相位干涉测量的信息理论分析
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摘要
惯性约束核聚变(ICF)是当今基础科学前沿领域之一,对国防事业和新能源开发有着极为重要的科学意义和应用价值。高功率固体激光装置作为ICF的驱动器,对所使用的大口径光学元件的中、低频制造误差提出了严格的要求。目前我国大口径光学元件中、低频位相信息的检测理论及其检测手段远不能满足工程需要。所以本文从信息论出发,建立了一套基于信息论的位相干涉检测理论,优化设计了干涉检测系统,实现了大口径光学元件中、低频制造误差的精密检测,得到了若干有意义的结果。
利用Wigner分布函数建立了光学元件波前信息量的理论模型,该模型用空间带宽积描述波前的信息量、用基于Wigner分布函数的局部功率谱密度(PSD)评价局部波前畸变,结合全孔径PSD分析,可更全面地描述和评价波前信息,并能具体指导光学元件的返修。
根据信息论建立了干涉成像系统信息容量的理论模型,该模型表明干涉成像系统的信息容量由系统的空间带宽积和信噪比决定,它有效地弥补了系统传递函数不能表征系统噪声的缺陷。根据统计光学建立了干涉成像系统信噪比的理论模型,以信噪比最大化为目标,优化设计了旋转毛玻璃、环形光源和CCD等关键器件。理论计算和实验结果表明:(1)为了获得高信噪比,应增大CCD的占空比和曝光时间;应控制旋转毛玻璃参数使旋转周期小于或等于CCD曝光时间、使光源相干长度为测试光和参考光间光程差的2至5倍。(2)环形光源的面积会影响系统的信噪比,当光源面积一定时环形光源抑制相干噪声的能力随内外径之比的增大而提高;利用环形光源可将平均信噪比从传统点光源模式下的5.2dB提高到8.6dB。
从参数的统计估计理论出发,建立了位相估计精密度与干涉条纹光强数据Fisher信息量的关系,分析了现有算法的位相估计精度。为了提高位相估计精度,提出了基于最小二乘迭代的抗振时域相移算法、多光束相移算法和空间载波相移算法,分别有效地补偿了环境振动引入的随机平移和倾斜相移误差、多光束或多表面干涉引入的高阶谐波误差和随机空间载波频率引入的空间相移误差。数值计算和实验结果表明本文提出的算法精度优于现有同类算法。应用本文算法,降低了大口径干涉仪对环境稳定性和相移器性能的要求,节约了制造成本。
为了测量光学元件中频段信息,以信息容量为目标函数,优化设计并研制了Φ100mm干涉仪系统,测试结果表明该系统一维空间带宽积大于100mm×2.5mm~(-1)、平均信噪比大于4dB。提出了采用子孔径PSD加权平均得到全孔径PSD的测量方法和干涉仪系统Wigner分布函数的标定及大口径光学元件中频信息的校准方法,实现了小口径干涉仪准确测量大口径光学元件的中频信息。
通过本文研究,使得干涉检测系统的分析方法从傅立叶光学过渡到信息论、性能评价指标从系统传递函数过渡到信息容量,为高分辨率高精度干涉检测系统的设计及大口径光学元件中、低频制造误差的检测提供了更有效的理论指导。优化后的Φ500mm波长调谐相移干涉仪和Φ100mm高分辨率干涉仪基本满足了大型激光装置波前检测指标要求,为我国神光Ⅲ装置干涉检测配套能力的建立提供了可靠技术支撑和保障。
Inertial Confinement Fusion (ICF), one of present significant research fields in the frontier of basic science, is of great scientific and practical meaning in national defense and exploitation of new energy resources. As the driver of ICF, the high power solid-state laser facility employs a lot of large aperture optical components, which must be characterized with a high degree of accuracy over low and middle frequency components of phase errors. However, our testing method and apparatus for such frequency components of phase information is far from meeting the requirement of SG-III laser system at present. Therefore, in this dissertation, an information-theoretic model of phase-measurement interferometry has been developed to analyze the transfer characteristics of phase information, optimize the interferometric system and provide a guide to measurement of low-middle frequency components of large optics. Some meaningful results are obtained as follows.
Firstly, an information-theoretic model of wavefront deformation of optical components is presented on the basis of Wigner distribution function. In this model, the degree of freedom of wavefront deformation is characterized by space-bandwidth product (SBP), and the tolerance of wavefront deformation is specified with power spectral density function (PSD) and Wigner distribution function.So it provides a comprehensive characterization and specification of wavefront deformation and a concrete guide to optical fabrication.
Secondly, the theoretical model of information capacity in interferometric imaging system is proposed by means of information theory. The model shows that the information capacity of the system depends on its space-bandwidth product (SBP) and signal-to-noise ratio (SNR). As an evaluating parameter of the system's performance, information capacity is more effective than system transfer function (STF) because the latter fails to express any information of SNR. Furthermore, the theoretical model of SNR in interferometric imaging system is derived according to statistical optics. By maximizing the objective function of SNR, optimization is employed to some key components such as rotating diffuser, ring source and CCD. According to the results of theoretical calculations and experiments, some conclusions are drawn as follows. (1) An increasing in fill factor and exposure time of CCD leads to an increasing in SNR of system. (2) To obtain high SNR, the rotating diffuser should be well controlled so that the rotating period is not longer than the exposure time of CCD, and the coherent length of optical intensity is about 2～5 times as long as the optical path difference (OPD) between reference and test beams. (3)By utilizing the ring source, the average SNR of the system increases from 5.2dB (tranditional point source) to 8.6dB because of the effect of source's area. Howerver, if given the equivalent area, the ability of ring source in reducing coherent noise is improved by increasing of the ratio of the inner and outer radii.
Thirdly, the relationship between the precision of phase estimation and the Fisher information of its correspondent intensity data is given on the basis of Cramer-Rao lower bound (CRLB). According to the relationship, the precisions of the existing algorithms are analyzed, including temporal phase-shifting method (TPS), spatial carrier phase shifting method (SCPS) and Fourier transform method (FFT). To obtain higher precision of phase estimation, a series of algorithms based on least-squares iteration are designed to deal with the problems of phase-shift miscalibration (including random translational errors and tilt-shift errors for TPS and random spatial carrier frequency for SCPS) and high-order harmonics (including multiple-beam Fizeau interferograms and multiple-surface interferograms with random phase shifts). The results of numerical simulations and experiments demonstrate that the proposed algorithms exhibit higher precision than the existing algorithms. With the proposed algorithm, the large aperture interferometer could provide the ability of precision metrology in dynamic environments, thus the accurate phase-shifting devices and the high performance optical platform are no longer required for large aperture interferometer, which greatly reduces the cost.
Fourthly, a 100-mm-aperture interferometer has been developed under the guidance of information capacity. The interferometer's test results indicate the one-dimension SBP and the average SNR are higher than 100mmx2.5mm"1 and 4dB, respectively. To measure mid spatial period error of large aperture optical components, sub-aperture measurement is adopted and the full-aperture PSD is estimated by weighted average of sub-aperture PSD. Considering that the system is not shift-invariant, the Wigner distribution of the system is calibrated to obtain accurate sub-aperture and full-aperture PSD.
To sum up, this dissertation presents a comprehensive analysis of phase measurement interferometry from the viewpoint of information theory. Thus, it offers us a better understanding of the transfer characteristic of phase information.The results mentioned above provide certain guiding value to interferometer design and measurement of mid-spatial period error of large-aperture optical components. Moreover, the optimized interferometers, the 500-mm aperture wavelength-tuning phase-shifting interferometer and the 100-mm-aperture high lateral resolution interferometer, whose measurement accuracy satisfies the requirement of the high power solid-state laser facility, will offer technical support and guarantee for optical measurement in SG-III laser system.
