偏轴光学系统矢量像差理论研究
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摘要
偏轴光学系统通过元件偏心倾斜消除传统共轴系统的中心遮拦，是近年来用于研究设计无遮拦反射式光学系统从而扩大视场的一种结构形式，而矢量像差理论是分析偏轴光学系统最重要和适合的理论方法。本论文针对矢量像差理论展开研究，主要内容为矢量像差理论和偏轴系统的像差特性研究、矢量像差计算及其指导偏轴光学系统的设计。
基于传统共轴光学系统的像差理论，矢量像差理论的像差表达式由标量形式写成矢量形式；偏轴光学系统像差场的表征上出现节点及像差贡献中心偏移的现象；概念上引入光轴光线替代共轴系统的旋转对称轴来描述偏轴系统的基本参量。对偏轴光学系统的一阶特性进行了分析，详细推导了球面和非球面光学元件的像差贡献中心。基于一阶特性给出偏轴系统像差的波差表达式和赛德尔表达式。从球面基准部分和非球面偏离部分两方面的像差贡献详细阐述了偏轴光学系统的五个三阶单色像差特性，特别的是用射影变换的方法分析了梯形畸变。
给出三级矢量像差理论的赛德尔表达式，这使得矢量像差理论进一步可以用来进行偏轴系统的像差计算。我们用矢量像差的方法计算了偏心倾斜两镜系统的三阶自由彗差点，结果与R.N.Wilson使用Schiefspiegler方法所求得结果一致，从而验证我们计算的准确性。通过这种方式首次实现使用矢量波像差理论做完整且准确的像差计算，并验证了计算的准确性。这是本论文核心的创新工作。矢量像差理论分析偏轴系统的像差特性，从而可用于指导偏轴光学系统设计和优化，但目前还并不完善。论文最后我们给出一个两片镜子的偏轴系统设计和一个大视场全反射的偏轴四镜系统设计举例，总结了偏轴光学系统设计难点，提出一些像差校正原则。
Off-axis optical system, namely optical system with tilted component, is onestructural style for designing wide-field reflecting optical system. Vector aberrationtheory is the significant and adaptive method to analyze off-axis optical system. Theprimary coverage in this dissertation is research of vector aberration theory,calculation of vector aberration theory and optical design of off-axis optical systemunder guidance of vector aberration theory. As a direct extension of rotationallysymmetrical wave aberration theory, expression of vector aberration theory can bewritten in a vector approach; aberration field of off-axis optical system appears thecharacteristic of aberration nodal and aberration displacement； Replacement ofrotationally symmetrical axis in centred system, Optical Axis Ray is to describeoff-axis optical system. The first-order properties of decentered and tilted opticalsystems are analyzed in detail, the relation formula between aberration contributioncenter and decenter and tilt of each optical component is derived. Based on first-orderproperties of off-axis optical system, vector aberration theory is given by the ways ofwavefront aberration and Seidel aberration. Two independent sets of aberrations areintroduced by each surface: one induced by the base sphere and the other induced bythe aspheric departure of the surface. These two sets of aberration terms can becombined vectorially to yield the final aberration contribution for the surface. The fivethird-order aberrations in decentered and tilted optical systems are described in detail. The distortion is analyzed based on a collinear transformation between the object andimage spaces.
Seidel aberration for third-order vector aberration theory is given. Thus vectoraberration theory can be used to calculate the aberration of off-axis optical system.Equations for third-order coma are derived by a vector approach. Coma-freecondition to remove misalignment induced coma was obtained. The coma-free pointin two-mirror telescopes is found as a conclusion of our coma-free condition, whichis in highly agreement with the result solved by R. N. Wilson using Schiefspieglertheory. By this way the aberration calculation of off-axis optical system isimplemented using vector aberration theory. This is the key originality innovation inthe dissertation.
It is pointed out that vector aberration theory is very effective in the aberrationanalyses of off-axis optical system; vector aberration theory can be used to calculateaberration of off-axis optical system; vector aberration theory can give useful designinsights for off-axis optical system. Based on the vector aberration theory conceivedby Shack, we design an tilted-component four-mirror optical system by cancel out its3rd-order coma and balance the astigmatism. Some problems in the design oftilted-component optical system are generalized, and some solutions are supplied forreference.
