基于条纹频率分析的位相展开新算法
|
摘要
基于条纹投影的光学三维传感技术自80年代提出以来，由于非接触、快速、精度高、自动化程度高、经济等优点，已得到了广泛的应用。位相展开是所有位相测量三维传感技术共同的问题。在实际应用中特别是测量复杂的物体三维面形时，由于噪声阴影等引起的截断位相不可靠及采样不足的问题，位相展开一直是其中的难点。虽然在近20年中有多种算法出现，但并没有一种算法能完全解决位相展开中的问题。
本文提出了一种基于条纹频率分析的位相展开新算法并将其应用于FTP和PMP中。新算法属于空间位相展开与路径有关的方法中利用可靠度函数寻找优化路径(Quality Guided Path Following Method)的方法之一，由数字加权滤波和调制度排序构成。数字加权滤波之后的调制度函数携带了条纹频率的信息，因此数字加权滤波将对于条纹频率的分析转化为对于调制度的分析，且根据偏离条纹基频的程度与位相可靠度之间的对应关系，可建立经过数字加权滤波之后的调制度函数与位相可靠度之间的关系。此时，调制度排序相当于对于位相可靠度排序，可找到一条优化的位相展开路径。沿此优化路径进行位相展开可将位相不可靠的点留到了位相展开的最后。这在很大程度上避免了沿位相不可靠点进行位相展开时引起的误差传播，在最坏的情况下，也能将位相展开的错误限制在局部范围。
新算法不仅保留了调制度函数本身处理局部阴影噪声等截断位相不可靠区域的能力，而且对于采样不足的区域有着很好的处理效果，适用于复杂的位相场展开。而且新算法避免了复杂的极点连接，提高了位相展开的自动化程度。
计算机模拟和实验证明了本文新算法的正确性与有效性。
Noncontact, high-precision, high-speed optical 3D sensing has been widely used since being presented in the nineteen eighties, in which phase-measurement technology is an important technology. Phase wrapping is a common problem in all phase-measurement techniques. Due to unreliable phase value and under-sampling in practical situation, especially when a complex shape is measured, phase unwrapping is a difficult step. There is no solution suitable to all the problems of phase unwrapping though many algorithms have been presented in the recent 20 years.
A new phase unwrapping algorithm is presented and is applied to FTP and PMP in this paper. The new algorithm is one of Quality Guided Path Following Methods, belonging to spatial phase unwrapping methods dependent on path. Its framework consists of digital weighted filtering and modulation ordering. By digital weighted filtering, the analysis of fringe frequency is converted into the analysis of fringe modulation. And based on the correlation between local spatial frequency and the reliability of phase data, the correlation between modulation after digital weighted filtering and the reliability can be set up. Thus modulation ordering at this moment is equal to reliability ordering, resulting in an optimized path. The unreliable pixels are left to the end of the path when phase unwrapping is proceeded along this path, which avoid error propagating. Even in the worse case the error is limited, if three is any. to local minimum areas.
With the ability of modulation to mask the unreliable areas such as noise, local shadow, and the ability to deal with under-sampling areas successfully, the new
algorithm can be applied to complex phase unwrapping. Also the new algorithm improves the automatization of phase unwrapping by avoiding complex pole joint.
Computer simulation and experiments prove the correctness and effectiveness of the new phase unwrapping algorithm.
本文提出了一种基于条纹频率分析的位相展开新算法并将其应用于FTP和PMP中。新算法属于空间位相展开与路径有关的方法中利用可靠度函数寻找优化路径(Quality Guided Path Following Method)的方法之一，由数字加权滤波和调制度排序构成。数字加权滤波之后的调制度函数携带了条纹频率的信息，因此数字加权滤波将对于条纹频率的分析转化为对于调制度的分析，且根据偏离条纹基频的程度与位相可靠度之间的对应关系，可建立经过数字加权滤波之后的调制度函数与位相可靠度之间的关系。此时，调制度排序相当于对于位相可靠度排序，可找到一条优化的位相展开路径。沿此优化路径进行位相展开可将位相不可靠的点留到了位相展开的最后。这在很大程度上避免了沿位相不可靠点进行位相展开时引起的误差传播，在最坏的情况下，也能将位相展开的错误限制在局部范围。
新算法不仅保留了调制度函数本身处理局部阴影噪声等截断位相不可靠区域的能力，而且对于采样不足的区域有着很好的处理效果，适用于复杂的位相场展开。而且新算法避免了复杂的极点连接，提高了位相展开的自动化程度。
计算机模拟和实验证明了本文新算法的正确性与有效性。
Noncontact, high-precision, high-speed optical 3D sensing has been widely used since being presented in the nineteen eighties, in which phase-measurement technology is an important technology. Phase wrapping is a common problem in all phase-measurement techniques. Due to unreliable phase value and under-sampling in practical situation, especially when a complex shape is measured, phase unwrapping is a difficult step. There is no solution suitable to all the problems of phase unwrapping though many algorithms have been presented in the recent 20 years.
