大梯度相位单幅干涉图的解相方法
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摘要
针对加工中的大梯度相位在线检测需求,提出一种基于数字叠栅移相方法和牛顿迭代算法的单幅干涉图解相方法。在不同待测相位下,将所提方法的结果与其他3种典型的单幅干涉图解相方法进行仿真对比,结果表明,所提方法的解相精度较高。对离焦球面产生的大梯度相位进行测量实验,并将实验结果与ZYGO公司生产的干涉仪机械移相测量结果进行对比,验证了所提方法的有效性。
To meet the requirement of on-line detection of large gradient phases in machining, a single interferogram phase retrieval method based on the digital moiré phase shift algorithm and the Newton iteration algorithm is proposed herein. In the simulation, we compared the proposed method with three typical phase retrieval methods for single interferogram under different phases to be measured. The results show that the proposed method has high accuracy. We then experimentally measured the large gradient phase produced by a defocused sphere, and compared our result with the measurement result of mechanical phase shift in the interferometer produced by ZYGO corporation. The effectiveness of the proposed method is verified.
To meet the requirement of on-line detection of large gradient phases in machining, a single interferogram phase retrieval method based on the digital moiré phase shift algorithm and the Newton iteration algorithm is proposed herein. In the simulation, we compared the proposed method with three typical phase retrieval methods for single interferogram under different phases to be measured. The results show that the proposed method has high accuracy. We then experimentally measured the large gradient phase produced by a defocused sphere, and compared our result with the measurement result of mechanical phase shift in the interferometer produced by ZYGO corporation. The effectiveness of the proposed method is verified.
引文
[1] Shi T,Yang Y Y,Zhang L,et al.Surface testing methods of aspheric optical elements[J].Chinese Optics,2014,7(1):26-46.师途,杨甬英,张磊,等.非球面光学元件的面形检测技术[J].中国光学,2014,7(1):26-46.
[2] Bruning J H,Herriott D R,Gallagher J E,et al.Digital wavefront measuring interferometer for testing optical surfaces and lenses[J].Applied Optics,1974,13(11):2693-2703.
[3] Fei L H,Lu X X,Wang H L,et al.Single-wavelength phase retrieval method from simultaneous multi-wavelength in-line phase-shifting interferograms[J].Optics Express,2014,22(25):30910-30923.
[4] Zhang W P,Lu X X,Fei L H,et al.Simultaneous phase-shifting dual-wavelength interferometry based on two-step demodulation algorithm[J].Optics Letters,2014,39(18):5375-5378.
[5] Zeng Y N,Lei H,Chang X Y,et al.Phase retrieval with one interferogram by reflecting off-axis microscopic interferometry[J].Chinese Journal of Lasers,2015,42(9):0908006.曾雅楠,雷海,常新宇,等.基于离轴显微干涉术的单幅干涉图相位求解[J].中国激光,2015,42(9):0908006.
[6] Liu D,Yang Y Y,Tian C,et al.Study on phase retrieval from single close fringe pattern with high precision[J].Chinese Journal of Lasers,2010,37(2):531-536.刘东,杨甬英,田超,等.高精度单幅闭合条纹干涉图相位重构技术[J].中国激光,2010,37(2):531-536.
[7] Qiu X,Zhong L Y,Li B B,et al.A rapid spatial carrier-frequency phase-shifting method based on the orthogonality of diamond diagonal vectors[J].IEEE Photonics Journal,2017,9(3):1-9.
[8] Lin J X,Ma X,Li S P,et al.Four-step spatial quasi-phase-shifting technique for phase demodulation from a single carrier fringe pattern[J].Laser & Optoelectronics Progress,2017,54(1):011203.林锦新,马骁,李仕萍,等.四步空域准相移单帧载频条纹相位解调技术[J].激光与光电子学进展,2017,54(1):011203.
[9] Lian Q S,Li Y,Chen S Z.Phase retrieval algorithm fusing multiple wavelets and total variation regularization[J].Acta Optica Sinica,2018,38(2):0220001.练秋生,李颖,陈书贞.融合多种小波与全变差正则化的相位恢复算法[J].光学学报,2018,38(2):0220001.
[10] Servin M,Marroquin J L,Cuevas F J.Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms[J].Journal of the Optical Society of America A,2001,18(3):689-695.
