Measurement error analysis of cross correlation algorithm with threshold centroiding method

Zhou, Hangcheng, Ma, Xiaoyu, Rao, Changhui

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For Russian citation (Opticheskii Zhurnal):

Hangcheng Zhou, Xiaoyu Ma, Changhui Rao Measurement error analysis of cross correlation algorithm with threshold centroiding method (Анализ ошибок измерений в методе порогового центроида с использованием кросс-корреляционного алгоритма) [на англ. яз.] // Оптический журнал. 2019. Т. 86. № 3. С. 47–55. http://doi.org/10.17586/1023-5086-2019-86-03-47-55

Hangcheng Zhou, Xiaoyu Ma, Changhui Rao Measurement error analysis of cross correlation algorithm with threshold centroiding method (Анализ ошибок измерений в методе порогового центроида с использованием кросс-корреляционного алгоритма) [in English] // Opticheskii Zhurnal. 2019. V. 86. № 3. P. 47–55. http://doi.org/10.17586/1023-5086-2019-86-03-47-55

For citation (Journal of Optical Technology):

Hangcheng Zhou, Xiaoyu Ma, and Changhui Rao, "Measurement error analysis of a cross correlation algorithm with a threshold centroiding method," Journal of Optical Technology. 86(3), 166-172 (2019). https://doi.org/10.1364/JOT.86.000166

Abstract:

The measurement error of the cross correlation algorithm with threshold centroiding method, which is not only related to the background noise variance, the image spatial variance, the size of the reference image, and the image sensor parameters, but also concerned with the half width at half maximum and the threshold value of cross correlation function, is derived theoretically in detail. Our general calculation formula of the measurement error of cross correlation algorithm with the optimal normalized threshold value of 0.6035 is fit for the arbitrary sampling condition and extended target. Furthermore, the experimental results of the measurement error of the cross correlation algorithm using different sunspots taken by the correlating Shack-Hartmann wave-front sensor are compared with the theoretical measurement error. The experiment results agree well with the theoretical results.

Keywords:

cross correlation algorithm, threshold centroiding method, measurement error, wave-front sensor, extended objects

Acknowledgements:

The work is funded by the National Natural Science Foundation of China under the contact No. 11178004. The authors acknowledge academician Wenhan Jiang, professor Xunjun Rao, Dr. Jinsheng Yang, Dr. Lanqiang Zhang and other colleagues in the Institute of Optics and Electronics, Chinese Academy of Sciences for their valuable advices and help to the work of this paper.

OCIS codes: 100.0100, 100.3008, 110.0110, 110.1080

References:

1. Rimmele T.R., Marino J. Solar adaptive optics // Living Rev. Sol. Phys. 2011. V. 8. № 2. P. 1–92.
2. Rao C.H., Zhu L., Zhang L.Q., Rao X.J., et al. Second generation solar adaptive optics for 1-m new vacuum solar telescope at the Fuxian solar observatory // Chin. Opt. Lett. 2015. V. 13. № 12. P. 120101-1–3
3. Rao C.H., Zhu L., Rao X.J., et al. First generation solar adaptive optics system for 1-m new vacuum solar telescope at fuxian solar observatory // Res. Astron. Astrophys. 2016. V. 16. № 2. P. 19–26.
4. Rao C.H., Zhu L., Rao X.J., et al. Instrument description and performance evaluation of a high-order adaptive optics system for the 1-m new vacuum solar telescope at Fuxian solar observatory // Astrophys. J. 2016. V. 833. № 2. P. 210–219.
5. Luhe O.V.D. Wavefront error measurement technique using extended, incoherent light sources // Opt. Eng. 1988. V. 27. № 12. P. 1078–1087.
6. Luhe O.V.D. Widener A.L., Rimmele T., et al. Solar feature correlation tracker for ground-based telescopes // Astron. Astrophys. 1989. V. 224. № 1–2. P. 351–360.
7. Rao C.H., Jiang W.H., Ling N., et al. Correlation tracking algorithms for low-contrast extended object // Intern. Soc. Optics and Photonics. San Diego, 2002. V. 4494. P. 245–251.
8. Zhou H.C., Zhang L.Q., Zhu L., et al. Comparison of correlation algorithms with correlating shack-hartmann wave-front images // in Real-time Photonic Measurements, Data Management, and Processing II / Beijing, 2016. V. 10026. P. 100261B.
9. Rao C.H., Zhu L., Rao X.J., et al. 37-element solar adaptive optics for 26-cm solar fine structure telescope at Yunnan astronomical observatory // Chin. Opt. Lett. 2010. V. 8. № 10. P. 966–968.