A new phase unwrapping algorithm is presented and is applied to FTP and PMP in this paper. The new algorithm is one of Quality Guided Path Following Methods, belonging to spatial phase unwrapping methods dependent on path. Its framework consists of digital weighted filtering and modulation ordering. By digital weighted filtering, the analysis of fringe frequency is converted into the analysis of fringe modulation. And based on the correlation between local spatial frequency and the reliability of phase data, the correlation between modulation after digital weighted filtering and the reliability can be set up. Thus modulation ordering at this moment is equal to reliability ordering, resulting in an optimized path. The unreliable pixels are left to the end of the path when phase unwrapping is proceeded along this path, which avoid error propagating. Even in the worse case the error is limited, if three is any. to local minimum areas.
With the ability of modulation to mask the unreliable areas such as noise, local shadow, and the ability to deal with under-sampling areas successfully, the new
algorithm can be applied to complex phase unwrapping. Also the new algorithm improves the automatization of phase unwrapping by avoiding complex pole joint.
Computer simulation and experiments prove the correctness and effectiveness of the new phase unwrapping algorithm.
引文
1．金国藩，李景镇，《激光测量学》，科学出版社(1998)．
2．苏显渝，李继陶，《信息光学》，科学出版社(1998)．
3. I. Kaisto, J. Kostamovaara, M. Manninen, and R. Myllyla, "Optical range finder for 1.5-10-m distance," Appl. Opt. 22, 3258-3263 (1983).
4. H. Takasaki, "Moir étopography," Appl. Opt. 9, 1467-1472 (1970).
5. M. Takeda, H, Ina, S. Koboyashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72(1), 156-160 (1982).
6. M. Takeda, K. Motoh, "Fourier transform profilometry for the automatic measurement of 3-D object shapes," Appl. Opt. 22 (24), 3977-3982 (1983).
7. M. Takeda, Q. Gu, M. Kinoshita, et al., "Frequency-multiplex Fourier-transform profilometry: A single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations," Appl. Opt. 36(22), 5347-5354 (1997).
8. Jian Li, Xian-Yu Su and Lu-Rong Gou, "An improved Fourier transform profilometry for automatic measurement of 3-D object shapes," Opt. Eng. 29(12), 1439-1444 (1990).
9. Xian-Yu Su, Jian Li and Lu-Rong Gou, "An improved Fourier transform profilometry, " Proc. SPIE 954, 241-244 (1990)
10. Jin-Feng Lin and Xian-Yu Su, "Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes," Opt. Eng. 34(11), 3297-3302(1995).
11. T. Dresel, G. Hansler, and H. Venzke, "Three-dimensional sensing of rough surfaces by coherence radar," Appl. Opt. 31,919-925 (1992).
12. V. Srinivasan, H. C. Liu, M. Halioua, "Automated phase measuring profilometry of 3-D diffuse object," Appl. Opt. 23(18), 3105-3108 (1984).
13. Xian-Yu Su, Wen-Sen Zhou, C. von Bally, and D. Vukicevic, "Automated phase-measuring profilometry using defocused projection of a Ronchi grating," Opt. Commun. 94(6), 561-573(1992).
14. Likun Su, Xianyu Su, Wansong Li, Liqun Xiang "Application of modulation measurement profilometry to objects with surface holes," Appl. Opt. 38(7), 1153-1158 (1999).
15. Wensen Zhou, Xianyu Su, "A direct mapping algorithm for phase-measuring profilometry," J. Modem Opt. 41(1), 89-94 (1994).
16. T. R. Judge, P. J. Bryanston-Cross, "A review of phase unwrapping techniques in fringe analysis," Opt. Lasers Eng. 21, 199-239 (1994).
17. Jarle Strand, Torfinn Taxt, "Perfomance evaluation of two-dimensional phase unwrapping algorithms," Appl. Opt.38(20), 4333-4344 (1999).