[11] Servin M,Marroquin J L,Quiroga J A.Regularized quadrature and phase tracking from a single closed-fringe interferogram[J].Journal of the Optical Society of America A,2004,21(3):411-419.
[12] Kulkarni R,Rastogi P.Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter[J].Applied Optics,2018,57(4):702-708.
[13] Feng L,Zeng Z G,Wu Y Q.Optical surface measurement using phase retrieval hybrid algorithm based on diffraction angular spectrum theory[J].Proceedings of SPIE,2013,8911:891111.
[14] Hao Q,Ning Y,Hu Y.Interferometric testing of aspheric surface[J].Metrology & Measurement Technology,2018,38(1):1-8.郝群,宁妍,胡摇.基于干涉法的非球面测量技术[J].计测技术,2018,38(1):1-8.
[15] Tian A L,Liu T,Liu J,et al.High precision wavefront reconstruction technology for single interferogram[J].Infrared and Laser Engineering,2015,44(4):1203-1207.田爱玲,刘婷,刘剑,等.单幅干涉条纹图的高精度波面重建技术[J].红外与激光工程,2015,44(4):1203-1207.
[16] Takeda M,Ina H,Kobayashi S.Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry[J].Journal of the Optical Society of America,1982,72(1):156-160.
[17] Massig J H,Heppner J.Fringe-pattern analysis with high accuracy by use of the Fourier-transform method:theory and experimental tests[J].Applied Optics,2001,40(13):2081-2088.
[18] Muňoz-Maciel J,Lecona-Peňa F G,Castillo-Quevedo C,et al.Phase recovery from a single interferogram using multiple Fourier transforms[J].Proceedings of SPIE,2006,6292:62920D.
[19] Muňoz-Maciel J,Casillas-Rodríguez F J,Mora-González M,et al.Phase recovery from a single interferogram with closed fringes by phase unwrapping[J].Applied Optics,2011,50(1):22-27.
[20] Ge Z T,Kobayashi F,Matsuda S,et al.Coordinate-transform technique for closed-fringe analysis by the Fourier-transform method[J].Applied Optics,2001,40(10):1649-1657.
[21] Liu H,Zhu Q,Hao Q.Design of novel part-compensating lens used in aspheric testing[J].Proceedings of SPIE,2003,5253:480-485.
[22] Liu H,Hao Q,Zhu Q.A novel aspheric surface testing method using part-compensating lens[J].Proceedings of SPIE,2005,5638:324-329.
[23] Hao Q,Wang S P,Hu Y,et al.Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements[J].Applied Optics,2016,55(35):9992-10001.
[24] Hao Q,Li T F,Hu Y,et al.Vertex radius of curvature error measurement of aspheric surface based on slope asphericity in partial compensation interferometry[J].Optics Express,2017,25(15):18107-18121.
[25] Hao Q,Wang S P,Hu Y,et al.Two-step carrier-wave stitching method for aspheric and freeform surface measurement with a standard spherical interferometer[J].Applied Optics,2018,57(17):4743-4750.
[2] Bruning J H,Herriott D R,Gallagher J E,et al.Digital wavefront measuring interferometer for testing optical surfaces and lenses[J].Applied Optics,1974,13(11):2693-2703.
[3] Fei L H,Lu X X,Wang H L,et al.Single-wavelength phase retrieval method from simultaneous multi-wavelength in-line phase-shifting interferograms[J].Optics Express,2014,22(25):30910-30923.
[4] Zhang W P,Lu X X,Fei L H,et al.Simultaneous phase-shifting dual-wavelength interferometry based on two-step demodulation algorithm[J].Optics Letters,2014,39(18):5375-5378.
[5] Zeng Y N,Lei H,Chang X Y,et al.Phase retrieval with one interferogram by reflecting off-axis microscopic interferometry[J].Chinese Journal of Lasers,2015,42(9):0908006.曾雅楠,雷海,常新宇,等.基于离轴显微干涉术的单幅干涉图相位求解[J].中国激光,2015,42(9):0908006.
[6] Liu D,Yang Y Y,Tian C,et al.Study on phase retrieval from single close fringe pattern with high precision[J].Chinese Journal of Lasers,2010,37(2):531-536.刘东,杨甬英,田超,等.高精度单幅闭合条纹干涉图相位重构技术[J].中国激光,2010,37(2):531-536.