利用Wigner分布函数建立了光学元件波前信息量的理论模型,该模型用空间带宽积描述波前的信息量、用基于Wigner分布函数的局部功率谱密度(PSD)评价局部波前畸变,结合全孔径PSD分析,可更全面地描述和评价波前信息,并能具体指导光学元件的返修。
根据信息论建立了干涉成像系统信息容量的理论模型,该模型表明干涉成像系统的信息容量由系统的空间带宽积和信噪比决定,它有效地弥补了系统传递函数不能表征系统噪声的缺陷。根据统计光学建立了干涉成像系统信噪比的理论模型,以信噪比最大化为目标,优化设计了旋转毛玻璃、环形光源和CCD等关键器件。理论计算和实验结果表明:(1)为了获得高信噪比,应增大CCD的占空比和曝光时间;应控制旋转毛玻璃参数使旋转周期小于或等于CCD曝光时间、使光源相干长度为测试光和参考光间光程差的2至5倍。(2)环形光源的面积会影响系统的信噪比,当光源面积一定时环形光源抑制相干噪声的能力随内外径之比的增大而提高;利用环形光源可将平均信噪比从传统点光源模式下的5.2dB提高到8.6dB。
从参数的统计估计理论出发,建立了位相估计精密度与干涉条纹光强数据Fisher信息量的关系,分析了现有算法的位相估计精度。为了提高位相估计精度,提出了基于最小二乘迭代的抗振时域相移算法、多光束相移算法和空间载波相移算法,分别有效地补偿了环境振动引入的随机平移和倾斜相移误差、多光束或多表面干涉引入的高阶谐波误差和随机空间载波频率引入的空间相移误差。数值计算和实验结果表明本文提出的算法精度优于现有同类算法。应用本文算法,降低了大口径干涉仪对环境稳定性和相移器性能的要求,节约了制造成本。
为了测量光学元件中频段信息,以信息容量为目标函数,优化设计并研制了Φ100mm干涉仪系统,测试结果表明该系统一维空间带宽积大于100mm×2.5mm~(-1)、平均信噪比大于4dB。提出了采用子孔径PSD加权平均得到全孔径PSD的测量方法和干涉仪系统Wigner分布函数的标定及大口径光学元件中频信息的校准方法,实现了小口径干涉仪准确测量大口径光学元件的中频信息。
通过本文研究,使得干涉检测系统的分析方法从傅立叶光学过渡到信息论、性能评价指标从系统传递函数过渡到信息容量,为高分辨率高精度干涉检测系统的设计及大口径光学元件中、低频制造误差的检测提供了更有效的理论指导。优化后的Φ500mm波长调谐相移干涉仪和Φ100mm高分辨率干涉仪基本满足了大型激光装置波前检测指标要求,为我国神光Ⅲ装置干涉检测配套能力的建立提供了可靠技术支撑和保障。
Inertial Confinement Fusion (ICF), one of present significant research fields in the frontier of basic science, is of great scientific and practical meaning in national defense and exploitation of new energy resources. As the driver of ICF, the high power solid-state laser facility employs a lot of large aperture optical components, which must be characterized with a high degree of accuracy over low and middle frequency components of phase errors. However, our testing method and apparatus for such frequency components of phase information is far from meeting the requirement of SG-III laser system at present. Therefore, in this dissertation, an information-theoretic model of phase-measurement interferometry has been developed to analyze the transfer characteristics of phase information, optimize the interferometric system and provide a guide to measurement of low-middle frequency components of large optics. Some meaningful results are obtained as follows.
Firstly, an information-theoretic model of wavefront deformation of optical components is presented on the basis of Wigner distribution function. In this model, the degree of freedom of wavefront deformation is characterized by space-bandwidth product (SBP), and the tolerance of wavefront deformation is specified with power spectral density function (PSD) and Wigner distribution function.So it provides a comprehensive characterization and specification of wavefront deformation and a concrete guide to optical fabrication.
Secondly, the theoretical model of information capacity in interferometric imaging system is proposed by means of information theory. The model shows that the information capacity of the system depends on its space-bandwidth product (SBP) and signal-to-noise ratio (SNR). As an evaluating parameter of the system's performance, information capacity is more effective than system transfer function (STF) because the latter fails to express any information of SNR. Furthermore, the theoretical model of SNR in interferometric imaging system is derived according to statistical optics. By maximizing the objective function of SNR, optimization is employed to some key components such as rotating diffuser, ring source and CCD. According to the results of theoretical calculations and experiments, some conclusions are drawn as follows. (1) An increasing in fill factor and exposure time of CCD leads to an increasing in SNR of system. (2) To obtain high SNR, the rotating diffuser should be well controlled so that the rotating period is not longer than the exposure time of CCD, and the coherent length of optical intensity is about 2～5 times as long as the optical path difference (OPD) between reference and test beams. (3)By utilizing the ring source, the average SNR of the system increases from 5.2dB (tranditional point source) to 8.6dB because of the effect of source's area. Howerver, if given the equivalent area, the ability of ring source in reducing coherent noise is improved by increasing of the ratio of the inner and outer radii.
Thirdly, the relationship between the precision of phase estimation and the Fisher information of its correspondent intensity data is given on the basis of Cramer-Rao lower bound (CRLB). According to the relationship, the precisions of the existing algorithms are analyzed, including temporal phase-shifting method (TPS), spatial carrier phase shifting method (SCPS) and Fourier transform method (FFT). To obtain higher precision of phase estimation, a series of algorithms based on least-squares iteration are designed to deal with the problems of phase-shift miscalibration (including random translational errors and tilt-shift errors for TPS and random spatial carrier frequency for SCPS) and high-order harmonics (including multiple-beam Fizeau interferograms and multiple-surface interferograms with random phase shifts). The results of numerical simulations and experiments demonstrate that the proposed algorithms exhibit higher precision than the existing algorithms. With the proposed algorithm, the large aperture interferometer could provide the ability of precision metrology in dynamic environments, thus the accurate phase-shifting devices and the high performance optical platform are no longer required for large aperture interferometer, which greatly reduces the cost.
Fourthly, a 100-mm-aperture interferometer has been developed under the guidance of information capacity. The interferometer's test results indicate the one-dimension SBP and the average SNR are higher than 100mmx2.5mm"1 and 4dB, respectively. To measure mid spatial period error of large aperture optical components, sub-aperture measurement is adopted and the full-aperture PSD is estimated by weighted average of sub-aperture PSD. Considering that the system is not shift-invariant, the Wigner distribution of the system is calibrated to obtain accurate sub-aperture and full-aperture PSD.
To sum up, this dissertation presents a comprehensive analysis of phase measurement interferometry from the viewpoint of information theory. Thus, it offers us a better understanding of the transfer characteristic of phase information.The results mentioned above provide certain guiding value to interferometer design and measurement of mid-spatial period error of large-aperture optical components. Moreover, the optimized interferometers, the 500-mm aperture wavelength-tuning phase-shifting interferometer and the 100-mm-aperture high lateral resolution interferometer, whose measurement accuracy satisfies the requirement of the high power solid-state laser facility, will offer technical support and guarantee for optical measurement in SG-III laser system.
引文
[1]王淦昌,袁之尚.惯性约束核聚变[M].合肥:安徽教育出版社,1996.
[2]W.J.Hogan,J.A.Paisner,Progress in the Title I Design of the National Ignition Facility[R].UCRL-JC-123560,1996.
[3]J.A.Paisner,J.R.Murray,The National Ignition Facility for Inertial Confinement Fusion[R].UCRL-JC-1ZS6S9,1997.
[4]T.S.Perry,B.H.Wilde.NIF System-Design Requirements for Nuclear-Weapons Physics Experiments[R].UCRL-ID-120738,1995.
[5]Michael Bray,Using First Principles in the Specifying of Optics for Large High-Power Lasers(Ⅰ):Application to the MegaJoule Laser(LMJ)[J].SPIE,1996;2775:328-344.
[6]许乔,高功率固体激光系统光学元件质量评价[D].博士后研究工作报告,绵阳:中国工程物理研究院,1999.
