Abstract
Compressed sensing leverages the sparsity of signals to reduce the amount of measurements required for its reconstruction. The Shack-Hartmann wavefront sensor meanwhile is a flexible sensor where its sensitivity and dynamic range can be adjusted based on applications. An investigation is done by using compressed sensing in surface measurements with the Shack-Hartmann wavefront sensor. The results show that compressed sensing paired with the Shack-Hartmann wavefront sensor can reliably measure surfaces accurately. The performance of compressed sensing is compared with those of the iterative modal-based wavefront reconstruction and Fourier demodulation of Shack-Hartmann spot images. Compressed sensing performs comparably to the modal based iterative wavefront reconstruction in both simulation and experiment while performing better than the Fourier demodulation in simulation.
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D. C. Yuan, H. Y. Zhao, X. Tao, S. B. Li, X. L. Zhu, and C. P. Zhang, “Aspheric surface measurement using capacitive sensors,” Sensors, 2017, 17(6): 1355-1–1355-16.
Y. Zhao, P. S. Li, C. S. Wang, and Z. B. Pu, “A novel fiber-optic sensor used for small internal curved surface measurement,” Sensors and Actuators A: Physical, 2000, 86(3): 211–215.
Y. D. Li and P. Gu, “Free-form surface inspection techniques state of the art review,” Computer-Aided Design, 2004, 36(13): 1395–1417.
X. Jiang, P. J. Scott, D. J. Whitehouse, and L. Blunt, “Paradigm shifts in surface metrology. part II. the current shift,” Proceedings of the Royal Society A: Mathematical, Physical and Engineering Science, 2007, 463(2085): 2071–2099.
J. Riedel, S. Stürwald, and R. Schmitt, “Scanning measurement of aspheres,” Measurement, 2016, 85: 249–254.
Y. Tang, X. Y. Su, Y. K. Liu, and H. L. Jing, “3D shape measurement of the aspheric mirror by advanced phase measuring deflectometry,” Optics Express, 2008, 16(19): 15090–15096.
J. H. Burge, “Applications of computer-generated holograms for interferometric measurement of large aspheric optics,” SPIE, 1995, 2576: 258–269.
C. R. Forest, C. R. Canizares, D. R. Neal, M. McGuirk, and M. L. Schattenburg, “Metrology of thin transparent optics using Shack-Hartmann wavefront sensing,” Optical Engineering, 2004, 43: 1–12.
B. C. Platt and R. Shack, “History and principles of Shack-Hartmann wavefront sensing,” Journal of Refractive Surgery, 2001, 17(5): S573–S577.
H. B. Yu, G. Y. Zhou, S. C. Fook, F. W. Lee, and S. H. Wang, “A tunable Shack-Hartmann wavefront sensor based on a liquid-filled microlens array,” Journal of Micromechanics and Microengineering, 2008, 18(10): 105017-1–105017-8.
G. Häusler, C. Richter, K. H. Leitz, and M. C. Knauer, “Microdeflectometry–a novel tool to acquire three-dimensional microtopography with nanometer height resolution,” Optics Letters, 2008, 33(4): 396–398.
W. Guo, L. Zhao, C. S. Tong, C. I. Ming, and S. C. Joshi, “Adaptive centroid-finding algorithm for freeform surface measurements,” Applied Optics, 2013, 52(10): D75–D83.
X. M. Yin, L. P. Zhao, X. Li, and Z. P. Fang, “Automatic centroid detection and surface measurement with a digital Shack-Hartmann wavefront sensor,” Measurement Science and Technology, 2010, 21(1): 015304-1–015304-17.
L. Zhao, N. Bai, X. Li, L. S. Ong, Z. P. Fang, and A. K. Asundi, “Efficient implementation of a spatial light modulator as a diffractive optical microlens array in a digital Shack-Hartmann wavefront sensor,” Applied Optics, 2006, 45(1): 90–94.
D. L. Donoho, “Compressed sensing,” IEEE Transactions on Information Theory, 2006, 52(4): 1289–1306.
M. S. Hosseini and O. V. Michailovich, “Derivative compressive sampling with application to phase unwrapping,” in Proceeding of 2009 17th European Signal Processing Conference, Glasgow, UK, 2009, pp. 115–119.
M. Rostami, O. V. Michailovich, and Z. Wang, “Surface reconstruction in gradient-field domain using compressed sensing,” IEEE Transactions on Image Processing, 2015, 24(5): 1628–1638.
M. Rostami, O. Michailovich, and Z. Wang, “Image deblurring using derivative compressed sensing for optical imaging application,” IEEE Transactions on Image Processing, 2012, 21(7): 3139–3149.
R. J. Noll, “Zernike polynomials and atmospheric turbulence,” Journal of the Optical Society of America, 1976, 66(3): 207–211.
N. A. Roddier, “Atmospheric wavefront simulation using Zernike polynomials,” 1990, 29(7): 1174–1180.
J. Polans, R. P. McNabb, J. A. Izatt, and S. Farsiu, “Compressed wavefront sensing,” Optics Letters, 2014, 39(5): 1189–1192.
Y. Carmon and E. Ribak, “Phase retrieval by demodulation of a Hartmann-Shack sensor,” Optics Communications, 2003, 215(4–6): 285–288.
H. Gong, O. Soloviev, M. Verhegen, and G. Vdovin, “Shack-Hartmann reflective micro profilometer,” SPIE, 2018, 10616: 106160M-1–106160M-7.
E. Sakhaee and A. Entezari, “Sparse partial derivatives and reconstruction from partial Fourier data,” in Proceeding of 2016 IEEE International Conference on Acoustics, Speech and Signal Processing, Brisbane, QLD, Australia, 2015, pp. 3621–3625.
M. Rostami, O. Michailovich, and Z. Wang, “Gradient-based surface reconstruction using compressed sensing,” in Proceeding of 2012 19th IEEE International Conference on Image Processing, Orlando, FL, USA, 2012, pp. 913–916.
G. M. Dai, “Modified Hartmann-Shack wavefront sensing and iterative wavefront reconstruction,” SPIE, 1994, 2201: 562–573.
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The authors gratefully acknowledge the support of funding from Ministry of Higher Education, Malaysia under the Grant No. FRGS/1/2016/STG02/MUSM/02/1.
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Chow, E.M.T., Guo, N., Chong, E. et al. Surface Measurement Using Compressed Wavefront Sensing. Photonic Sens 9, 115–125 (2019). https://doi.org/10.1007/s13320-018-0521-x
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DOI: https://doi.org/10.1007/s13320-018-0521-x