Compressed sensing technology for atmospheric turbulence wavefront slope measurement can greatly improve the wavefront signal measurement speed, while reducing the pressure of wavefront measurement system hardware. Different from the existing wavefront slope measurement method, the compressed sensing wavefront measurement increase a process which from sparse measurement of wavefront slope value to the reconstruction of the wavefront slope signal. Therefore, a fast and accurate wavefront slope reconstruction algorithm is needed if the compressed sensing technology is used for wavefront measurement. Smoothed L0 Norm (SL0) algorithm is an optimized iterative reconstruction algorithm with approximate L0 norm estimation, and compared with other algorithms, it is not necessary to know the sparsity of the signal in advance, and the calculation is low and the estimation accuracy is high. Based on the SL0 algorithm, this paper implements a subregion parallel algorithm-Block-Smoothed L0 Norm (B-SL0) which can quickly and accurately reconstruct the signal by measuring the wavefront slope signal in subarea and parallel operations through theoretical analysis and experiments. The experimental results show that B-SL0 is significantly better than other existing reconstruction algorithms in the calculation time and accuracy, and explore the feasibility of compressed sensing technology for measurement of atmospheric turbulence wavefront preliminarily.
Research on reconstruction of atmospheric turbulence wavefront compressed sensing measurement
First published at:Apr 01, 2018
1 Lin X D, Xue C, Liu X Y, et al. Current status and research development of wavefront correctors for adaptive optics[J]. Chinese Optics, 2012, 5(4): 337–351.
2 Xian H. Design and optimization of wavefront sensor for adaptive optics system[D]. Chengdu: University of Electronic Science and Technology of China, 2008.
3 Niu C J, Yu S J, Han X E. Analysis about effect of wavefront sensorless adaptive optics on optical communication[J]. Laser & Optoelectronics Progress, 2015, 52(8): 080102.
4 Zhang Q, Jiang W H, Xu B. Study of zonal wavefront reconstruction adapting for Hartmann-Shack wavefront sensor[J]. High Power Laser and Particle Beams, 1998, 10(2): 229–233.
5 Yazdani R, Fallah H. Wavefront sensing for a Shack–Hartmann sensor using phase retrieval based on a sequence of intensity patterns[J]. Applied Optics, 2017, 56(5): 1358–1364. DOI:10.1364/AO.56.001358
6 Rostami M, Michailovich O, Wang Z. Image deblurring using derivative compressed sensing for optical imaging application[J]. IEEE Transactions on Image Processing, 2012, 21(7): 3139–3149. DOI:10.1109/TIP.2012.2190610
7 Polans J, Mcnabb R P, Izatt J A, et al. Compressed wavefront sensing[J]. Optics Letters, 2014, 39(5): 1189–1192. DOI:10.1364/OL.39.001189
8 Donoho D L. Compressed sensing[J]. IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306. DOI:10.1109/TIT.2006.871582
9 Ren Y M, Zhang Y N, Li Y. Advances and perspective on compressed sensing and application on image processing[J]. Acta Automatica Sinia, 2014, 40(8): 1563–1575.
10 Tsaig Y, Donoho D L. Extensions of compressed sensing[J]. Signal Processing, 2006, 86(3): 549–571. DOI:10.1016/j.sigpro.2005.05.029
11 Candès E J, Romberg J, Tao T. Robust uncertainty principles: exact signal reconstruction from highly incomplete frequency information[J]. IEEE Transactions on Information Theory, 2006, 52(2): 489–509. DOI:10.1109/TIT.2005.862083
12 Candes E J, Tao T. Near-optimal signal recovery from random projections: universal encoding strategies[J]. IEEE Transactions on Information Theory, 2006, 52(12): 5406–5425. DOI:10.1109/TIT.2006.885507
13 Mallat S G, Zhang Z F. Matching pursuits with time-frequency dictionaries[J]. IEEE Transactions on Signal Processing, 1993, 41(12): 3397–3415. DOI:10.1109/78.258082
14 Tropp J A, Gilbert A C. Signal recovery from random measurements via orthogonal matching pursuit[J]. IEEE Transactions on Information Theory, 2007, 53(12): 4655–4666. DOI:10.1109/TIT.2007.909108
15 Yin W, Morgan S, Yang J F, et al. Practical compressive sensing with Toeplitz and circulant matrices[J]. Proceedings of SPIE, 2010, 7744: 77440K.
16 Applebaum L, Howard S D, Searle S, et al. Chirp sensing codes: Deterministic compressed sensing measurements for fast recovery[J]. Applied & Computational Harmonic Analysis, 2009, 26(2): 283–290.
17 Mohimani H, Babaie-zadeh M, Jutten C. A fast approach for overcomplete sparse decomposition based on smoothed 10 norm[J]. IEEE Transactions on Signal Processing, 2009, 57(1): 289–301. DOI:10.1109/TSP.2008.2007606
18 Mohimani G H, Babaie-zadeh M, Jutten C. Fast sparse representation based on smoothed l0 norm[C]//Proceedings of the 7th International Conference on Independent Component Analysis and Signal Separation. Springer-Verlag, 2007: 389–396.
19 Candes, Emmanuel J. The restricted isometry property and its implications for compressed sensing[J]. Comptes rendus-Mathematique, 2008, 346(9): 589–592.
20 Cai T T, Wang L, Xu G W. New bounds for restricted isometry constants[J]. IEEE Transactions on Information Theory, 2010, 56(9): 4388–4394. DOI:10.1109/TIT.2010.2054730
21 Cai D M, Wang K, Jia P, et al. Sampling methods of power spectral density method simulating atmospheric turbulence phase screen[J]. Journal of physics, 2014, 63(10): 104217. DOI:10.7498/aps.63.104217
蔡冬梅, 王昆, 贾鹏, 等.功率谱反演大气湍流随机相位屏采样方法的研究.物理学报, 2014, 63(10): 104217. DOI:10.7498/aps.63.104217
22 Zhang Z L. Research on the simulation system of indoor atmospheric turbulence[D]. Taiyuan: Taiyuan University of Technology, 2017.
23 Li Y J, Zhu W Y, Rao R Z. Simulation of random phase screen of non-Kolmogorov atmospheric turbulence[J]. Infrared and Laser Engineering, 2016, 45(12): 1211001.
Supported by Young Scientist Funds of National Natural Science Foundation of China (11503018) and Joint Research Fund in Astronomy (U1631133)
Get Citation: Li Can, Cai Dongmei, Jia Peng, et al. Research on reconstruction of atmospheric turbulence wavefront compressed sensing measurement[J]. Opto-Electronic Engineering, 2018, 45(4): 170617.