[7]彭翰生,张小民,范滇元,朱健强.高功率固体激光装置的发展与工程科学问题[J].中国工程科学,2001;3(3):1-8.
[8]刘红捷,高功率激光束中高频波前畸变特性的研究[D].硕士学位论文,绵阳:中国工程物理研究院,2005
[9]J.K.Lawson,C.R.Wolfe,K.R.Manes,et al.Specification of optical components using the power spectral density function[J].SPIE,1995;2536:38-50.
[10]J.H.Campbell,R.Hawley-Fedder,C.J.Stolz,et al.NIF Optical Materials and Fabrication Technologies:An Overview[J].SPIE,2004;5341:84-101.
[11]Kenneth Goldberg.Testing EUV optics with EUV light:If you can measure it,you can make it[A],SPIE.Newsroom:Optical Design & Engineering[C],2006.
[12]P.Hariharan.Optical Interferometry[M].New York:Academic Press,2003.
[13]张蓉竹,ICF系统光学元件高精度波前检测技术研究[D],博士学位论文,成都:四川大学,2003.
[14]Joe Lamb,James Semrad,James Wyant,Chiayu Ai.Optical and mechanical design considerations in the construction of a 24 inch phase shitting interferometer[J].SPIE,1997;3047:415-426.
[15]C.Ai,R.Knowiden,R.Lamb.Design of 24" Phase-Shifting Fizeau interferometer[J].SPIE,1997;3134:447-455.
[16]Michael Bray,Audrey Liard,Genevieve Chabassier.Laser MegaJoule optics(Ⅰ):New methods of optical specification[J].SPIE,1999;3739:449-460.
[17]Audrey Liard,Michael Bray,Genevieve Chabassier.Laser MegaJoule optics(Ⅱ):Wavefront analysis in the testing of large components[J].SP1E,1999;3739:461-472.
[18]Michael Bray.Localised Wavefrom Deformations:propagation in non-linear media(Ⅱ)(a simple but accurate computational method)[J].SPIE,1998;3492:946--956.
[19]Liqun Chai,Qiao Xu,Yingjie Yu,Yah Deng,Jiancheng Xu.500-mm-aperture wavelength-tuning phase-shifting interferometer[J].SPIE.2005;5856:589-596.
[20]Xu Jiancheng,Sheng Guiping,Chai Liqun,Xu Qiao,Deng Yan.Design of coherent optical interferometric system[A].SPIE,2006;6150:61501B-1.
[21]徐建程,高分辨率波前干涉检测技术研究[D].硕士学位论文,绵阳:中国工程物理研究院,2006.
[22]吴新民,光干涉测试中的抗振技术研究[D].博士学位论文,南京:南京理工大学,2002.
[23]左芬,陈磊.同步移相抗振光干涉测量技术研究进展[J].激光与光电子学进展,2006;43(11):43-48.
[24]J.E.Millerd,N.J.Brock,J.B.Hayes,M.B.North-Morris,M.Novak,J.C.Wyant.Pixelated phase-mask dynamic interferometer[J].SPIE,2004;5531:304-314.
[25]Klaus Freischlad,Ron Eng,James B.Hadaway.Interferometer for testing in vibration environments [J].SPIE,2002;4777:311-322.
[26]C.Roddier,F.Roddier,Interferogram analysis using Fourier transform techniques[J].Appl.Opt.1987;26:1668-1673.
[27]M.A.Gdeisatk,D.R.Burton,and M.J.Lalor.Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform[J].Appl.Opt.,2006;45(34):8722-8732.
[28]Bradley T.Kimbrough,Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors[J].Appl.Opt.2006;45:4554-4562.
[29]C.J.Morgan.Least-squares estimation in phase-measurement interferometry[J].Opt.Lett.1982;7:368-1370.
[30]白剑,程上彝,杨国光.大口径镜面的多孔径拼接技术[J].光学学报,1997;17(7):953-956
[31]M.Bray.Stitching interferometry:Side effects and PSD[J].SPIE,1999;3782:443-452.
[32]Mingyi Chen,Hongwei Guo,Yingjie Yu,et al.Recent developments of multi-aperture overlap-scanning technique[J].SPIE,2004;5180:393-401.
[33]X.Hou,F.Wu,and L.Yang,et.al.Full-aperture wavefront reconstruction from annular subaperture interferometric data by us of Zernike annular ploynomials and a matrix method for testing large aspheric surfaces[J].Appl Opt,2006;45(15):3442-3455.
[34]高志山,光学表面轮廓功率谱密度对象质的影响及干涉测试研究[D].博士学位论文,南京:南京理工大学,2000.
[35]L.L.Deck.Apparatus and method for reducing the effects of coherent artifact in an interferometer [P].United stated patents,2003;US6643024
[36]Bradley Trent Kimbrough.Path matched vibration insensitive Fizeau interferometer[D].PhD Dissertation,Arizona:The University of Arizona,2006.
[37]P.E.Murphy.Interferometric metrology of aspheric surfaces[D].PhD Dissertation,University of Rochester,2000.
[38]Romuald Jiozwicki.Influence of spherical aberration of an interferometric system on the measurement error in the case of a finite fringe observation field[J].Appl.Opt.1991;30:3119-3125.
[39]Romuald Jiozwicki.Influence of aberrations of Fizeau interferometer elements on measurement errors[J].Appl.Opt.1991;30:3126-3132.
[40]C.Huang.Propagation errors in precision Fizeau interferometry[J].Appl.Opt.,1993;32:7016-7021.
[41]A.E.Lowman and J.E.Greivenkamp.Interferometer induced wavefront errors when testing in a non-null configuration[J].SPIE,1994;2004:173-178.
[42]戴亚平,谢虎,李银柱等.功率谱密度传输性质的理论分析与数值模拟[J].中国激光,2001;28(4):337-342.
[43]戴亚平,光学表面评价参数——功率谱密度的传输性质分析[D].博士学位论文,北京:中国科学院,2000.
[44]E.L.Novak.Measurement and analysis optimization of large aperture laser Fizeau interferometer[D],PhD Dissertation,Arizona:The University of Arizona,1998.
[45]Peter Takacs,Michelle X.O.Li,Karen Furenlid.A Step-Height Standard for Surface Profiler Calibration [A],Optical Scattering:Applications,Measurement and Theory Ⅱ,Proc.SPIE[C],1993;1993:65-74.
[46]Erik Novak,Chiayu Ai,James C.Wyant.Transfer function characterization of laser Fizeau interferometer for high spatial frequency phase measurements[J].SPIE,1997;3134:114-121.
[47]J.K.Lawson,D.M.Aikens,R.E.English,et al.Power spectral densily specification for high-power laser systems[J].SPIE,1996;2775:345-356.
[48]J.K.Lawson,C.R.Wolfe,K.R.Manes,el al.Specification ofoplical components using the power spectral density function[J].SPIE,1995;2536:38-50.
[49]S.K.Park,R.A.Schowengerdt,M.A.Kaczynski.Modulation-transfer-ftmction analysis for sampled image systems[J].Applied Optics,1984;23(15):2572-2582.
[50]徐建程,许乔,彭翰生.大口径干涉仪系统传递函数的修正和校准.强激光与粒子光束,2008;20(8):1293-1296.
[51]高晋占,微弱信号检测[M],北京:清华大学出版社,2002.
[52]Morteza Shahram,Peyman Milanfar.Statistical and information-theoretic analysis of resolution in imaging[J].IEEE Transactions on information theory.2006;52(8):3411-3437.
[53]C.E.Shannon.A mathematical theory of communication,Bell System Technical Journal,vol 27:379-423and 623-4556,July and October 1948.
[54]Douglas Alan Hope.An information-theoretic study of image formation,detection and post-processing [D].PDH dissertation,Albuquerque,New Mexico:The University of New Mexico.2004.
[55]陶纯堪,陶纯匡.光学信息论[M].北京:科学出版社,1999.
[56]C.L.Fales,EO.Huck,R.W.Samms.Imaging design for improved information capacity[J],Appl.Opt.,1984:23(6):872-888.