基于传统共轴光学系统的像差理论，矢量像差理论的像差表达式由标量形式写成矢量形式；偏轴光学系统像差场的表征上出现节点及像差贡献中心偏移的现象；概念上引入光轴光线替代共轴系统的旋转对称轴来描述偏轴系统的基本参量。对偏轴光学系统的一阶特性进行了分析，详细推导了球面和非球面光学元件的像差贡献中心。基于一阶特性给出偏轴系统像差的波差表达式和赛德尔表达式。从球面基准部分和非球面偏离部分两方面的像差贡献详细阐述了偏轴光学系统的五个三阶单色像差特性，特别的是用射影变换的方法分析了梯形畸变。
给出三级矢量像差理论的赛德尔表达式，这使得矢量像差理论进一步可以用来进行偏轴系统的像差计算。我们用矢量像差的方法计算了偏心倾斜两镜系统的三阶自由彗差点，结果与R.N.Wilson使用Schiefspiegler方法所求得结果一致，从而验证我们计算的准确性。通过这种方式首次实现使用矢量波像差理论做完整且准确的像差计算，并验证了计算的准确性。这是本论文核心的创新工作。矢量像差理论分析偏轴系统的像差特性，从而可用于指导偏轴光学系统设计和优化，但目前还并不完善。论文最后我们给出一个两片镜子的偏轴系统设计和一个大视场全反射的偏轴四镜系统设计举例，总结了偏轴光学系统设计难点，提出一些像差校正原则。
Off-axis optical system, namely optical system with tilted component, is onestructural style for designing wide-field reflecting optical system. Vector aberrationtheory is the significant and adaptive method to analyze off-axis optical system. Theprimary coverage in this dissertation is research of vector aberration theory,calculation of vector aberration theory and optical design of off-axis optical systemunder guidance of vector aberration theory. As a direct extension of rotationallysymmetrical wave aberration theory, expression of vector aberration theory can bewritten in a vector approach; aberration field of off-axis optical system appears thecharacteristic of aberration nodal and aberration displacement； Replacement ofrotationally symmetrical axis in centred system, Optical Axis Ray is to describeoff-axis optical system. The first-order properties of decentered and tilted opticalsystems are analyzed in detail, the relation formula between aberration contributioncenter and decenter and tilt of each optical component is derived. Based on first-orderproperties of off-axis optical system, vector aberration theory is given by the ways ofwavefront aberration and Seidel aberration. Two independent sets of aberrations areintroduced by each surface: one induced by the base sphere and the other induced bythe aspheric departure of the surface. These two sets of aberration terms can becombined vectorially to yield the final aberration contribution for the surface. The fivethird-order aberrations in decentered and tilted optical systems are described in detail. The distortion is analyzed based on a collinear transformation between the object andimage spaces.
Seidel aberration for third-order vector aberration theory is given. Thus vectoraberration theory can be used to calculate the aberration of off-axis optical system.Equations for third-order coma are derived by a vector approach. Coma-freecondition to remove misalignment induced coma was obtained. The coma-free pointin two-mirror telescopes is found as a conclusion of our coma-free condition, whichis in highly agreement with the result solved by R. N. Wilson using Schiefspieglertheory. By this way the aberration calculation of off-axis optical system isimplemented using vector aberration theory. This is the key originality innovation inthe dissertation.
It is pointed out that vector aberration theory is very effective in the aberrationanalyses of off-axis optical system; vector aberration theory can be used to calculateaberration of off-axis optical system; vector aberration theory can give useful designinsights for off-axis optical system. Based on the vector aberration theory conceivedby Shack, we design an tilted-component four-mirror optical system by cancel out its3rd-order coma and balance the astigmatism. Some problems in the design oftilted-component optical system are generalized, and some solutions are supplied forreference.
