基于傅里叶变换的哈特曼波前重构算法比较
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摘要
为了快速准确的对含有噪声和倾斜误差的斜率数据进行重建,采用理论分析、仿真模拟及实验验证相结合的方法,对哈特曼波前重构中基于傅里叶变换的三种常用重建算法——傅里叶级数展开法(FFT)、反对称偏导积分法(ASDI)、离散余弦级数展开法(DCT)的正确性和适用性作了对比研究。结果表明:FFT算法运行速度最快,DCT算法次之,ASDI算法速度最慢;其中ASDI算法效果相对较好,但该种算法会受倾斜误差影响,导致重建精度降低甚至重建失败; FFT算法抗噪性最强,但重建时要求边界符合周期性延拓条件,当不满足条件时边缘误差较大; DCT算法不适合处理小型数据集。
In order to rebuild the slope data with the noise and tilt error rapidly and accurately,three common reconstruction algorithms of Fourier series expansion method( FFT),the anti-symmetric partial derivative integral method( ASDI),discrete cosine series expansion method( DCT),based on Fourier transform in Hartmann wavefront reconstruction,are compared with the method of theoretical analysis,computer simulation and experimental to validated the correctness and applicability. The results show that FFT algorithm is the fastest,followed by DCT algorithm and ASDI algorithm. Among them,the ASDI algorithm has relatively good effect,but this algorithm will be affected by the tilt error,resulting in the reduction of the reconstruction precision and even the reconstruction failure. FFT algorithm has the strongest noise resistance,but the boundary is required to meet the periodic extension condition when reconstruction is performed. DCT algorithm is not suitable for tiny size data set.
In order to rebuild the slope data with the noise and tilt error rapidly and accurately,three common reconstruction algorithms of Fourier series expansion method( FFT),the anti-symmetric partial derivative integral method( ASDI),discrete cosine series expansion method( DCT),based on Fourier transform in Hartmann wavefront reconstruction,are compared with the method of theoretical analysis,computer simulation and experimental to validated the correctness and applicability. The results show that FFT algorithm is the fastest,followed by DCT algorithm and ASDI algorithm. Among them,the ASDI algorithm has relatively good effect,but this algorithm will be affected by the tilt error,resulting in the reduction of the reconstruction precision and even the reconstruction failure. FFT algorithm has the strongest noise resistance,but the boundary is required to meet the periodic extension condition when reconstruction is performed. DCT algorithm is not suitable for tiny size data set.
引文
[1]程利群,景文博,王晓曼.夏克-哈特曼波前传感器光斑质心探测方法比较与分析[J].长春理工大学学报(自然科学版),2014,3:23-26.
[2]李晶,巩岩,呼新荣,等.哈特曼-夏克波前传感器的高精度质心探测方法[J].中国激光,2014,41(3):246-252.
[3] ZHAO S. Application and Development of Wavefront Sensor Technology[J]. 2017,6(3):154.
[4]李萌阳,李大海,赵霁文,等.基于方形域内标准正交矢量多项式的波前重建[J].光学学报,2014,34(7):136-142.
[5] ETTL S,KAMINSKI J,KNAUER M C,et al. Shape reconstruction from gradient data[J]. Applied Optics,2008,47(12):2091-7.
[6] VISSER C C D,BRUNNER E,VERHAEGEN M,et al.Nonlinear spline wavefront reconstruction through momentbased Shack-Hartmann sensor measurements[J]. Optics Express,2017,25(10):11514.
[7] SOUTHWELL W H. Wave-front estimation from wavefront slope measurements[J]. Journal of the Optical Society of America,1980,70(8):998-1006.
[8] LI G,LI Y,LIU K,et al. Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry.[J]. Journal of the Optical Society of America A Optics Image Science&Vision,2013,30(7):1448-1459.
[9] PATHAK B,BORUAH B R. Improved wavefront reconstruction algorithm for Shack-Hartmann type wavefront sensors[J]. Journal of Optics,2014,16(5):915-918.
[10] HUANG L,XUE J,GAO B,et al. Spline based least squares integration for two-dimensional shape or wavefront reconstruction[J]. Optics&Lasers in Engineering,2017,91:221-226.
[11] VOGEL C R,YANG Q. Multigrid algorithm for leastsquares wavefront reconstruction[J]. Applied Optics,2006,45(4):705-15.
[12] BHR M,BREUβM,QUéAU Y,et al. Fast and accurate surface normal integration on non-rectangular domains[J].Computational visual media,2017,3(2):1-23.
[13] FRANKOT R T,CHELLAPPA R. A method for enforcing integrability in shape from shading algorithms[J]. IEEE Transactions on Pattern Analysis&Machine Intelligence,1988,10(4):439-451.
[14] WEI T,KLETTE R. On Depth Recovery from Gradient Vector Fields[M]. Algorithms,Architectures And Information Systems Security. 2007:75-95.
[15]荆海龙,苏显渝,刘元坤,等.基于条纹反射的镜面测量及三维重建算法分析[J].光电工程,2008,35(10):37-42.
[16] BON P,MONNERET S,WATTELLIER B. Noniterative boundary-artifact-free wavefront reconstruction from its derivatives[J]. Applied Optics,2012,51(23):5698-704.
[17]杨旭,陈波,李小阳,等.远距离数字离轴全息中基于图像指标优化的相位误差校正方法[J].激光杂志,2017,38(04):96-100.