[57]F.O.Huck,C.L.Fales.Image gathering and processing:information and fidelity[J].J.Opt.Soc.Am.1985;2(10):1644-1666.
[58]F.O.Huek,C.L,Fales,J.A.Mcormick,et al.Image gathering system design for information and fidelity [J].J.Opt.Soc.Am,1988;5(3):285-299.
[59]S.Jone,Z.Rahrnan,EO.Huck,et al.Information theoretical assessment of digital image system [J].Optical engineering,1990;1309:53-66.
[60]F.O.Huck,C.L.Fales,R.Alter Gartenberg etal.Infonnation - theoretical assessment of sampled imaging systems[J].optical Engineering,1999;38(5):742-762.
[61]W.C.Chou,M.A.Neifeld.Information-based optical design for binary-valued imagery[J].Appl.Opt.,2000;39(11):1731-1742.
[62]迟学芬.基于信息理论的采样成像系统评价与系统技术研究[D],博士论文,北京:中国科学院研究 生院,2003.
[63]W Lukosz.Optical systems with resolvmg powers exceedmg the classical limit[J].J.Opt.Soc.Am 1966;56:1463-1472.
[64]I.J.Cox,C.J.R.Sheppard.Information capacity and resolution in an optical system[J].J.Opt.Soc.Am 1986;3(8):1152-1158.
[65]A.W Lohmann,R.G Dorsch,D.Mendlovic,Z.Zalevsky,and C.Ferreira.Space-bandwidth product of optical signals and systems[J].J.Opt.Soc.Am.1996;13:470-473.
[66]D.Mendlovic and A.W Lohmann.Space-bandwidth product adaptation and its application for superresolution:fundamentals[J].J.Opt.Soc.Am.1997;14:558-562.
[67]张蓉竹,许乔,顾元元等.大口径光学元件检测中的主要误差及其影响[J].强激光与粒子束,2001;13(2):133-136.
[68]许乔,顾元元等.大口径光学元件波前功率谱密度检测[J].光学学报,2001;21(3):344-347.
[69]J.K.Lawson,D.M.Aikens,R.E.English,et al.Surface figure and roughness tolerances for NIF optics and the interpretation of the gradient,P-V wavefront and RMS specifications[J].SPIE,1999;3782:510-517
[70]C.D.Wolfe,J.K.Lawson.The measurement and analysis of wavefront structure from large aperture ICF optics[A].Proc of the 1stAnnual Solid Laser for Application to ICF[C].1995;2633:361-385
[71]Michael Bray,Andre Roussel.Using First Principles in the specifying of optics for large high power lasers(Ⅰ) - Application to the MegaJoule Laser(LMJ),Specification,Production and testing of Optical Components and Systems[J].SPIE,1996;2775:328-344.
[72]罗军辉,MATLAB 7.0在图象处理中的应用[M].北京:机械:工业出版社,2005.
[73]V.I.Bespalov,V.I.Talanov.Filamentary structure of light beams in nonlinear liquids[J].JETP Lett.1966;3(11):307-310.
[74]N.C.Kothafi and S.C.Abbi.Instability Growth and Filamentation of Very Intense Laser Beams in Self-Focusing Media:General and Mathematical Physics[J].Prog.Theor.Phys.1990;83:414-442
[75]文双春,钱列加,范滇元.强光束局部小尺度调制致多路成丝现象研究物理学报[J].2003;52(7):1640-1644.
[76]M.Bray,A.Liard,G.Chabassier,Laser megajoule optics:Ⅰ.New methods of optical specification [J].SPIE 1999;3739:449-460.
[77]M.Bray,G.Chabassier.Localized wavefront deformations—propagation in nonlinear media Ⅱ:A simple but accurate computational method[J].SPIE.1999;3492:480-494.
[78]J.W.Goodman.Introduction to Fourier Optics[M],(McGraw-Hill,New York),1996.
[79]E.Wigner.On the quantum correction for thermodynamic equilibrium[J].Phys.Rev.,1932;40:749-759.
[80]M.J.Bastiaans.The Wigner distribution function applied to optical signals and systems[J].Opt.Comm.,1978;25(1):26-30.
[81]ISO10110.Optics and optical instruments-Preparation of drawings for optical elements and systems-part 8 surface texture.1997:1-9.
[82]R.E.English,D.M.Aikens,W.T.Whister,et al.Implementation of ISO10110 optical drawing standards for the National Ignition Facility[J].SPIE,1995;2536:51-56.
[83]J.R.Taylor,R.Chow,K.A.Primdahl,et al.Specification of optical components for a high average-power laser environment[J].SPIE,1997,3134:11-22.
[84]M.Bom and E.Wolf.Principles of Optics[M](Pergamon,NewYork),1980.
[85]A.J.den Dekker and A.van den Bos.Resolution:a survey[J].J.Opt.Soc.Am.A 1997;14:547-557.
[86]M.J.Bastiaans.Wigner distribution function and its application to first-order optics[J].J.Opt.Soc.Am.1979;69:1710-1716.
[87]Weiqing Pan.Double Wigner distribution function of a first-order optical system with a hard-edge aperture[J].Appl.Opt.2008;47:45-51.
[88]C.Gonzalo,J.Bescos,L.R.Berdel-Valdos,and J.Santamafia.Space-variant filtering through the Wigner distribution function[JI.Appl.Opt.1989;28:730-736.
[89]许乔.高功率固体激光系统光学元件评价方法[R].2000.1绵阳:863-416-5专题会议.
[90]J.W.Goodman.Speckle Phenomena in Optics[M].(Roberts & Company),2006.
[91]L L Deck.Apparatus and method for reducing the effects of coherent artifact in an interferometer[P].United States Patent:6643024,2003.
[92]Michael.Apparatus and method for reducing the effects of coherent artifact in an interferometer[P].United States Patent:6804011,2004.
[93]徐建程,许乔,柴立群,基于旋滤波法的干涉条纹预处理技术[J].强激光与粒子束,2006;18(1):69-72.
[94]L.L Deck.Interferometric methods and systems using low coherence illumination[P].United States patent:6028670,2000.
[95]Freischlad,Extended source low coherence intefferometer for flatness[P].United States Patent:5737081,1998.
[96]Wai-Hon Lee.Computer-Generated Holograms:Techniques and Applications[J].Progress in Optics ⅩⅥ.E.Wolf,editor,North-Holland,1978.
[97]李继陶.统计光学基础[M].成都:四川大学出版社,1988年.
[98]徐建程,许乔,柴立群.基于互信息的干涉成像采样系统性能分析[J].光子学报,2008;37(8):1608-161.
[99]徐建程,邓燕,柴立群,等.CCD对高空间分辨率波前干涉检测的影响[J].光子学报,2006;35(5):793-796.
[100]R.H.Vollmerhausen,R.G.Driggers.Analysis of sampled imaging systems[M].SPIE PRESS,Bellingham,Washington USA,1999:46-138,
[101]吕晓旭,钟丽云,张以谟.相移相位测量的全息再现算法及测量误差分析[J].光学学报,2006;26:1367-1371.
[102]K.Creath.Phase-measurement interferometry techniques,in Progress in Optics 26,E.Wolf,Editor (Elsevier,New York) 1988:349-393.
[103]K.Creath.Temporal phase measurement methods,in Intefferogram Analysis,D.Robinson and G.Reid,eds.London:IOP Publishing,1993:95-140.
[104]D.Malacara,M.Servin,and Z.Malacara.Interferogram Analysis for Optical Testing[M],Marcel Dekker Inc.,New York(1998).
[105]Yves Surrel.Design of algorithms for phase measurements by the use of phase stepping[J].Appl.Opt. 1996;35(1):51-60.
[106]M.Takeda,H.Ina and S.Kobayashi.Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry[J].J.Opt.Soc.Am.1982;72:156-160.