18. H. O. Saldner. J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector", Opt. Eng. 36(2), 610-615, (1997).
19. H. O. Saldner, J. M. Huntley, "Temporal phase unwrapping: application to surface profiling of discontinuous objects," Appl. Opt. 36(13), 2770-2775 (1997).
20. Hong Zhang, Michael J. Lalor, David R. Burton, "Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry". Appl. Opt. 38(16), 3534-3541 (1999).
21. J. M. Huntley, H. O. Saldner, "Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms," Meas. Sci. Technol. 8(9), 986-992 (1997).
22. Jielin Li, HongJun Su, Xianyu Su, "Two-frequency grating used in phase-measuring profilometry," Appl. Opt. 36(1), 277-280 (1997).
23. Yudong Hao, Yang Zhao, Dacheng Li, "Multlfrequency grating prejection Profilometry based on the nonlinear excess fraction method," Appl. Opt. 38(19), 4106-4110 (1999).
24．郝煜栋，赵洋，李达成，“非线性小数重合法及其在轮廓测量中的应用，”光学学报 19(11)，1518-1522，(1999)．
25. D. G. Ghiglia, G. A. Mastin. L. A. Romero, "Cellular-automata method for phase unwrapping", J. Opt. Soc. Am. (A) 4(1), 267-280 (1987).
26. A. Spik, D, W. Robinson, "Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor," Opt. Lasers Eng. 14(1), 25-37 (1991).
27．谭松新，苏显渝，“细胞机自动位相展开算法用于三维传感，”光学学报 17(1)，112-116，(1997)．
28. Ghiglia D. C., Romero L. A., "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am, (A) 11(1), 107-117(1994).
29. M. D. Pritt, "Phase unwrapping by means of multigrid techniques for interferometric SAR," IEEE Trans. Geosci. Remote Sens. 34, 728-738 (1996).
30. J. Strand, T. Taxt, and A. K. Jain, "two-dimensional phase unwrapping using a block least-squares method," IEEE Trans. Image Process. 8, 375-386 (1999).
31. J. M. Huntley, "Noise-immune phase unwrapping algorithm," Appl. Opt. 28, 3260-3270 (1989).
32. Goldstein R. M., Zevker H. A, Werner C. L.," Satellite radar interferometry: two-dimensional phase unwrapping," Radio science 23(4), 713-720 (1988).
33. T. J. Flynn, " Consistent 2-D Phase unwrapping guided by a quality map," Proc. International Geoscience and Romote Sensing Symposium (Institute of Electrical and Electronics Eng., New York), 2057-2059 (1996).
34. Xianyu Su, G. Von Bally, and D. Vukicevic, "Phase-steppinggrating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98(1), 141-150 (1993).
35. Xianyu Su, A. M. Zarubin, and G. Von Bally, "Modulation analysis of phase-shifting holographic intefferograms," Opt. Commun. 105(5), 379-387 (1994).
36. D. J. Bone, "Fourier fringe analysis: the two-dimensional phase unwrapping problem," Appl. Opt. 30, 3627-3632 (1991).
37. Y. Xu, C. Ai, "Simple and effective phase unwrapping technique", Proc. SPIE 2003, 254-263(1993).
38. Xianyu Su, Wen-Sen Zhou, "Complex object profilometry and its application for dentistry," Proc. SPIE. 2132, 484-489 (1994).
39. Xianyu Su, "Phase unwrapping techniques for 3-D shape measurement," Proc. SPIE. 2866, 460-465 (1996).
40. Jielin Li, Xianyu Su, Jitao Li, "Phase unwrapping algorithm based on reliability and edgedetection," Opt. Eng. 36(6),1685-1690 (1997).
41．李继陶，苏显渝，“光弹性测量中的位相展开，”光学学报 17(11)，1538-1541(1997)．
42. Xianyu Su, Am Zarubin, G Vonbally, "Modulation Analysis of Phase-Shifted Holographic Interferograms," Opt. Commun. 105(5-6), 379-387(1994).
43．苏显渝，谭松新，向立群等，“基于傅立叶变换轮廓术方法的复杂物体三维面形测量，”光学学报 18(9)，1228-1233(1998)．
44. Soille P, "Morphological phase unwrapping," Opt. Lasers Eng. 32(4), 339-352 (1999).
45．吴春才，苏显渝，“动态过程的三维面形测量，”光电子激光 7(5)，273-278(1996)．
46. Xianyu Su, Wenjing Chen, Qichan Zhang, Yiping Chao, "Dynamic 3-D shape measurement method based on FTP", Opt. Lasers Eng. 2001 (to be published).
