基于电子虚拟样板的非球面检测技术研究
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摘要
光学制造技术的发展，尤其是非球面加工技术的兴起，促进了空间光学的发展，大视场、高分辨率、长焦距的航天相机离轴三反系统设计的引进对非球面的加工和检测都是很大的挑战，非球面的检测技术越来越成为光学加工的瓶颈，
本文从检测角度出发，提出了基于电子虚拟样板的非球面检测技术概念，建立电子虚拟样板的数学模型。在检测非球面波前时，我们改变以往传统的零位补偿检验手段，而利用高分辨率的CCD相机直接对被检非球面进行数据采样，并把获得的干涉条纹和预先储存在储存器里的参考干涉图进行叠加，从而得到电子莫尔条纹，然后对获得的电子莫尔条纹进行低通滤波，滤掉噪声中含有的高频成分，以提高图像的信噪比。
接着，我们对滤波后的电子莫尔条纹经过四步数字相移，获得四幅数字干涉图；经模2π处理，并作位相展开，获得位相展开分布图；为了验证电子虚拟样板技术可行性，最后我们利用Zernike多项式拟合，得到Zernike多项式拟合后的面形。
基于电子虚拟样板的非球面技术不需要补偿器进行补偿，这就避免了由于引进补偿器而给系统带来的误差和装调的难度。在电子莫尔虚拟样板中，改变了传统非球面检测Offner零位检测手段，而采用直接对被测表面进行采样，获得虚拟样板的检测技术。同时我们讨论了多种非零位检测技术，象Sub-Nyquist技术，高分辨率CCD直接采样技术。
Development of optical manufacturing, especially aspherical manufacturing, boosted the developing of space optics. Aspheric testing for large departures from reference wavefronts becomes the bottleneck of optical manufacturing. Off-axis TMA system presented in space cameras for large field, high resolution, long focal length challenges the manufacturing and testing for aspheric components .
In this paper, we present the idea of virtual plate for aspheric testing based on moire phase-shifting technology, i.e. when testing steep aspheric wavefronts, interferometry directly used CCD camera for high resolution to obtain supervision with interferometry saved in the frame memory produces moire patterns. Finally, we cancel the noise (mainly in the high frequency) by means of low pass frequency .At last, we obtain digital four patterns by four step phase-shifting technology. Using modulo In to display phase, we got the fringe of the phase . In order to prove its feasibility , we contract the result of simulation with the result of the Zernike polynomial.
The advantage of electronic moire phase-shifting technology is that sample directly avoids the system error and difficulty of calibration and aligning by optical compensators being applied.
In electronic moire phase-shifting virtual plane technology, we began to research testing for the large departures from referent wavefronts and change the pattern of Offner Null testing in conventional aspheric testing, finally present the idea of electronic virtual plane. Meanwhile we discuss several types of aspheric non-null testing such as Sub-Nyquist, high-resolution CCD camera to sample directly.
本文从检测角度出发，提出了基于电子虚拟样板的非球面检测技术概念，建立电子虚拟样板的数学模型。在检测非球面波前时，我们改变以往传统的零位补偿检验手段，而利用高分辨率的CCD相机直接对被检非球面进行数据采样，并把获得的干涉条纹和预先储存在储存器里的参考干涉图进行叠加，从而得到电子莫尔条纹，然后对获得的电子莫尔条纹进行低通滤波，滤掉噪声中含有的高频成分，以提高图像的信噪比。
接着，我们对滤波后的电子莫尔条纹经过四步数字相移，获得四幅数字干涉图；经模2π处理，并作位相展开，获得位相展开分布图；为了验证电子虚拟样板技术可行性，最后我们利用Zernike多项式拟合，得到Zernike多项式拟合后的面形。
基于电子虚拟样板的非球面技术不需要补偿器进行补偿，这就避免了由于引进补偿器而给系统带来的误差和装调的难度。在电子莫尔虚拟样板中，改变了传统非球面检测Offner零位检测手段，而采用直接对被测表面进行采样，获得虚拟样板的检测技术。同时我们讨论了多种非零位检测技术，象Sub-Nyquist技术，高分辨率CCD直接采样技术。
Development of optical manufacturing, especially aspherical manufacturing, boosted the developing of space optics. Aspheric testing for large departures from reference wavefronts becomes the bottleneck of optical manufacturing. Off-axis TMA system presented in space cameras for large field, high resolution, long focal length challenges the manufacturing and testing for aspheric components .