[107]M.Pirga and M.Kujawinska.Two directional spatial-cartier phase-shifting method for analysis of crossed and closed fringe patterns[J].Opt.Eng.1995;34:2459-2466.
[108]Steven M.Kay.统计信号处理基础——估计与检测理论[M].北京:电子工业出版社,2006.
[109]R.Langoju,A.Patil,and P.Rastogi.Resolution enhanced Fourier transform method for the estimation of multiple phases in interferometry[J].Opt.Lett.,2005;30:3326-3328.
[110]R.Langoju,A.Patil and P.Rastogi.Phase-shifting interferometry in the presence of nonlinear phase steps,harmonics,and noise[J].Opt.Lett.2006;31:1058-1060.
[111]Jiancheng Xu,Qiao Xu,Liqun Chai and Hansheng Peng.Algorithm for multiple-beam Fizeau interferograms with arbitrary phase shifts[J].Optics Express,2008;16(23):18922-18932.
[112]Jiancheng Xu,Qiao xu,and Liqun Chai.Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts[J].Appl.opt.,2008;47:480-485.
[113]Jiancheng Xu,Qiao Xu,and Liqun Chai.An iterative algorithm for interferograms with random phase shifts and high-order harmonics[J].J.Opt.A:Pure Appl.Opt.2008;10(9):95004-95008.
[114]Y.Surrel,Additive noise effect in digital phase detection[J],Appl.opt.1997;36:271-276.
[115]K.Okada,A.Sato,J.Tsujiuchi.Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry[J].opt.Commun.1991;84:118-124.
[116]Z.Wang,B.Han.Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms[J].Opt.Lett.2004;29:1671-1673.
[117]M.Chen,H.Guo,and C.Wei.Algorithm immune to tilt phase-shifting error for phase-shifting interferometers[J].Appl.Opt.2000;39:3894-3898.
[118]Jiancheng Xu,Qiao Xu,and Liqun Chai.Tilt-shift determination and compensation in phase-shifting interferometry[J].J.Opt.A:Pure Appl.Opt.2008;10(7):75011-75016.
[119]K.A.Goldberg and J.Bokor.Fourier-transform method of phase-shift determination[J].Appl.Opt.2001;40:2886-2894.
[120]P.Hariharan.Phase-shifting interferometry:minimization of systematic errors[J].Opt.Eng.2000;39:967-969.
[121]B.V.Dorrio,J.Bianco-Garcia,C.Lopez,A.F.Doval,R.Soto,J.L.Femandez,and M.Perez-Amor.Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile[J].Appl.Opt.1996;35:61-64.
[122]罗志勇,陈朝晖,顾英姿,等.基于数值模拟的高准确度五步相移算法研究[J].光学学报,2006;26(11):1687-1690.
[123]G.Bonsch,H.Bohme.Phase-determination of Fizeau interferences by phase-shifting interferometry[J].Optik,1989;82(4):161-164.
[124]高志山,陈进榜,何勇,等.波面功率谱密度中频波段的干涉测试研究[J].中国激光,2000;27(4):327-331.
[125]Chiayu Ai.Multimode laser Fizeau interferometer for measuring the surface of a thin transparent plate[J], Appl Opt.1997;36(31):8135-8138.
[126]徐建程,石崎凯,柴立群等.三表面干涉条纹空域傅立叶分析[J].中国激光,2006;33(9):1260-1264
[127]Peter de Groot.Measurement of transparent plates with wavelength-tuned phase-shifting interferometry [J].Appl.Opt.2000;39(16):2658-2663.
[128]K.Okada,H.Sakuta,T.Ose,et al.Separate measurements of surface shapes and refractive index inhomogineity of an optical element using tunable-source phase shifting interferometry[J].Appl.Opt.1990;29(22):3280-3285.
[129]徐建程,石琦凯,柴立群,邓燕,许乔.基于最小二乘迭代的多表面干涉条纹分析[J].光学学报,2008;28(7):1307-1312.
[130]M.Takeda.Spatial-carrier fringe-pattern analysis and its applications to precision interfemmetry and profilometry:an overview[J].Indus.Metrol.1990;1:79-99.
[131]J.Schwider.Advanced evaluation techniques in interferometry,in Progress in Optics ⅩⅩⅧ,E.Wolff,ed.Elsevier,Amsterdam,1990,pp.271-359.
[132]T.Bothe,J.Burke,and H.Helmers.Spatial phase shifting in electronic speckle pattern interferometry:minimization of phase-reconstruction errors[J].Appl.Opt.1997;36:5310-5316.
[133]钱克矛,缪泓,伍小平.一种用于动态过程测量的实时偏振相移方法[J].光学学报,2001;21(1):64-67.
[134]左芬,陈磊,徐春生,基于二维光栅分光的同步移相干涉测量技术[J].光学学报,2007;27(4):663-667.
[135]Matt Novak,James Millerd,Neal Brock et al.Analysis of a micropolarizer army-based simultaneous phase-shifting Interferometer[J].Appl.Opt.,2005;44(32):6861-6868.
[136]P.H.Chan and P.J.Bryanston-Cross.Spatial phase stepping method of fringe-pattern analysis[J].Opt.Lasers Eng.1995;23:343-354.
[137]M.Servin and F.J.Cuevas.A novel technique for spatial phase-shifting interferometry[J].J.Mod.Opt.1995;42:1853-1862.
[138]Jiancheng Xu,Qiao Xu and Hansheng Peng.Spatial carrier phase-shifting algorithm based on least-squares iteration[J].Appl.Opt.,2008;47(29):5446-5453.
[139]H.Guo,Q.Yang,and M.Chen.Local frequency estimation for the fringe pattern with a spatial carrier:principle and applications[J].Appl.Opt.2007;46:1057-1065.
[140]M.Pirga and M.Kujawinska.Errors in two-dimensional spatial-carrier phase shifting method for closed fringe pattern analysis[J].SPIE,1996;2860:72-83.
[141]E.L.Church.Fractal surface finish[J].Appl.Opt.1988;27(8):1518-1526.
[142]L.L.Deck,J.A.Soobitsky.Phase-shifting via wavelength tuning in very large aperture interferometers [J].SPIE,1999;3782:432-441.
[143]Peter de Groot.Measurement of transparent plates with wavelength-tuned phase-shifting interferometry [J].Appl.Opt.,2000;39(16):2658-2663.
[144]徐晨,陈磊.光学平面绝对检验方法的研究[J].光学技术,2006;32:775-778.
[145]B.S.Fritz.Absolute calibration of an optical flat[J].Optical Engineering,1984;23(4):379-383.
[146]C.Ai,J.C.Wyant,et al.Method and apparatus for absolute measurement of entire surfaces of flats[P].U.S Patent:5502566,1996.
[147]张蓉竹,杨春林,石琦凯等.子孔径拼接干涉检测及其精度分析[J].光学学报,2003;23:1241-1244.
[148]王朝暄.大口径光学平面干涉检测的子孔径拼接研究[D].硕士论文,南京:南京理工大学,2007.
[149]许乔,顾元元,柴林,等.大口径干涉仪系统传递函数校准[J].强激光与粒子束,2001;13(3):321-324.
[150]徐建程,许乔,邓燕,柴立群.环形光源在干涉仪系统中的应用[J].强激光与粒子光束,2008;20(3):367-370.
[2]W.J.Hogan,J.A.Paisner,Progress in the Title I Design of the National Ignition Facility[R].UCRL-JC-123560,1996.
[3]J.A.Paisner,J.R.Murray,The National Ignition Facility for Inertial Confinement Fusion[R].UCRL-JC-1ZS6S9,1997.
[4]T.S.Perry,B.H.Wilde.NIF System-Design Requirements for Nuclear-Weapons Physics Experiments[R].UCRL-ID-120738,1995.
[5]Michael Bray,Using First Principles in the Specifying of Optics for Large High-Power Lasers(Ⅰ):Application to the MegaJoule Laser(LMJ)[J].SPIE,1996;2775:328-344.
