 56, 520–544. [Google Scholar] [CrossRef] [Green Version]
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Li, L.; Zhang, Y.; Zhu, Y.; Dai, Y.; Zhang, X.; Liang, X. Absolute Distance Measurement Based on SelfMixing Interferometry Using Compressed Sensing. Appl. Sci. 2022, 12, 8635. https://doi.org/10.3390/app12178635
Li L, Zhang Y, Zhu Y, Dai Y, Zhang X, Liang X. Absolute Distance Measurement Based on SelfMixing Interferometry Using Compressed Sensing. Applied Sciences. 2022; 12(17):8635. https://doi.org/10.3390/app12178635
Chicago/Turabian StyleLi, Li, Yue Zhang, Ye Zhu, Ya Dai, Xuan Zhang, and Xuwen Liang. 2022. "Absolute Distance Measurement Based on SelfMixing Interferometry Using Compressed Sensing" Applied Sciences 12, no. 17: 8635. https://doi.org/10.3390/app12178635