In this paper, we present the idea of virtual plate for aspheric testing based on moire phase-shifting technology, i.e. when testing steep aspheric wavefronts, interferometry directly used CCD camera for high resolution to obtain supervision with interferometry saved in the frame memory produces moire patterns. Finally, we cancel the noise (mainly in the high frequency) by means of low pass frequency .At last, we obtain digital four patterns by four step phase-shifting technology. Using modulo In to display phase, we got the fringe of the phase . In order to prove its feasibility , we contract the result of simulation with the result of the Zernike polynomial.
The advantage of electronic moire phase-shifting technology is that sample directly avoids the system error and difficulty of calibration and aligning by optical compensators being applied.
In electronic moire phase-shifting virtual plane technology, we began to research testing for the large departures from referent wavefronts and change the pattern of Offner Null testing in conventional aspheric testing, finally present the idea of electronic virtual plane. Meanwhile we discuss several types of aspheric non-null testing such as Sub-Nyquist, high-resolution CCD camera to sample directly.
引文
1．史光辉，“卫星对地观测高分辨率光学系统和设计问题”，光学精密工程，1999，Vol．7 No．1 P．16-24
2．杨秉新，“国外航天侦察相机和测绘相机发展概况”，航天返回与遥感，Vol．19，NO．2，P16，1998
3．杨秉新，“高分辨率CA-990侦察相机”，航天CCD相机论文集，中国空间技术研究院
4. Korsch D. Three mirror space telescope. Opt Eng. 1975, 14(6): 533-535
5. Johnson R Barry. Wide field of view three-mirror telescopes having a common optical axis .Opt Een, 1988,27(1): 1046-050
6. Cook L G. Three-mirror anastigmat used off-axis in aperture and field. Proc SPIE, 1979,183:207-211
7. Jones, Lloyd R., "Development of a wide-field-of-view, unobscured, three-mirror anastigmat", Proc. SPIE Vol. 1762, p. 39-49, 1993
8. Sinclair, R. Lawrence; Arsenault, Roger H.; Hudyma, Russell M., "Wide field-of-view three-mirror telescope designed for improved manufacturability", Proc. SPIE Vol. 1970, p. 139-147, 1993
9. Geyl, Roland, "Design and fabrication of a three-mirror, flat-field anastigmat for high-resolution earth observation", Proc. SPIE Vol. 2210, p. 739-746, 1994
10. Martin, Hubert M.; Allen, R. G.; Angel, J. Roger P.; Burge, James H.; Davison, Warren B.; Derigne, S.T.; Dettmann, Lee R.; Ketelsen, Dean A.; Kittrell, W. C.; Miller, Stephen M.; Strittmatter, Peter A.; West, Steve C. "Fabrication and measured quality of the MMT primary mirror", Proc. SPIE Vol. 3352, p. 194-204, 1998
11. V.V. Gorelik, V.I. Kashirin, and N.R. Suleimanov, "Lapping of aspherical surfaces by analastically deformed tool", Sov. J. Opt, Technol. 56 (8), Aug. 1989
12. Oliver W. Fahnle, Hedser van Brug, and hans J. Frankena, "Fluid jet polishing of optical surface", Applied optics, Vol. 37, No. 28, 6771-6773,1998
13. K.B. Paxton, G.H. Conners, and R.J. Cooley, "Uniform polishing of convex aspheres with an elastic lap", Applied Optics Vol. 14, NO. 9, 2274-2279,1975
14. R. A. Jones, "Rapid optical fabrication with computer-controlled optical surfacing", Optical Engineering, 30(12), 1962-1967, 1991
15. R. A. Jones, "Fabrication of a large, thin, off-axis aspheric mirror", Optical Engineering, 33(12), 4067-4075, 1994
16. R. A. Jones, "Computer simulation of smoothing during computer-controlled optical polishing", Applied Optics, 34(7),
1162-1169, 1995
17． D. Golini, W. J. Rupp, J. Zimmerman, "Microgrinding: new technique for rapid fabrication of large mirrors" , SPIE Proceedings, 1113, 204-210, 1989