[6]许乔,高功率固体激光系统光学元件质量评价[D].博士后研究工作报告,绵阳:中国工程物理研究院,1999.
[7]彭翰生,张小民,范滇元,朱健强.高功率固体激光装置的发展与工程科学问题[J].中国工程科学,2001;3(3):1-8.
[8]刘红捷,高功率激光束中高频波前畸变特性的研究[D].硕士学位论文,绵阳:中国工程物理研究院,2005
[9]J.K.Lawson,C.R.Wolfe,K.R.Manes,et al.Specification of optical components using the power spectral density function[J].SPIE,1995;2536:38-50.
[10]J.H.Campbell,R.Hawley-Fedder,C.J.Stolz,et al.NIF Optical Materials and Fabrication Technologies:An Overview[J].SPIE,2004;5341:84-101.
[11]Kenneth Goldberg.Testing EUV optics with EUV light:If you can measure it,you can make it[A],SPIE.Newsroom:Optical Design & Engineering[C],2006.
[12]P.Hariharan.Optical Interferometry[M].New York:Academic Press,2003.
[13]张蓉竹,ICF系统光学元件高精度波前检测技术研究[D],博士学位论文,成都:四川大学,2003.
[14]Joe Lamb,James Semrad,James Wyant,Chiayu Ai.Optical and mechanical design considerations in the construction of a 24 inch phase shitting interferometer[J].SPIE,1997;3047:415-426.
[15]C.Ai,R.Knowiden,R.Lamb.Design of 24" Phase-Shifting Fizeau interferometer[J].SPIE,1997;3134:447-455.
[16]Michael Bray,Audrey Liard,Genevieve Chabassier.Laser MegaJoule optics(Ⅰ):New methods of optical specification[J].SPIE,1999;3739:449-460.
[17]Audrey Liard,Michael Bray,Genevieve Chabassier.Laser MegaJoule optics(Ⅱ):Wavefront analysis in the testing of large components[J].SP1E,1999;3739:461-472.
[18]Michael Bray.Localised Wavefrom Deformations:propagation in non-linear media(Ⅱ)(a simple but accurate computational method)[J].SPIE,1998;3492:946--956.
[19]Liqun Chai,Qiao Xu,Yingjie Yu,Yah Deng,Jiancheng Xu.500-mm-aperture wavelength-tuning phase-shifting interferometer[J].SPIE.2005;5856:589-596.
[20]Xu Jiancheng,Sheng Guiping,Chai Liqun,Xu Qiao,Deng Yan.Design of coherent optical interferometric system[A].SPIE,2006;6150:61501B-1.
[21]徐建程,高分辨率波前干涉检测技术研究[D].硕士学位论文,绵阳:中国工程物理研究院,2006.
[22]吴新民,光干涉测试中的抗振技术研究[D].博士学位论文,南京:南京理工大学,2002.
[23]左芬,陈磊.同步移相抗振光干涉测量技术研究进展[J].激光与光电子学进展,2006;43(11):43-48.
[24]J.E.Millerd,N.J.Brock,J.B.Hayes,M.B.North-Morris,M.Novak,J.C.Wyant.Pixelated phase-mask dynamic interferometer[J].SPIE,2004;5531:304-314.
[25]Klaus Freischlad,Ron Eng,James B.Hadaway.Interferometer for testing in vibration environments [J].SPIE,2002;4777:311-322.
[26]C.Roddier,F.Roddier,Interferogram analysis using Fourier transform techniques[J].Appl.Opt.1987;26:1668-1673.
[27]M.A.Gdeisatk,D.R.Burton,and M.J.Lalor.Spatial carrier fringe pattern demodulation by use of a two-dimensional continuous wavelet transform[J].Appl.Opt.,2006;45(34):8722-8732.
[28]Bradley T.Kimbrough,Pixelated mask spatial carrier phase shifting interferometry algorithms and associated errors[J].Appl.Opt.2006;45:4554-4562.
[29]C.J.Morgan.Least-squares estimation in phase-measurement interferometry[J].Opt.Lett.1982;7:368-1370.
[30]白剑,程上彝,杨国光.大口径镜面的多孔径拼接技术[J].光学学报,1997;17(7):953-956
[31]M.Bray.Stitching interferometry:Side effects and PSD[J].SPIE,1999;3782:443-452.
[32]Mingyi Chen,Hongwei Guo,Yingjie Yu,et al.Recent developments of multi-aperture overlap-scanning technique[J].SPIE,2004;5180:393-401.
[33]X.Hou,F.Wu,and L.Yang,et.al.Full-aperture wavefront reconstruction from annular subaperture interferometric data by us of Zernike annular ploynomials and a matrix method for testing large aspheric surfaces[J].Appl Opt,2006;45(15):3442-3455.
[34]高志山,光学表面轮廓功率谱密度对象质的影响及干涉测试研究[D].博士学位论文,南京:南京理工大学,2000.
[35]L.L.Deck.Apparatus and method for reducing the effects of coherent artifact in an interferometer [P].United stated patents,2003;US6643024
[36]Bradley Trent Kimbrough.Path matched vibration insensitive Fizeau interferometer[D].PhD Dissertation,Arizona:The University of Arizona,2006.
[37]P.E.Murphy.Interferometric metrology of aspheric surfaces[D].PhD Dissertation,University of Rochester,2000.
[38]Romuald Jiozwicki.Influence of spherical aberration of an interferometric system on the measurement error in the case of a finite fringe observation field[J].Appl.Opt.1991;30:3119-3125.
[39]Romuald Jiozwicki.Influence of aberrations of Fizeau interferometer elements on measurement errors[J].Appl.Opt.1991;30:3126-3132.
[40]C.Huang.Propagation errors in precision Fizeau interferometry[J].Appl.Opt.,1993;32:7016-7021.
[41]A.E.Lowman and J.E.Greivenkamp.Interferometer induced wavefront errors when testing in a non-null configuration[J].SPIE,1994;2004:173-178.
[42]戴亚平,谢虎,李银柱等.功率谱密度传输性质的理论分析与数值模拟[J].中国激光,2001;28(4):337-342.
[43]戴亚平,光学表面评价参数——功率谱密度的传输性质分析[D].博士学位论文,北京:中国科学院,2000.
[44]E.L.Novak.Measurement and analysis optimization of large aperture laser Fizeau interferometer[D],PhD Dissertation,Arizona:The University of Arizona,1998.
[45]Peter Takacs,Michelle X.O.Li,Karen Furenlid.A Step-Height Standard for Surface Profiler Calibration [A],Optical Scattering:Applications,Measurement and Theory Ⅱ,Proc.SPIE[C],1993;1993:65-74.
[46]Erik Novak,Chiayu Ai,James C.Wyant.Transfer function characterization of laser Fizeau interferometer for high spatial frequency phase measurements[J].SPIE,1997;3134:114-121.
[47]J.K.Lawson,D.M.Aikens,R.E.English,et al.Power spectral densily specification for high-power laser systems[J].SPIE,1996;2775:345-356.
[48]J.K.Lawson,C.R.Wolfe,K.R.Manes,el al.Specification ofoplical components using the power spectral density function[J].SPIE,1995;2536:38-50.
[49]S.K.Park,R.A.Schowengerdt,M.A.Kaczynski.Modulation-transfer-ftmction analysis for sampled image systems[J].Applied Optics,1984;23(15):2572-2582.
[50]徐建程,许乔,彭翰生.大口径干涉仪系统传递函数的修正和校准.强激光与粒子光束,2008;20(8):1293-1296.
[51]高晋占,微弱信号检测[M],北京:清华大学出版社,2002.
[52]Morteza Shahram,Peyman Milanfar.Statistical and information-theoretic analysis of resolution in imaging[J].IEEE Transactions on information theory.2006;52(8):3411-3437.
[53]C.E.Shannon.A mathematical theory of communication,Bell System Technical Journal,vol 27:379-423and 623-4556,July and October 1948.