引文
[1]韩昌元．近代高分辨地球成像商业卫星[J]．中国光学与应用光学，2010，3(3)：201-208
[2]薛鸣球，沈为民．轻小型高分辨率TDI CCD相机的光学设计[M]．北京：科学出版社，2005
[3]禹秉熙，郑玉权，胡辛，等．光学遥感成像[M]．北京：科学出版社，2001
[4]史光辉．卫星对地观测高分辨率光学系统和设计问题[J]．光学精密工程，1999，1(7)：16-24
[5]张科科，阮宁娟，傅丹鹰．国外空间用三反离轴相机发展分析与思考[J]．航天返回与遥感，2008，29(3)：63-70
[6]杨秉新．美国IKONOS和QuickBird2卫星相机的主要性能和特点分析及看法[J]．航天返回与遥感，2002，23(4)：10-12
[7]常军，翁志成，姜会林，等．长焦距空间三反光学系统的设计[J]．光学精密工程，2001，9(4)：315-318
[8]常军，翁志成，姜会林，等．用于空间的三反射镜光学系统设计[J]．光学学报，2003，23(2)：712-716
[9]韩昌元．高分辨力空间相机光学系统研究[J]．光学精密工程，2008，16(11)：2164-2172
[10]潘君骅，李新南．偏轴两镜系统的设计光学系统[J]．光学学报，1994，14(8)：867-871
[11]Junhua Pan, Xinnan Li. Design of a Tilted Two-Mirror System [J]. OPTICALREVIEW,1994,2(1):246-247
[12]A.E. Conrady. Decentered lens systems. Mon. Not. R. Astron,1919,79:384-390
[13]H.A. Buchdahl. Optical Aberration Coefficients [M]. Oxford University Press，London，1954
[14]B. D. Stone and G. W. Forbes. Characterization of first-order optical properties forasymmetric systems [J]. J.Opt.Soc.Am.A,1992,9(3):478—489
[15]B. D. Stone and G. W. Forbes. Foundations of first-order layout for asymmetricsystems: an application of Hamilton's methods [J]. J.Opt.Soc.Am.A,1992,9(1):96–109
[16]. D. Stone and G. W. Forbes. First-order layout of asymmetric systems composedof three spherical mirrors [J]. J.Opt.Soc.Am.A,1992,9(1):110-120
[17]B. D. Stone and G. W. Forbes. Forms of the characteristic function for asymmetricsystems that form sharp images to the first order [J]. J.Opt.Soc.Am.A,1992,9(5):820—831
[18]B. D. Stone and G. W. Forbes. First-order layout of asymmetric systems: sharpimagery of a single plane object [J]. J.Opt.Soc.Am.A,1992,9(5):832—843
[19]H. J. Steffens. The development of Newtonian optics in England [M]. London:Science History Publications,1977
[20]R. A. Smith. A compleat system of optics [M]. London: Cambridge press,1978
[21]H. H. Hopkins. The wave theory of aberrations [M].Oxford: Oxford on Clarendonpress,1950
[22]H. A. Buchdahl. An introduction to Hamiltonian optics [M].London: CambridgeUniversity press,1970
[23]W. T. Welford. Aberrations of optical systems [M].Bristol: Adam Hilger,1986
[24]M. Born, E.Wolf. Principle of Optics [M].London: Cambridge UniversityPress.7thEdition,2005
[25]R.A. Buchroeder. Tilted component optical systems [D]:[博士学位论文].Tucson: University of Arizona,1976
[26]R.A. Buchroeder. Tilted-component telescopes Part1: Theory [J].Applied Optics,1970,9(9):2169-2171
[27]H. A. Buchdahl. Systems without symmetries: foundations of a theory ofLagrangian aberration coefficients [J]. J.Opt.Soc.Am.A,1972,62(11):1314-1324
[28]R. V. Shack, K. P. Thompson. Influence of alignment errors of a telescope systemon its aberration field. Proceedings of SPIE,1980,251:146-153
[29]K. P. Thompson. Aberration fields in tilted and decentered optical systems [D]:
[博士学位论文]. Tucson: University of Arizona,1980
[30]K. P. Thompson. A graphic approach to the analysis of perturbed optical systems[C]. Proceedings of SPIE,1980.237:127-134
[31]K. P. Thompson. Description of the third-order optical aberrations of near-circularpupil optical systems without symmetry [J]. J.Opt.Soc.Am.A,2005,22(7):389-1401