18． Cao Tianning, "Computer-controlled polishing of parabolic surfaces" , Chinese Journal of Scientific Instrument, 11(40) , 402-407, 1993
19． 王权陡,“离轴非球面加工与检测”,博士论文PP30-52,2001
20． Offner and D. Malacara, "Null Tests Using Compensators, " in Optical Shop Testing, 2nd Ed., D. Malacara, Ed. (Wiley, New York, 1992) , pp. 427-454
21． A. J. MacGovem and J. C. Wyant, "Computer Generated Holograms for Testing Optical Elements," Appl. Gpt. 10(3) , 619-624, 1971
22． B. Dorband and Hans J. Tiziani, "Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors," Appl. Optics 24(16) , 2604-2611, 1985
23． J. E. Greivenkamp and J. H. Bruning, "Phase-Shifting Interferometry," in Optical Shop Testing, 2nd Ed., D. Malacara, Ed. (Wiley, New York, 1992) , pp. 501-598
24． A. P. Semenov, A. S. Savel' ev, and M. A. Abdulkadyrov, "Analysis of errors of automated shaping of optical surfaces on the AD series of machinges using the AD1 program", Sov. J. Opt. Vol. 57(1) , P. 44-46, 1990
25． Malacara D. Optical shop testing [M]. Wiley &Son: New York, 1992:pp501-589．
26． Stahl H P. Aspheric surface technique [J]. SPIE, 1990,1332,66-76．
27． Abe Offer .A null corrector for paraboloidal mirror [J]. Applied Optics, 1963,2(2) : 153-155
28． Martin. J. Bastinaans, " Wigner distribution moments in fractional Fourier transform systems" , Journal of the Optical Society of America A, Vol.19, No. 9, 2002
29． Zhang Xuejun, etc "Manufacturing and testing of two off-axis aspherical mirror" , SPIE. Vol 4451,2001
30． Zhang Xuejun ,etc "Recent progress on asphere manufacturing and testing at CIOM", SPIE,Vol4231,pp24-31, 2000．
31． Wang Quandou, "Study on CCOS technique to make off-axis aspherical mirrors" , ph. D thesis, 2001．
32 Stephen D Fantone. Holographic interferometer for testing aspheric molds and molded parts[J], Applied Optics , 1983, 22(8) :1121-1226．
33． Bernd Dorband, Hans J Tiziani. Testing aspheric surface with computer-generated holograms: analysis of adjustment and shape errors [J]. Applied Optics, 1985,24(6) : 2604-2661．
34． Daniel Malacara , Interferogram analysis for optical testing , New York, 1998．
35． J. E. Greivenkamp, "Sub-Nyquist interferometry, " Appl. Opt.
26,5245-5258 (1987)
36． J. Kato, Video-rate fringe analyzer based on phase-shifting electronic moire patterns, 1997, Applied Optics, Vol. 36 NO. 32
37． J. M. Huntley, " Noise-immune phase unwrapping algorithm, " Appl. Opt. 28, 3268-3270(1989)
38． A. Peled and Bede Liu. Digital Processing Theory .Design and Implementation .New York:John Wiley &Sons , Inc, 1976
39． Rabiner L R and Gold B .Theory and Application of digital Signal Processing,Prentice-Hall Inc., 1975
40． Taylor R J .Digital Filter Design Handbook .New York :Marce Dekker., 1983
41． Hedser Van Brug "phase-step calibration for phase-stepped interferometry",Applied Optics , Vol. 38,No. 16, 3549-3555(1999) ;
42． Y-cheng and J. C. Wyant , " phase shifter calibration in the phase shifting interferometry" , Applied Optics , Vol.24,3049-3052(1985)
43． P. Hariharan, B. F. Ored, and T. Eiju, " digital phase shifting intergferometry :a simple error-compensating phase calculation algorithm" , Applied Optics , Vol. 26, 2504-2506
44． P. Hariharan, B. F. Ored, and T. Eiju, " digital phase shifting intergferometry :a simple error-compensating phase calculation algorithm" , Applied Optics , Vol. 26, 2504-2509
45． Hongbin Chen "Wavefront fitting of interferometry with Zernike polynomials" , Optical Engieering , 41(7) 1561-1569(July 2002) .