[54]Douglas Alan Hope.An information-theoretic study of image formation,detection and post-processing [D].PDH dissertation,Albuquerque,New Mexico:The University of New Mexico.2004.
[55]陶纯堪,陶纯匡.光学信息论[M].北京:科学出版社,1999.
[56]C.L.Fales,EO.Huck,R.W.Samms.Imaging design for improved information capacity[J],Appl.Opt.,1984:23(6):872-888.
[57]F.O.Huck,C.L.Fales.Image gathering and processing:information and fidelity[J].J.Opt.Soc.Am.1985;2(10):1644-1666.
[58]F.O.Huek,C.L,Fales,J.A.Mcormick,et al.Image gathering system design for information and fidelity [J].J.Opt.Soc.Am,1988;5(3):285-299.
[59]S.Jone,Z.Rahrnan,EO.Huck,et al.Information theoretical assessment of digital image system [J].Optical engineering,1990;1309:53-66.
[60]F.O.Huck,C.L.Fales,R.Alter Gartenberg etal.Infonnation - theoretical assessment of sampled imaging systems[J].optical Engineering,1999;38(5):742-762.
[61]W.C.Chou,M.A.Neifeld.Information-based optical design for binary-valued imagery[J].Appl.Opt.,2000;39(11):1731-1742.
[62]迟学芬.基于信息理论的采样成像系统评价与系统技术研究[D],博士论文,北京:中国科学院研究 生院,2003.
[63]W Lukosz.Optical systems with resolvmg powers exceedmg the classical limit[J].J.Opt.Soc.Am 1966;56:1463-1472.
[64]I.J.Cox,C.J.R.Sheppard.Information capacity and resolution in an optical system[J].J.Opt.Soc.Am 1986;3(8):1152-1158.
[65]A.W Lohmann,R.G Dorsch,D.Mendlovic,Z.Zalevsky,and C.Ferreira.Space-bandwidth product of optical signals and systems[J].J.Opt.Soc.Am.1996;13:470-473.
[66]D.Mendlovic and A.W Lohmann.Space-bandwidth product adaptation and its application for superresolution:fundamentals[J].J.Opt.Soc.Am.1997;14:558-562.
[67]张蓉竹,许乔,顾元元等.大口径光学元件检测中的主要误差及其影响[J].强激光与粒子束,2001;13(2):133-136.
[68]许乔,顾元元等.大口径光学元件波前功率谱密度检测[J].光学学报,2001;21(3):344-347.
[69]J.K.Lawson,D.M.Aikens,R.E.English,et al.Surface figure and roughness tolerances for NIF optics and the interpretation of the gradient,P-V wavefront and RMS specifications[J].SPIE,1999;3782:510-517
[70]C.D.Wolfe,J.K.Lawson.The measurement and analysis of wavefront structure from large aperture ICF optics[A].Proc of the 1stAnnual Solid Laser for Application to ICF[C].1995;2633:361-385
[71]Michael Bray,Andre Roussel.Using First Principles in the specifying of optics for large high power lasers(Ⅰ) - Application to the MegaJoule Laser(LMJ),Specification,Production and testing of Optical Components and Systems[J].SPIE,1996;2775:328-344.
[72]罗军辉,MATLAB 7.0在图象处理中的应用[M].北京:机械:工业出版社,2005.
[73]V.I.Bespalov,V.I.Talanov.Filamentary structure of light beams in nonlinear liquids[J].JETP Lett.1966;3(11):307-310.
[74]N.C.Kothafi and S.C.Abbi.Instability Growth and Filamentation of Very Intense Laser Beams in Self-Focusing Media:General and Mathematical Physics[J].Prog.Theor.Phys.1990;83:414-442
[75]文双春,钱列加,范滇元.强光束局部小尺度调制致多路成丝现象研究物理学报[J].2003;52(7):1640-1644.
[76]M.Bray,A.Liard,G.Chabassier,Laser megajoule optics:Ⅰ.New methods of optical specification [J].SPIE 1999;3739:449-460.
[77]M.Bray,G.Chabassier.Localized wavefront deformations—propagation in nonlinear media Ⅱ:A simple but accurate computational method[J].SPIE.1999;3492:480-494.
[78]J.W.Goodman.Introduction to Fourier Optics[M],(McGraw-Hill,New York),1996.
[79]E.Wigner.On the quantum correction for thermodynamic equilibrium[J].Phys.Rev.,1932;40:749-759.
[80]M.J.Bastiaans.The Wigner distribution function applied to optical signals and systems[J].Opt.Comm.,1978;25(1):26-30.
[81]ISO10110.Optics and optical instruments-Preparation of drawings for optical elements and systems-part 8 surface texture.1997:1-9.
[82]R.E.English,D.M.Aikens,W.T.Whister,et al.Implementation of ISO10110 optical drawing standards for the National Ignition Facility[J].SPIE,1995;2536:51-56.
[83]J.R.Taylor,R.Chow,K.A.Primdahl,et al.Specification of optical components for a high average-power laser environment[J].SPIE,1997,3134:11-22.
[84]M.Bom and E.Wolf.Principles of Optics[M](Pergamon,NewYork),1980.
[85]A.J.den Dekker and A.van den Bos.Resolution:a survey[J].J.Opt.Soc.Am.A 1997;14:547-557.
[86]M.J.Bastiaans.Wigner distribution function and its application to first-order optics[J].J.Opt.Soc.Am.1979;69:1710-1716.
[87]Weiqing Pan.Double Wigner distribution function of a first-order optical system with a hard-edge aperture[J].Appl.Opt.2008;47:45-51.
[88]C.Gonzalo,J.Bescos,L.R.Berdel-Valdos,and J.Santamafia.Space-variant filtering through the Wigner distribution function[JI.Appl.Opt.1989;28:730-736.
[89]许乔.高功率固体激光系统光学元件评价方法[R].2000.1绵阳:863-416-5专题会议.
[90]J.W.Goodman.Speckle Phenomena in Optics[M].(Roberts & Company),2006.
[91]L L Deck.Apparatus and method for reducing the effects of coherent artifact in an interferometer[P].United States Patent:6643024,2003.
[92]Michael.Apparatus and method for reducing the effects of coherent artifact in an interferometer[P].United States Patent:6804011,2004.
[93]徐建程,许乔,柴立群,基于旋滤波法的干涉条纹预处理技术[J].强激光与粒子束,2006;18(1):69-72.
[94]L.L Deck.Interferometric methods and systems using low coherence illumination[P].United States patent:6028670,2000.
[95]Freischlad,Extended source low coherence intefferometer for flatness[P].United States Patent:5737081,1998.
[96]Wai-Hon Lee.Computer-Generated Holograms:Techniques and Applications[J].Progress in Optics ⅩⅥ.E.Wolf,editor,North-Holland,1978.
[97]李继陶.统计光学基础[M].成都:四川大学出版社,1988年.
[98]徐建程,许乔,柴立群.基于互信息的干涉成像采样系统性能分析[J].光子学报,2008;37(8):1608-161.
[99]徐建程,邓燕,柴立群,等.CCD对高空间分辨率波前干涉检测的影响[J].光子学报,2006;35(5):793-796.
[100]R.H.Vollmerhausen,R.G.Driggers.Analysis of sampled imaging systems[M].SPIE PRESS,Bellingham,Washington USA,1999:46-138,
[101]吕晓旭,钟丽云,张以谟.相移相位测量的全息再现算法及测量误差分析[J].光学学报,2006;26:1367-1371.
[102]K.Creath.Phase-measurement interferometry techniques,in Progress in Optics 26,E.Wolf,Editor (Elsevier,New York) 1988:349-393.
[103]K.Creath.Temporal phase measurement methods,in Intefferogram Analysis,D.Robinson and G.Reid,eds.London:IOP Publishing,1993:95-140.
[104]D.Malacara,M.Servin,and Z.Malacara.Interferogram Analysis for Optical Testing[M],Marcel Dekker Inc.,New York(1998).