[32]K. P. Thompson. Multinodal fifth-order optical aberrations of optical systemswithout rotational symmetry: spherical aberration [J]. J.Opt.Soc.Am.A,2009,26(5):1090-1100
[33]K. P. Thompson. Multinodal fifth-order optical aberrations of optical systemswithout rotational symmetry: the comatic aberrations [J]. J.Opt.Soc.Am.A,2010，27(6):1490–1504
[34]K. P. Thompson. Multinodal fifth-order optical aberrations of optical systemswithout rotational symmetry: the astigmatic aberrations [J]. J.Opt.Soc.Am.A,2011,28(5):821-836
[35]J. R. Rogers. Aberrations of unobsured reflective optical systems [D]:[博士学位论文]. Tucson: University ofArizona,1983
[36]J. R. Rogers. Vector aberration theory and the design of off-axis systems [C].Proceedings of SPIE,1985,554:76-81
[37]J. R. Rogers. Practical tilted mirror systems [C]. Proceedings of SPIE,1986,679:12-16
[38]J. R. Rogers. Design techniques for systems containing tilted components[C].Proceedings of SPIE,1999,3737:286-300
[39]J. R. Rogers. Techniques and tools for obtaining symmetrical performance fromtilted-component systems [J]. Optical Engineering,2000,39(7):1776-1787
[40]T. E. Jewell, R. V. Shack. Aberration field properties of simple non-axiallysymmetric optical systems [C]. Proc. of SPIE,1985,554：128-138
[41]J. M. Sasian. Imagery of the Bilateral Symmetrical Optical System [D]:[博士学位论文]. Tucson: University ofArizona,1988
[42]L. B. Moore, A. M. Hvisc, J. M.Sasian. Aberration fields of a combination ofplane symmetric systems [J].Optics Express,2008,16(20):15655-15670
[43]J. M.Sasian. Design of a Schwarzschild flat-field, anastigmatic, unobstructed,wide-field telescope [J]. Optical Engineering,1990,20(1):1-5
[44]J. M.Sasian. How to approach the design of a bilateral symmetric optical system[J]. Optical Engineering,1994,33(6):2045-2061
[45]J. M.Sasian. Review of methods for the design of unsymmetrical optcal systems[C]. Proceedings of SPIE,1991,1396:453-466
[46]R. A. Buchroeder, A. S. Leonard. Wide-Field Tilted-Component Telescope: aLeonard Extended Yolo All-Reflecting System [J]. APPLIED OPTICS,1972,11(7)：1649-1651
[47]Michael Brunn．Unobstructed all-reflecting telescopes of the schiefspiegler type
[P]．United States Patent，5142417．1992-08-25
[48]Orestes N. Stavroudis, M. Schiefspiegler: an off-axis reflecting optical system [J].Optical Engineering,1994,33(1),116—124
[49]A. Kutter, Der Schiefspiegler. Biberacher Verlagsdruckerei, Biberach an der Riss(1953)
[50]Kristof Seidl, Jens Knobbe, and Heinrich Grüger. Design of an all-reflectiveunobscured optical-power zoom objective [J]. APPLIED OPTICS,2009,48(21):4097-4107
[51]Gilberto Moretto and Jeff R. Kuhn. Off-axis systems for4-m class telescopes [J].APPLIED OPTICS,1998,37(16):3539-3546
[52]Thierry VIARD, Pierre BODIN, A. MAGNAN, A. BAGLIN. COROTTELESCOPE (COROTEL)[C]. Proc. of SPIE,2007,6693：66930B-1-66930B-12
[53]Ozan Cakmakci, Brendan Moore, Hassan Foroosh, Jannick P.Rolland. Optimallocal shape description for rotationally non-symmetric optical surface design andanalysis [J].Optics Express,2008,16(3):1583-1589