46． J. Z. Yan, " Algorithm for wavefront fitting using Zernike polynomials " , Opt. Prec.Eng. 7,119-128(1999)
47． J.Y.Wyant and D. E. silva "wavefront interpretation with Zernike polynomials",Applied Optics,Vol. 19,No.9,1,May 1980．
48． Daniel Malacara "wavefront fitting with discrete orthogonal polynomials in a unit radius circle" , Optical Engineering, Vol.29,No. 6(1990)
2．杨秉新，“国外航天侦察相机和测绘相机发展概况”，航天返回与遥感，Vol．19，NO．2，P16，1998
3．杨秉新，“高分辨率CA-990侦察相机”，航天CCD相机论文集，中国空间技术研究院
4. Korsch D. Three mirror space telescope. Opt Eng. 1975, 14(6): 533-535
5. Johnson R Barry. Wide field of view three-mirror telescopes having a common optical axis .Opt Een, 1988,27(1): 1046-050
6. Cook L G. Three-mirror anastigmat used off-axis in aperture and field. Proc SPIE, 1979,183:207-211
7. Jones, Lloyd R., "Development of a wide-field-of-view, unobscured, three-mirror anastigmat", Proc. SPIE Vol. 1762, p. 39-49, 1993
8. Sinclair, R. Lawrence; Arsenault, Roger H.; Hudyma, Russell M., "Wide field-of-view three-mirror telescope designed for improved manufacturability", Proc. SPIE Vol. 1970, p. 139-147, 1993
9. Geyl, Roland, "Design and fabrication of a three-mirror, flat-field anastigmat for high-resolution earth observation", Proc. SPIE Vol. 2210, p. 739-746, 1994
10. Martin, Hubert M.; Allen, R. G.; Angel, J. Roger P.; Burge, James H.; Davison, Warren B.; Derigne, S.T.; Dettmann, Lee R.; Ketelsen, Dean A.; Kittrell, W. C.; Miller, Stephen M.; Strittmatter, Peter A.; West, Steve C. "Fabrication and measured quality of the MMT primary mirror", Proc. SPIE Vol. 3352, p. 194-204, 1998
11. V.V. Gorelik, V.I. Kashirin, and N.R. Suleimanov, "Lapping of aspherical surfaces by analastically deformed tool", Sov. J. Opt, Technol. 56 (8), Aug. 1989
12. Oliver W. Fahnle, Hedser van Brug, and hans J. Frankena, "Fluid jet polishing of optical surface", Applied optics, Vol. 37, No. 28, 6771-6773,1998
13. K.B. Paxton, G.H. Conners, and R.J. Cooley, "Uniform polishing of convex aspheres with an elastic lap", Applied Optics Vol. 14, NO. 9, 2274-2279,1975
14. R. A. Jones, "Rapid optical fabrication with computer-controlled optical surfacing", Optical Engineering, 30(12), 1962-1967, 1991
15. R. A. Jones, "Fabrication of a large, thin, off-axis aspheric mirror", Optical Engineering, 33(12), 4067-4075, 1994
16. R. A. Jones, "Computer simulation of smoothing during computer-controlled optical polishing", Applied Optics, 34(7),
1162-1169, 1995
17． D. Golini, W. J. Rupp, J. Zimmerman, "Microgrinding: new technique for rapid fabrication of large mirrors" , SPIE Proceedings, 1113, 204-210, 1989
18． Cao Tianning, "Computer-controlled polishing of parabolic surfaces" , Chinese Journal of Scientific Instrument, 11(40) , 402-407, 1993
19． 王权陡,“离轴非球面加工与检测”,博士论文PP30-52,2001
20． Offner and D. Malacara, "Null Tests Using Compensators, " in Optical Shop Testing, 2nd Ed., D. Malacara, Ed. (Wiley, New York, 1992) , pp. 427-454
21． A. J. MacGovem and J. C. Wyant, "Computer Generated Holograms for Testing Optical Elements," Appl. Gpt. 10(3) , 619-624, 1971
22． B. Dorband and Hans J. Tiziani, "Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors," Appl. Optics 24(16) , 2604-2611, 1985