47. Hongjun Su, Jielin Li, Xianyu Su, "Phase unwrapping without the influence of carrier frequency," Opt. Eng. 36(6), 1799-1805 (1997).
48. Asundi A, Zhou WS, "Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill," Appl. Opt. 37(23), 5416-5420 (1998).
49．王鸣，马力，李达成，杜文华，”级数相位去包裹算法”，光学学报20(11)，1524-1527(2000)．
2．苏显渝，李继陶，《信息光学》，科学出版社(1998)．
3. I. Kaisto, J. Kostamovaara, M. Manninen, and R. Myllyla, "Optical range finder for 1.5-10-m distance," Appl. Opt. 22, 3258-3263 (1983).
4. H. Takasaki, "Moir étopography," Appl. Opt. 9, 1467-1472 (1970).
5. M. Takeda, H, Ina, S. Koboyashi, "Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry," J. Opt. Soc. Am. 72(1), 156-160 (1982).
6. M. Takeda, K. Motoh, "Fourier transform profilometry for the automatic measurement of 3-D object shapes," Appl. Opt. 22 (24), 3977-3982 (1983).
7. M. Takeda, Q. Gu, M. Kinoshita, et al., "Frequency-multiplex Fourier-transform profilometry: A single-shot three-dimensional shape measurement of objects with large height discontinuities and/or surface isolations," Appl. Opt. 36(22), 5347-5354 (1997).
8. Jian Li, Xian-Yu Su and Lu-Rong Gou, "An improved Fourier transform profilometry for automatic measurement of 3-D object shapes," Opt. Eng. 29(12), 1439-1444 (1990).
9. Xian-Yu Su, Jian Li and Lu-Rong Gou, "An improved Fourier transform profilometry, " Proc. SPIE 954, 241-244 (1990)
10. Jin-Feng Lin and Xian-Yu Su, "Two-dimensional Fourier transform profilometry for the automatic measurement of three-dimensional object shapes," Opt. Eng. 34(11), 3297-3302(1995).
11. T. Dresel, G. Hansler, and H. Venzke, "Three-dimensional sensing of rough surfaces by coherence radar," Appl. Opt. 31,919-925 (1992).
12. V. Srinivasan, H. C. Liu, M. Halioua, "Automated phase measuring profilometry of 3-D diffuse object," Appl. Opt. 23(18), 3105-3108 (1984).
13. Xian-Yu Su, Wen-Sen Zhou, C. von Bally, and D. Vukicevic, "Automated phase-measuring profilometry using defocused projection of a Ronchi grating," Opt. Commun. 94(6), 561-573(1992).
14. Likun Su, Xianyu Su, Wansong Li, Liqun Xiang "Application of modulation measurement profilometry to objects with surface holes," Appl. Opt. 38(7), 1153-1158 (1999).
15. Wensen Zhou, Xianyu Su, "A direct mapping algorithm for phase-measuring profilometry," J. Modem Opt. 41(1), 89-94 (1994).
16. T. R. Judge, P. J. Bryanston-Cross, "A review of phase unwrapping techniques in fringe analysis," Opt. Lasers Eng. 21, 199-239 (1994).
17. Jarle Strand, Torfinn Taxt, "Perfomance evaluation of two-dimensional phase unwrapping algorithms," Appl. Opt.38(20), 4333-4344 (1999).
18. H. O. Saldner. J. M. Huntley, "Profilometry using temporal phase unwrapping and a spatial light modulator-based fringe projector", Opt. Eng. 36(2), 610-615, (1997).
19. H. O. Saldner, J. M. Huntley, "Temporal phase unwrapping: application to surface profiling of discontinuous objects," Appl. Opt. 36(13), 2770-2775 (1997).
20. Hong Zhang, Michael J. Lalor, David R. Burton, "Spatiotemporal phase unwrapping for the measurement of discontinuous objects in dynamic fringe-projection phase-shifting profilometry". Appl. Opt. 38(16), 3534-3541 (1999).
21. J. M. Huntley, H. O. Saldner, "Shape measurement by temporal phase unwrapping: comparison of unwrapping algorithms," Meas. Sci. Technol. 8(9), 986-992 (1997).
22. Jielin Li, HongJun Su, Xianyu Su, "Two-frequency grating used in phase-measuring profilometry," Appl. Opt. 36(1), 277-280 (1997).
23. Yudong Hao, Yang Zhao, Dacheng Li, "Multlfrequency grating prejection Profilometry based on the nonlinear excess fraction method," Appl. Opt. 38(19), 4106-4110 (1999).