[54]J. M. Rodgers and K. P. Thompson. Benefits of Freeform Mirror Surfaces inOptical Design [J]. Proceedings of the American Society of Precision Engineering,2004, Winter Topical Meeting on Freeform Optics,31,73-78
[55]Kenneth Garrard, Thomas Bruegge, Jeff Hoffman, Thomas Dowa, Alex Sohn.Design tools for freeform optics [C]. Proc. of SPIE,2004,5874-10
[56]Kyle Fuerschbach, Jannick P. Rolland, and Kevin P. Thompson. A new family ofoptical systems employing φ-polynomial surfaces [J].Optics Express,2011,19(22):21919-21928
[57]王之江．光学设计理论基础[M]．北京：科学出版社，1985
[58]杨新军，王肇圻，母国光等．偏心和倾斜光学系统的像差特性[J]．光子学报，2005，34(11)：1658-1662
[59]车驰骋，李英才等．基于矢量波像差理论的计算机辅助装调技术研究[J]．光子学报，2008，37(8)：1630-1634
[60]樊学武，陈荣利，马臻等．偏心和倾斜光学系统初级像差理论的研究[J]．光子学报，2004，33(4)：494-496
[61]吕丽军，石亮．平面对称光学系统像差理论的扩展[J]．光学精密工程，2009，17(12)：2975-2982
[62]Li-Jun Lu and Zhi-Yong Deng. Geometric characteristics of aberrations ofplane-symmetric optical systems [J]. APPLIED OPTICS,2009,48(36):6946-6960
[63]张虎．矢量像差理论及其在离轴头盔显示系统设计中的应用[D]．[博士学位论文]．长春：中国科学院长春光学精密机械与物理研究所，2010
[64]王之江，顾培森．实用光学技术手册[M]．北京：机械工业出版社，2007
[65]李林．现代光学设计方法[M]．北京：北京理工大学出版社，2009
[66]萧泽新．工程光学设计[M]．北京：电子工业出版社，2008
[67]李士贤，李林．光学设计手册[M]．北京：北京理工大学出版社，1996
[68]W. R. Hamilton. Report Brit. Assoc.,1833,3,360
[69]C. F. Gauss. Dioptrische Untersuchungen. Gottinger Abh.,1841,1
[70]L. Seidel. Astron. Nachr.,1856,43,289
[71]E. Abbe. Schultzes Arch. f. mikr. Anat.,1873,9,413-468
[72]张以谟．应用光学[M]．北京：电子工业出版社，2008
[73]波恩，沃耳夫．光学原理[M]．北京：电子工业出版社，2005
[74]R. N. Wilson. Reflecting telescope optics I [M]. Berlin: Springer-Verlag press,1996
[75]J. Petzval. Bericht uber optische Untersuchungen, Ber. Kais. Akad. Wien, Math.Naturwiss. Kl.,24(1857),50,92,129
[76]K. Bahner. Teleskope in Handbuch der Physik,1967, Vol. XXIX, Springer Verlag,Heidelberg,227-342
[77]潘君骅．光学非球面的设计加工与检验[M]．苏州：苏州大学出版社．2004
[78]Dietrich Korsch. Reflective optics [M]. San Diego: ACADEMIC PRESS, INC.1991
[79]W. A. Kleinhans. Aberrations of a sequence of conic mirrors [J]. APPLIEDOPTICS,1976,15(9)：2283-2287
[80]H. P. Brueggemann. Conic Mirrors [M]. London: Focal Press,1968
[81]郁道银，谈恒英．工程光学[M]．北京：机械工业出版社，2006
[82]Robert R. Shannon. The art and science of optical design [M]. CambridgeUniversity Press,1997
[83]T. Scheimpflug. Die Herstellung von Karten und Pl nen auf photographischemWege [J]. J. Royal Acad. Sci.,1907, Vienna116,235—266
[84]José Sasián. Theory of sixth-order wave aberrations [J]. APPLIED OPTICS,2010,49(16)：2283-2287
[85]A. Kutter. Der Schiefspiergler,1953, Verlag F. Weichardt, Biberach
[86]A. Kutter. Bauanleitung fur den Kosmosschiefspiegler,1964, Franckh'scheVerlagshandlung, Stuttgart
[87]Brian A. McLeod. Collimation of Fast Wide-Filed Telescopes[J]. Publications ofthe Astronomical Society of the Pacific,1996,108:217-219
[88]Ray N. Wilson. Concerning the Alignment of Modern Telescopes: Theory,Practice, and Tolerances Illustrated by the ESO NTT [J]. Publications of theAstronomical Society of the Pacific,1997,109:53-60
[89]Baichuan Ren, Guang Jin, Xing Zhong. Third-order coma-free point in twomirror telescopes by a vector approach.[J]. APPLIED OPTICS,2011,50(21)：3918-3923