10. Luhe O.V.D. A study of a correlation tracking method to improve imaging quality of ground-based solar telescopes // Astron. Astrophys. 1983. V. 119. № 1. P. 85–94.
11. Rao C.H., Zhu L., Rao X.J., et al. Performance of the 37-element solar adaptive optics for the 26 cm solar fine structure telescope at Yunnan astronomical observatory // Appl. Opt. 2010. V. 49. № 10. P. G129–G135.
12. Marino J. Expected performance of solar adaptive optics in large aperture telescopes // Opt. Eng. 2012 V. 51. № 10. P. 101709-1–7.
13. Miura N., Yokoyama F., Nefu M., et al. Optical setup and wavefront sensor for solar adaptive opticsat the domeless solar telescope, Hida observatory // Adaptive Optics Systems II. 2010. V. 7736. P. 773654-1–8.
14. Cao W., Gorceix N., Coulter R., et al. Scientific instrumentation for the 1.6 m new solar telescope in big bear // Astron. Nachr. 2010. V. 331. № 6. P. 636–639.
15. Lukin V., Botygina N., Emaleev O., et al. Wavefront sensors for adaptive optical systems // Meas. Sci. Rev. 2010. V. 10. № 3. P. 102–107.
16. Löfdahl M.G. Evaluation of image-shift measurement algorithms for solar Shack-Hartmann wavefront sensors // Astron. Astrophys. 2010. V. 524. P. 1–19.
17. Johansson U. Cross-correlation techniques with different interpolation methods in adaptive optics // Degree of Master. Stockholm University, Faculty of Science, Department of Astronomy. Institute for Solar Physics, 2010.
18. Bailey H.H., Blackwell F.W., Lowery C.L., et al. Image correlation: Part 1. Simulation and analysis // Rand Corp. Santa Monica CA. 1976. V. 2057. № 1-PR. P. 1–67.
19. Wessely H.W. Image correlation. Part II. Theoretical basis // Rand Corp. Santa Monica Calif. 1976. V. 2057. № 2-PR. P. 1–32.
20. Wessely H.W. Real time and post facto solar image correction // Proc. 13th National Solar Observatory. Sacramento Peak Summer Workshop. 1993. P. 124–128.
21. Michau V., Conan J.M., Fusco T. Shack-Hartmann wavefront sensing with extended sources // Atmospheric Optical Modeling, Measurement, and Simulation II. Intern. Soc. Optics and Photonics / California, 2006. V. 6303. P. 63030B.
22. Marino J. Long exposure point spread function estimation from solar adaptive optics loop data // Thesis. Ph D. New Jersey Institute of Technology, 2011.
23. Berkefeld T., Schmidt W., Soltau D., et al. The wave-front correction system for the sunrise balloon-borne solar observatory // Sol. Phys. 2011. V. 268. № 1. P. 103–123.
24. Cain S.C. Design of an image projection correlating wavefront sensor for adaptive optics // Opt. Eng. 2004. V. 43. № 7. P. 1670–1681.
25. Michau V. Calcul de la precision de mesure d’un analyseur de Shack-Hartmann fonctionnant avec une source etendue // in Internal. ONERA Report / Onera, France, 2002.
26. Dvornychenko V.N. Bounds on (deterministic) correlation functions with application to registration // IEEE Trans. Pattern Analysis and Machine Intelligence. 1983. V. 2. № 2. P. 206–213.
27. Huang T.S., Tsai R.Y. Image sequence analysis: Motion estimation // in Image Sequence Analysis / Berlin: Springer Heidelberg, 1981. P. 1–18.
28. Bainbridge-Smith A., Lane R.G. Determining optical flow using a differential method // Image Vision Comput. 1997. V. 15. № 1. P. 11–22.
29. Liu Z., Xu J., Gu B. Z., et al. New vacuum solar telescope and observations with high resolution // Res. Astron. Astrophys. 2014. V. 14. № 6. P. 705–718.
30. Guo Y.M., Ma X.Y., Rao C.H. Optimal closed-loop bandwidth of tip-tilt correction loop in adaptive optics system // Acta Physica Sinica. 2014. V. 63. № 6. P. 069502-1–5.