24．郝煜栋，赵洋，李达成，“非线性小数重合法及其在轮廓测量中的应用，”光学学报 19(11)，1518-1522，(1999)．
25. D. G. Ghiglia, G. A. Mastin. L. A. Romero, "Cellular-automata method for phase unwrapping", J. Opt. Soc. Am. (A) 4(1), 267-280 (1987).
26. A. Spik, D, W. Robinson, "Investigation of the cellular automata method for phase unwrapping and its implementation on an array processor," Opt. Lasers Eng. 14(1), 25-37 (1991).
27．谭松新，苏显渝，“细胞机自动位相展开算法用于三维传感，”光学学报 17(1)，112-116，(1997)．
28. Ghiglia D. C., Romero L. A., "Robust two-dimensional weighted and unweighted phase unwrapping that uses fast transforms and iterative methods," J. Opt. Soc. Am, (A) 11(1), 107-117(1994).
29. M. D. Pritt, "Phase unwrapping by means of multigrid techniques for interferometric SAR," IEEE Trans. Geosci. Remote Sens. 34, 728-738 (1996).
30. J. Strand, T. Taxt, and A. K. Jain, "two-dimensional phase unwrapping using a block least-squares method," IEEE Trans. Image Process. 8, 375-386 (1999).
31. J. M. Huntley, "Noise-immune phase unwrapping algorithm," Appl. Opt. 28, 3260-3270 (1989).
32. Goldstein R. M., Zevker H. A, Werner C. L.," Satellite radar interferometry: two-dimensional phase unwrapping," Radio science 23(4), 713-720 (1988).
33. T. J. Flynn, " Consistent 2-D Phase unwrapping guided by a quality map," Proc. International Geoscience and Romote Sensing Symposium (Institute of Electrical and Electronics Eng., New York), 2057-2059 (1996).
34. Xianyu Su, G. Von Bally, and D. Vukicevic, "Phase-steppinggrating profilometry: utilization of intensity modulation analysis in complex objects evaluation," Opt. Commun. 98(1), 141-150 (1993).
35. Xianyu Su, A. M. Zarubin, and G. Von Bally, "Modulation analysis of phase-shifting holographic intefferograms," Opt. Commun. 105(5), 379-387 (1994).
36. D. J. Bone, "Fourier fringe analysis: the two-dimensional phase unwrapping problem," Appl. Opt. 30, 3627-3632 (1991).
37. Y. Xu, C. Ai, "Simple and effective phase unwrapping technique", Proc. SPIE 2003, 254-263(1993).
38. Xianyu Su, Wen-Sen Zhou, "Complex object profilometry and its application for dentistry," Proc. SPIE. 2132, 484-489 (1994).
39. Xianyu Su, "Phase unwrapping techniques for 3-D shape measurement," Proc. SPIE. 2866, 460-465 (1996).
40. Jielin Li, Xianyu Su, Jitao Li, "Phase unwrapping algorithm based on reliability and edgedetection," Opt. Eng. 36(6),1685-1690 (1997).
41．李继陶，苏显渝，“光弹性测量中的位相展开，”光学学报 17(11)，1538-1541(1997)．
42. Xianyu Su, Am Zarubin, G Vonbally, "Modulation Analysis of Phase-Shifted Holographic Interferograms," Opt. Commun. 105(5-6), 379-387(1994).
43．苏显渝，谭松新，向立群等，“基于傅立叶变换轮廓术方法的复杂物体三维面形测量，”光学学报 18(9)，1228-1233(1998)．
44. Soille P, "Morphological phase unwrapping," Opt. Lasers Eng. 32(4), 339-352 (1999).
45．吴春才，苏显渝，“动态过程的三维面形测量，”光电子激光 7(5)，273-278(1996)．
46. Xianyu Su, Wenjing Chen, Qichan Zhang, Yiping Chao, "Dynamic 3-D shape measurement method based on FTP", Opt. Lasers Eng. 2001 (to be published).
47. Hongjun Su, Jielin Li, Xianyu Su, "Phase unwrapping without the influence of carrier frequency," Opt. Eng. 36(6), 1799-1805 (1997).
48. Asundi A, Zhou WS, "Fast phase-unwrapping algorithm based on a gray-scale mask and flood fill," Appl. Opt. 37(23), 5416-5420 (1998).
49．王鸣，马力，李达成，杜文华，”级数相位去包裹算法”，光学学报20(11)，1524-1527(2000)．