[2]薛鸣球，沈为民．轻小型高分辨率TDI CCD相机的光学设计[M]．北京：科学出版社，2005
[3]禹秉熙，郑玉权，胡辛，等．光学遥感成像[M]．北京：科学出版社，2001
[4]史光辉．卫星对地观测高分辨率光学系统和设计问题[J]．光学精密工程，1999，1(7)：16-24
[5]张科科，阮宁娟，傅丹鹰．国外空间用三反离轴相机发展分析与思考[J]．航天返回与遥感，2008，29(3)：63-70
[6]杨秉新．美国IKONOS和QuickBird2卫星相机的主要性能和特点分析及看法[J]．航天返回与遥感，2002，23(4)：10-12
[7]常军，翁志成，姜会林，等．长焦距空间三反光学系统的设计[J]．光学精密工程，2001，9(4)：315-318
[8]常军，翁志成，姜会林，等．用于空间的三反射镜光学系统设计[J]．光学学报，2003，23(2)：712-716
[9]韩昌元．高分辨力空间相机光学系统研究[J]．光学精密工程，2008，16(11)：2164-2172
[10]潘君骅，李新南．偏轴两镜系统的设计光学系统[J]．光学学报，1994，14(8)：867-871
[11]Junhua Pan, Xinnan Li. Design of a Tilted Two-Mirror System [J]. OPTICALREVIEW,1994,2(1):246-247
[12]A.E. Conrady. Decentered lens systems. Mon. Not. R. Astron,1919,79:384-390
[13]H.A. Buchdahl. Optical Aberration Coefficients [M]. Oxford University Press，London，1954
[14]B. D. Stone and G. W. Forbes. Characterization of first-order optical properties forasymmetric systems [J]. J.Opt.Soc.Am.A,1992,9(3):478—489
[15]B. D. Stone and G. W. Forbes. Foundations of first-order layout for asymmetricsystems: an application of Hamilton's methods [J]. J.Opt.Soc.Am.A,1992,9(1):96–109
[16]. D. Stone and G. W. Forbes. First-order layout of asymmetric systems composedof three spherical mirrors [J]. J.Opt.Soc.Am.A,1992,9(1):110-120
[17]B. D. Stone and G. W. Forbes. Forms of the characteristic function for asymmetricsystems that form sharp images to the first order [J]. J.Opt.Soc.Am.A,1992,9(5):820—831
[18]B. D. Stone and G. W. Forbes. First-order layout of asymmetric systems: sharpimagery of a single plane object [J]. J.Opt.Soc.Am.A,1992,9(5):832—843
[19]H. J. Steffens. The development of Newtonian optics in England [M]. London:Science History Publications,1977
[20]R. A. Smith. A compleat system of optics [M]. London: Cambridge press,1978
[21]H. H. Hopkins. The wave theory of aberrations [M].Oxford: Oxford on Clarendonpress,1950
[22]H. A. Buchdahl. An introduction to Hamiltonian optics [M].London: CambridgeUniversity press,1970
[23]W. T. Welford. Aberrations of optical systems [M].Bristol: Adam Hilger,1986
[24]M. Born, E.Wolf. Principle of Optics [M].London: Cambridge UniversityPress.7thEdition,2005
[25]R.A. Buchroeder. Tilted component optical systems [D]:[博士学位论文].Tucson: University of Arizona,1976
[26]R.A. Buchroeder. Tilted-component telescopes Part1: Theory [J].Applied Optics,1970,9(9):2169-2171
[27]H. A. Buchdahl. Systems without symmetries: foundations of a theory ofLagrangian aberration coefficients [J]. J.Opt.Soc.Am.A,1972,62(11):1314-1324
[28]R. V. Shack, K. P. Thompson. Influence of alignment errors of a telescope systemon its aberration field. Proceedings of SPIE,1980,251:146-153
[29]K. P. Thompson. Aberration fields in tilted and decentered optical systems [D]:
[博士学位论文]. Tucson: University of Arizona,1980
[30]K. P. Thompson. A graphic approach to the analysis of perturbed optical systems[C]. Proceedings of SPIE,1980.237:127-134
[31]K. P. Thompson. Description of the third-order optical aberrations of near-circularpupil optical systems without symmetry [J]. J.Opt.Soc.Am.A,2005,22(7):389-1401