[18]李小阳,陈波,张湧涛,等.波前曲率传感器的实时波前重构方法[J].激光杂志,2017,38(01):12-15.
[19] HUANG L,IDIR M,ZUO C,et al. Comparison of two-dimensional integration methods for shape reconstruction from gradient data[J]. Optics&Lasers in Engineering,2015,64:1-11.
[20]段海峰,杨泽平,张雨东.快速傅里叶算法在哈特曼—夏克传感器波前重构算法中的应用[J].光学学报,2003,23(2):240-244.
[21] QUéAU Y,DUROU J D,AUJOL J F. Normal Integration:A Survey[J]. Journal of Mathematical Imaging&Vision,2017,1:1-18.
[22]王华英,于梦杰,刘飞飞,等.基于快速傅里叶变换的四种相位解包裹算法[J].强激光与粒子束,2013,25(5):1129-1133.
[23] TALMI A,RIBAK E N. Wavefront reconstruction from its gradients.[J]. Journal of the Optical Society of America A Optics Image Science&Vision,2006,23(2):288-297.
[24]罗智锋.激光小尺度畸变波前探测误差分析及其补偿研究[D].成都:四川大学,2006.
[25]黄德权,周文超,邱红,等.哈特曼测量大气相干长度研究[J].强激光与粒子束,2016,38(7):21-23.
[2]李晶,巩岩,呼新荣,等.哈特曼-夏克波前传感器的高精度质心探测方法[J].中国激光,2014,41(3):246-252.
[3] ZHAO S. Application and Development of Wavefront Sensor Technology[J]. 2017,6(3):154.
[4]李萌阳,李大海,赵霁文,等.基于方形域内标准正交矢量多项式的波前重建[J].光学学报,2014,34(7):136-142.
[5] ETTL S,KAMINSKI J,KNAUER M C,et al. Shape reconstruction from gradient data[J]. Applied Optics,2008,47(12):2091-7.
[6] VISSER C C D,BRUNNER E,VERHAEGEN M,et al.Nonlinear spline wavefront reconstruction through momentbased Shack-Hartmann sensor measurements[J]. Optics Express,2017,25(10):11514.
[7] SOUTHWELL W H. Wave-front estimation from wavefront slope measurements[J]. Journal of the Optical Society of America,1980,70(8):998-1006.
[8] LI G,LI Y,LIU K,et al. Improving wavefront reconstruction accuracy by using integration equations with higher-order truncation errors in the Southwell geometry.[J]. Journal of the Optical Society of America A Optics Image Science&Vision,2013,30(7):1448-1459.
[9] PATHAK B,BORUAH B R. Improved wavefront reconstruction algorithm for Shack-Hartmann type wavefront sensors[J]. Journal of Optics,2014,16(5):915-918.
[10] HUANG L,XUE J,GAO B,et al. Spline based least squares integration for two-dimensional shape or wavefront reconstruction[J]. Optics&Lasers in Engineering,2017,91:221-226.
[11] VOGEL C R,YANG Q. Multigrid algorithm for leastsquares wavefront reconstruction[J]. Applied Optics,2006,45(4):705-15.
[12] BHR M,BREUβM,QUéAU Y,et al. Fast and accurate surface normal integration on non-rectangular domains[J].Computational visual media,2017,3(2):1-23.
[13] FRANKOT R T,CHELLAPPA R. A method for enforcing integrability in shape from shading algorithms[J]. IEEE Transactions on Pattern Analysis&Machine Intelligence,1988,10(4):439-451.
[14] WEI T,KLETTE R. On Depth Recovery from Gradient Vector Fields[M]. Algorithms,Architectures And Information Systems Security. 2007:75-95.
[15]荆海龙,苏显渝,刘元坤,等.基于条纹反射的镜面测量及三维重建算法分析[J].光电工程,2008,35(10):37-42.
[16] BON P,MONNERET S,WATTELLIER B. Noniterative boundary-artifact-free wavefront reconstruction from its derivatives[J]. Applied Optics,2012,51(23):5698-704.
[17]杨旭,陈波,李小阳,等.远距离数字离轴全息中基于图像指标优化的相位误差校正方法[J].激光杂志,2017,38(04):96-100.
[18]李小阳,陈波,张湧涛,等.波前曲率传感器的实时波前重构方法[J].激光杂志,2017,38(01):12-15.
[19] HUANG L,IDIR M,ZUO C,et al. Comparison of two-dimensional integration methods for shape reconstruction from gradient data[J]. Optics&Lasers in Engineering,2015,64:1-11.
[20]段海峰,杨泽平,张雨东.快速傅里叶算法在哈特曼—夏克传感器波前重构算法中的应用[J].光学学报,2003,23(2):240-244.
[21] QUéAU Y,DUROU J D,AUJOL J F. Normal Integration:A Survey[J]. Journal of Mathematical Imaging&Vision,2017,1:1-18.
[22]王华英,于梦杰,刘飞飞,等.基于快速傅里叶变换的四种相位解包裹算法[J].强激光与粒子束,2013,25(5):1129-1133.
[23] TALMI A,RIBAK E N. Wavefront reconstruction from its gradients.[J]. Journal of the Optical Society of America A Optics Image Science&Vision,2006,23(2):288-297.
[24]罗智锋.激光小尺度畸变波前探测误差分析及其补偿研究[D].成都:四川大学,2006.
[25]黄德权,周文超,邱红,等.哈特曼测量大气相干长度研究[J].强激光与粒子束,2016,38(7):21-23.