23． J. E. Greivenkamp and J. H. Bruning, "Phase-Shifting Interferometry," in Optical Shop Testing, 2nd Ed., D. Malacara, Ed. (Wiley, New York, 1992) , pp. 501-598
24． A. P. Semenov, A. S. Savel' ev, and M. A. Abdulkadyrov, "Analysis of errors of automated shaping of optical surfaces on the AD series of machinges using the AD1 program", Sov. J. Opt. Vol. 57(1) , P. 44-46, 1990
25． Malacara D. Optical shop testing [M]. Wiley &Son: New York, 1992:pp501-589．
26． Stahl H P. Aspheric surface technique [J]. SPIE, 1990,1332,66-76．
27． Abe Offer .A null corrector for paraboloidal mirror [J]. Applied Optics, 1963,2(2) : 153-155
28． Martin. J. Bastinaans, " Wigner distribution moments in fractional Fourier transform systems" , Journal of the Optical Society of America A, Vol.19, No. 9, 2002
29． Zhang Xuejun, etc "Manufacturing and testing of two off-axis aspherical mirror" , SPIE. Vol 4451,2001
30． Zhang Xuejun ,etc "Recent progress on asphere manufacturing and testing at CIOM", SPIE,Vol4231,pp24-31, 2000．
31． Wang Quandou, "Study on CCOS technique to make off-axis aspherical mirrors" , ph. D thesis, 2001．
32 Stephen D Fantone. Holographic interferometer for testing aspheric molds and molded parts[J], Applied Optics , 1983, 22(8) :1121-1226．
33． Bernd Dorband, Hans J Tiziani. Testing aspheric surface with computer-generated holograms: analysis of adjustment and shape errors [J]. Applied Optics, 1985,24(6) : 2604-2661．
34． Daniel Malacara , Interferogram analysis for optical testing , New York, 1998．
35． J. E. Greivenkamp, "Sub-Nyquist interferometry, " Appl. Opt.
26,5245-5258 (1987)
36． J. Kato, Video-rate fringe analyzer based on phase-shifting electronic moire patterns, 1997, Applied Optics, Vol. 36 NO. 32
37． J. M. Huntley, " Noise-immune phase unwrapping algorithm, " Appl. Opt. 28, 3268-3270(1989)
38． A. Peled and Bede Liu. Digital Processing Theory .Design and Implementation .New York:John Wiley &Sons , Inc, 1976
39． Rabiner L R and Gold B .Theory and Application of digital Signal Processing,Prentice-Hall Inc., 1975
40． Taylor R J .Digital Filter Design Handbook .New York :Marce Dekker., 1983
41． Hedser Van Brug "phase-step calibration for phase-stepped interferometry",Applied Optics , Vol. 38,No. 16, 3549-3555(1999) ;
42． Y-cheng and J. C. Wyant , " phase shifter calibration in the phase shifting interferometry" , Applied Optics , Vol.24,3049-3052(1985)
43． P. Hariharan, B. F. Ored, and T. Eiju, " digital phase shifting intergferometry :a simple error-compensating phase calculation algorithm" , Applied Optics , Vol. 26, 2504-2506
44． P. Hariharan, B. F. Ored, and T. Eiju, " digital phase shifting intergferometry :a simple error-compensating phase calculation algorithm" , Applied Optics , Vol. 26, 2504-2509
45． Hongbin Chen "Wavefront fitting of interferometry with Zernike polynomials" , Optical Engieering , 41(7) 1561-1569(July 2002) .
46． J. Z. Yan, " Algorithm for wavefront fitting using Zernike polynomials " , Opt. Prec.Eng. 7,119-128(1999)
47． J.Y.Wyant and D. E. silva "wavefront interpretation with Zernike polynomials",Applied Optics,Vol. 19,No.9,1,May 1980．
48． Daniel Malacara "wavefront fitting with discrete orthogonal polynomials in a unit radius circle" , Optical Engineering, Vol.29,No. 6(1990)