[32]K. P. Thompson. Multinodal fifth-order optical aberrations of optical systemswithout rotational symmetry: spherical aberration [J]. J.Opt.Soc.Am.A,2009,26(5):1090-1100
[33]K. P. Thompson. Multinodal fifth-order optical aberrations of optical systemswithout rotational symmetry: the comatic aberrations [J]. J.Opt.Soc.Am.A,2010，27(6):1490–1504
[34]K. P. Thompson. Multinodal fifth-order optical aberrations of optical systemswithout rotational symmetry: the astigmatic aberrations [J]. J.Opt.Soc.Am.A,2011,28(5):821-836
[35]J. R. Rogers. Aberrations of unobsured reflective optical systems [D]:[博士学位论文]. Tucson: University ofArizona,1983
[36]J. R. Rogers. Vector aberration theory and the design of off-axis systems [C].Proceedings of SPIE,1985,554:76-81
[37]J. R. Rogers. Practical tilted mirror systems [C]. Proceedings of SPIE,1986,679:12-16
[38]J. R. Rogers. Design techniques for systems containing tilted components[C].Proceedings of SPIE,1999,3737:286-300
[39]J. R. Rogers. Techniques and tools for obtaining symmetrical performance fromtilted-component systems [J]. Optical Engineering,2000,39(7):1776-1787
[40]T. E. Jewell, R. V. Shack. Aberration field properties of simple non-axiallysymmetric optical systems [C]. Proc. of SPIE,1985,554：128-138
[41]J. M. Sasian. Imagery of the Bilateral Symmetrical Optical System [D]:[博士学位论文]. Tucson: University ofArizona,1988
[42]L. B. Moore, A. M. Hvisc, J. M.Sasian. Aberration fields of a combination ofplane symmetric systems [J].Optics Express,2008,16(20):15655-15670
[43]J. M.Sasian. Design of a Schwarzschild flat-field, anastigmatic, unobstructed,wide-field telescope [J]. Optical Engineering,1990,20(1):1-5
[44]J. M.Sasian. How to approach the design of a bilateral symmetric optical system[J]. Optical Engineering,1994,33(6):2045-2061
[45]J. M.Sasian. Review of methods for the design of unsymmetrical optcal systems[C]. Proceedings of SPIE,1991,1396:453-466
[46]R. A. Buchroeder, A. S. Leonard. Wide-Field Tilted-Component Telescope: aLeonard Extended Yolo All-Reflecting System [J]. APPLIED OPTICS,1972,11(7)：1649-1651
[47]Michael Brunn．Unobstructed all-reflecting telescopes of the schiefspiegler type
[P]．United States Patent，5142417．1992-08-25
[48]Orestes N. Stavroudis, M. Schiefspiegler: an off-axis reflecting optical system [J].Optical Engineering,1994,33(1),116—124
[49]A. Kutter, Der Schiefspiegler. Biberacher Verlagsdruckerei, Biberach an der Riss(1953)
[50]Kristof Seidl, Jens Knobbe, and Heinrich Grüger. Design of an all-reflectiveunobscured optical-power zoom objective [J]. APPLIED OPTICS,2009,48(21):4097-4107
[51]Gilberto Moretto and Jeff R. Kuhn. Off-axis systems for4-m class telescopes [J].APPLIED OPTICS,1998,37(16):3539-3546
[52]Thierry VIARD, Pierre BODIN, A. MAGNAN, A. BAGLIN. COROTTELESCOPE (COROTEL)[C]. Proc. of SPIE,2007,6693：66930B-1-66930B-12
[53]Ozan Cakmakci, Brendan Moore, Hassan Foroosh, Jannick P.Rolland. Optimallocal shape description for rotationally non-symmetric optical surface design andanalysis [J].Optics Express,2008,16(3):1583-1589