[7] Qiu X,Zhong L Y,Li B B,et al.A rapid spatial carrier-frequency phase-shifting method based on the orthogonality of diamond diagonal vectors[J].IEEE Photonics Journal,2017,9(3):1-9.
[8] Lin J X,Ma X,Li S P,et al.Four-step spatial quasi-phase-shifting technique for phase demodulation from a single carrier fringe pattern[J].Laser & Optoelectronics Progress,2017,54(1):011203.林锦新,马骁,李仕萍,等.四步空域准相移单帧载频条纹相位解调技术[J].激光与光电子学进展,2017,54(1):011203.
[9] Lian Q S,Li Y,Chen S Z.Phase retrieval algorithm fusing multiple wavelets and total variation regularization[J].Acta Optica Sinica,2018,38(2):0220001.练秋生,李颖,陈书贞.融合多种小波与全变差正则化的相位恢复算法[J].光学学报,2018,38(2):0220001.
[10] Servin M,Marroquin J L,Cuevas F J.Fringe-follower regularized phase tracker for demodulation of closed-fringe interferograms[J].Journal of the Optical Society of America A,2001,18(3):689-695.
[11] Servin M,Marroquin J L,Quiroga J A.Regularized quadrature and phase tracking from a single closed-fringe interferogram[J].Journal of the Optical Society of America A,2004,21(3):411-419.
[12] Kulkarni R,Rastogi P.Phase unwrapping algorithm using polynomial phase approximation and linear Kalman filter[J].Applied Optics,2018,57(4):702-708.
[13] Feng L,Zeng Z G,Wu Y Q.Optical surface measurement using phase retrieval hybrid algorithm based on diffraction angular spectrum theory[J].Proceedings of SPIE,2013,8911:891111.
[14] Hao Q,Ning Y,Hu Y.Interferometric testing of aspheric surface[J].Metrology & Measurement Technology,2018,38(1):1-8.郝群,宁妍,胡摇.基于干涉法的非球面测量技术[J].计测技术,2018,38(1):1-8.
[15] Tian A L,Liu T,Liu J,et al.High precision wavefront reconstruction technology for single interferogram[J].Infrared and Laser Engineering,2015,44(4):1203-1207.田爱玲,刘婷,刘剑,等.单幅干涉条纹图的高精度波面重建技术[J].红外与激光工程,2015,44(4):1203-1207.
[16] Takeda M,Ina H,Kobayashi S.Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry[J].Journal of the Optical Society of America,1982,72(1):156-160.
[17] Massig J H,Heppner J.Fringe-pattern analysis with high accuracy by use of the Fourier-transform method:theory and experimental tests[J].Applied Optics,2001,40(13):2081-2088.
[18] Muňoz-Maciel J,Lecona-Peňa F G,Castillo-Quevedo C,et al.Phase recovery from a single interferogram using multiple Fourier transforms[J].Proceedings of SPIE,2006,6292:62920D.
[19] Muňoz-Maciel J,Casillas-Rodríguez F J,Mora-González M,et al.Phase recovery from a single interferogram with closed fringes by phase unwrapping[J].Applied Optics,2011,50(1):22-27.
[20] Ge Z T,Kobayashi F,Matsuda S,et al.Coordinate-transform technique for closed-fringe analysis by the Fourier-transform method[J].Applied Optics,2001,40(10):1649-1657.
[21] Liu H,Zhu Q,Hao Q.Design of novel part-compensating lens used in aspheric testing[J].Proceedings of SPIE,2003,5253:480-485.
[22] Liu H,Hao Q,Zhu Q.A novel aspheric surface testing method using part-compensating lens[J].Proceedings of SPIE,2005,5638:324-329.
[23] Hao Q,Wang S P,Hu Y,et al.Virtual interferometer calibration method of a non-null interferometer for freeform surface measurements[J].Applied Optics,2016,55(35):9992-10001.
[24] Hao Q,Li T F,Hu Y,et al.Vertex radius of curvature error measurement of aspheric surface based on slope asphericity in partial compensation interferometry[J].Optics Express,2017,25(15):18107-18121.
[25] Hao Q,Wang S P,Hu Y,et al.Two-step carrier-wave stitching method for aspheric and freeform surface measurement with a standard spherical interferometer[J].Applied Optics,2018,57(17):4743-4750.