[105]Yves Surrel.Design of algorithms for phase measurements by the use of phase stepping[J].Appl.Opt. 1996;35(1):51-60.
[106]M.Takeda,H.Ina and S.Kobayashi.Fourier-transform method of fringe-pattern analysis for computer-based topography and interferometry[J].J.Opt.Soc.Am.1982;72:156-160.
[107]M.Pirga and M.Kujawinska.Two directional spatial-cartier phase-shifting method for analysis of crossed and closed fringe patterns[J].Opt.Eng.1995;34:2459-2466.
[108]Steven M.Kay.统计信号处理基础——估计与检测理论[M].北京:电子工业出版社,2006.
[109]R.Langoju,A.Patil,and P.Rastogi.Resolution enhanced Fourier transform method for the estimation of multiple phases in interferometry[J].Opt.Lett.,2005;30:3326-3328.
[110]R.Langoju,A.Patil and P.Rastogi.Phase-shifting interferometry in the presence of nonlinear phase steps,harmonics,and noise[J].Opt.Lett.2006;31:1058-1060.
[111]Jiancheng Xu,Qiao Xu,Liqun Chai and Hansheng Peng.Algorithm for multiple-beam Fizeau interferograms with arbitrary phase shifts[J].Optics Express,2008;16(23):18922-18932.
[112]Jiancheng Xu,Qiao xu,and Liqun Chai.Iterative algorithm for phase extraction from interferograms with random and spatially nonuniform phase shifts[J].Appl.opt.,2008;47:480-485.
[113]Jiancheng Xu,Qiao Xu,and Liqun Chai.An iterative algorithm for interferograms with random phase shifts and high-order harmonics[J].J.Opt.A:Pure Appl.Opt.2008;10(9):95004-95008.
[114]Y.Surrel,Additive noise effect in digital phase detection[J],Appl.opt.1997;36:271-276.
[115]K.Okada,A.Sato,J.Tsujiuchi.Simultaneous calculation of phase distribution and scanning phase shift in phase shifting interferometry[J].opt.Commun.1991;84:118-124.
[116]Z.Wang,B.Han.Advanced iterative algorithm for phase extraction of randomly phase-shifted interferograms[J].Opt.Lett.2004;29:1671-1673.
[117]M.Chen,H.Guo,and C.Wei.Algorithm immune to tilt phase-shifting error for phase-shifting interferometers[J].Appl.Opt.2000;39:3894-3898.
[118]Jiancheng Xu,Qiao Xu,and Liqun Chai.Tilt-shift determination and compensation in phase-shifting interferometry[J].J.Opt.A:Pure Appl.Opt.2008;10(7):75011-75016.
[119]K.A.Goldberg and J.Bokor.Fourier-transform method of phase-shift determination[J].Appl.Opt.2001;40:2886-2894.
[120]P.Hariharan.Phase-shifting interferometry:minimization of systematic errors[J].Opt.Eng.2000;39:967-969.
[121]B.V.Dorrio,J.Bianco-Garcia,C.Lopez,A.F.Doval,R.Soto,J.L.Femandez,and M.Perez-Amor.Phase error calculation in a Fizeau interferometer by Fourier expansion of the intensity profile[J].Appl.Opt.1996;35:61-64.
[122]罗志勇,陈朝晖,顾英姿,等.基于数值模拟的高准确度五步相移算法研究[J].光学学报,2006;26(11):1687-1690.
[123]G.Bonsch,H.Bohme.Phase-determination of Fizeau interferences by phase-shifting interferometry[J].Optik,1989;82(4):161-164.
[124]高志山,陈进榜,何勇,等.波面功率谱密度中频波段的干涉测试研究[J].中国激光,2000;27(4):327-331.
[125]Chiayu Ai.Multimode laser Fizeau interferometer for measuring the surface of a thin transparent plate[J], Appl Opt.1997;36(31):8135-8138.
[126]徐建程,石崎凯,柴立群等.三表面干涉条纹空域傅立叶分析[J].中国激光,2006;33(9):1260-1264
[127]Peter de Groot.Measurement of transparent plates with wavelength-tuned phase-shifting interferometry [J].Appl.Opt.2000;39(16):2658-2663.
[128]K.Okada,H.Sakuta,T.Ose,et al.Separate measurements of surface shapes and refractive index inhomogineity of an optical element using tunable-source phase shifting interferometry[J].Appl.Opt.1990;29(22):3280-3285.
[129]徐建程,石琦凯,柴立群,邓燕,许乔.基于最小二乘迭代的多表面干涉条纹分析[J].光学学报,2008;28(7):1307-1312.
[130]M.Takeda.Spatial-carrier fringe-pattern analysis and its applications to precision interfemmetry and profilometry:an overview[J].Indus.Metrol.1990;1:79-99.
[131]J.Schwider.Advanced evaluation techniques in interferometry,in Progress in Optics ⅩⅩⅧ,E.Wolff,ed.Elsevier,Amsterdam,1990,pp.271-359.
[132]T.Bothe,J.Burke,and H.Helmers.Spatial phase shifting in electronic speckle pattern interferometry:minimization of phase-reconstruction errors[J].Appl.Opt.1997;36:5310-5316.
[133]钱克矛,缪泓,伍小平.一种用于动态过程测量的实时偏振相移方法[J].光学学报,2001;21(1):64-67.
[134]左芬,陈磊,徐春生,基于二维光栅分光的同步移相干涉测量技术[J].光学学报,2007;27(4):663-667.
[135]Matt Novak,James Millerd,Neal Brock et al.Analysis of a micropolarizer army-based simultaneous phase-shifting Interferometer[J].Appl.Opt.,2005;44(32):6861-6868.
[136]P.H.Chan and P.J.Bryanston-Cross.Spatial phase stepping method of fringe-pattern analysis[J].Opt.Lasers Eng.1995;23:343-354.
[137]M.Servin and F.J.Cuevas.A novel technique for spatial phase-shifting interferometry[J].J.Mod.Opt.1995;42:1853-1862.
[138]Jiancheng Xu,Qiao Xu and Hansheng Peng.Spatial carrier phase-shifting algorithm based on least-squares iteration[J].Appl.Opt.,2008;47(29):5446-5453.
[139]H.Guo,Q.Yang,and M.Chen.Local frequency estimation for the fringe pattern with a spatial carrier:principle and applications[J].Appl.Opt.2007;46:1057-1065.
[140]M.Pirga and M.Kujawinska.Errors in two-dimensional spatial-carrier phase shifting method for closed fringe pattern analysis[J].SPIE,1996;2860:72-83.
[141]E.L.Church.Fractal surface finish[J].Appl.Opt.1988;27(8):1518-1526.
[142]L.L.Deck,J.A.Soobitsky.Phase-shifting via wavelength tuning in very large aperture interferometers [J].SPIE,1999;3782:432-441.
[143]Peter de Groot.Measurement of transparent plates with wavelength-tuned phase-shifting interferometry [J].Appl.Opt.,2000;39(16):2658-2663.
[144]徐晨,陈磊.光学平面绝对检验方法的研究[J].光学技术,2006;32:775-778.
[145]B.S.Fritz.Absolute calibration of an optical flat[J].Optical Engineering,1984;23(4):379-383.
[146]C.Ai,J.C.Wyant,et al.Method and apparatus for absolute measurement of entire surfaces of flats[P].U.S Patent:5502566,1996.
[147]张蓉竹,杨春林,石琦凯等.子孔径拼接干涉检测及其精度分析[J].光学学报,2003;23:1241-1244.
[148]王朝暄.大口径光学平面干涉检测的子孔径拼接研究[D].硕士论文,南京:南京理工大学,2007.
[149]许乔,顾元元,柴林,等.大口径干涉仪系统传递函数校准[J].强激光与粒子束,2001;13(3):321-324.
[150]徐建程,许乔,邓燕,柴立群.环形光源在干涉仪系统中的应用[J].强激光与粒子光束,2008;20(3):367-370.