[54]J. M. Rodgers and K. P. Thompson. Benefits of Freeform Mirror Surfaces inOptical Design [J]. Proceedings of the American Society of Precision Engineering,2004, Winter Topical Meeting on Freeform Optics,31,73-78
[55]Kenneth Garrard, Thomas Bruegge, Jeff Hoffman, Thomas Dowa, Alex Sohn.Design tools for freeform optics [C]. Proc. of SPIE,2004,5874-10
[56]Kyle Fuerschbach, Jannick P. Rolland, and Kevin P. Thompson. A new family ofoptical systems employing φ-polynomial surfaces [J].Optics Express,2011,19(22):21919-21928
[57]王之江．光学设计理论基础[M]．北京：科学出版社，1985
[58]杨新军，王肇圻，母国光等．偏心和倾斜光学系统的像差特性[J]．光子学报，2005，34(11)：1658-1662
[59]车驰骋，李英才等．基于矢量波像差理论的计算机辅助装调技术研究[J]．光子学报，2008，37(8)：1630-1634
[60]樊学武，陈荣利，马臻等．偏心和倾斜光学系统初级像差理论的研究[J]．光子学报，2004，33(4)：494-496
[61]吕丽军，石亮．平面对称光学系统像差理论的扩展[J]．光学精密工程，2009，17(12)：2975-2982
[62]Li-Jun Lu and Zhi-Yong Deng. Geometric characteristics of aberrations ofplane-symmetric optical systems [J]. APPLIED OPTICS,2009,48(36):6946-6960
[63]张虎．矢量像差理论及其在离轴头盔显示系统设计中的应用[D]．[博士学位论文]．长春：中国科学院长春光学精密机械与物理研究所，2010
[64]王之江，顾培森．实用光学技术手册[M]．北京：机械工业出版社，2007
[65]李林．现代光学设计方法[M]．北京：北京理工大学出版社，2009
[66]萧泽新．工程光学设计[M]．北京：电子工业出版社，2008
[67]李士贤，李林．光学设计手册[M]．北京：北京理工大学出版社，1996
[68]W. R. Hamilton. Report Brit. Assoc.,1833,3,360
[69]C. F. Gauss. Dioptrische Untersuchungen. Gottinger Abh.,1841,1
[70]L. Seidel. Astron. Nachr.,1856,43,289
[71]E. Abbe. Schultzes Arch. f. mikr. Anat.,1873,9,413-468
[72]张以谟．应用光学[M]．北京：电子工业出版社，2008
[73]波恩，沃耳夫．光学原理[M]．北京：电子工业出版社，2005
[74]R. N. Wilson. Reflecting telescope optics I [M]. Berlin: Springer-Verlag press,1996
[75]J. Petzval. Bericht uber optische Untersuchungen, Ber. Kais. Akad. Wien, Math.Naturwiss. Kl.,24(1857),50,92,129
[76]K. Bahner. Teleskope in Handbuch der Physik,1967, Vol. XXIX, Springer Verlag,Heidelberg,227-342
[77]潘君骅．光学非球面的设计加工与检验[M]．苏州：苏州大学出版社．2004
[78]Dietrich Korsch. Reflective optics [M]. San Diego: ACADEMIC PRESS, INC.1991
[79]W. A. Kleinhans. Aberrations of a sequence of conic mirrors [J]. APPLIEDOPTICS,1976,15(9)：2283-2287
[80]H. P. Brueggemann. Conic Mirrors [M]. London: Focal Press,1968
[81]郁道银，谈恒英．工程光学[M]．北京：机械工业出版社，2006
[82]Robert R. Shannon. The art and science of optical design [M]. CambridgeUniversity Press,1997
[83]T. Scheimpflug. Die Herstellung von Karten und Pl nen auf photographischemWege [J]. J. Royal Acad. Sci.,1907, Vienna116,235—266
[84]José Sasián. Theory of sixth-order wave aberrations [J]. APPLIED OPTICS,2010,49(16)：2283-2287
[85]A. Kutter. Der Schiefspiergler,1953, Verlag F. Weichardt, Biberach
[86]A. Kutter. Bauanleitung fur den Kosmosschiefspiegler,1964, Franckh'scheVerlagshandlung, Stuttgart
[87]Brian A. McLeod. Collimation of Fast Wide-Filed Telescopes[J]. Publications ofthe Astronomical Society of the Pacific,1996,108:217-219
[88]Ray N. Wilson. Concerning the Alignment of Modern Telescopes: Theory,Practice, and Tolerances Illustrated by the ESO NTT [J]. Publications of theAstronomical Society of the Pacific,1997,109:53-60
[89]Baichuan Ren, Guang Jin, Xing Zhong. Third-order coma-free point in twomirror telescopes by a vector approach.[J]. APPLIED OPTICS,2011,50(21)：3918-3923