大孔径长焦距全画幅变焦镜头结构计算与优化设计
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摘要
提出了广义拉格朗日乘子(GLM)算法、内点法和修正序列二次规划算法三种优化算法。采用像差分布合理的正-负-正-负-正镜头结构,设定合理的普适性参数,利用所提的三种方法计算获得了变焦范围为30～100mm、恒定F数为2.8、视场角为24.421°～71.608°的全画幅变焦镜头的高斯结构,并分析对比了三种优化算法。利用实际镜组替换由GLM算法获取的高斯结构,采用全球面设计,获得了满足成像要求的全画幅变焦镜头的优化设计,三条变焦和补偿曲线均具有良好的线性度,系统调制传递函数在50lp/mm处的平均值均大于0.1,该全球面设计为后期基于非球面优化设计提供了良好的初始结构。
Three optimization algorithms of generalized Lagrangian multiplier(GLM),interior point and modified sequence quadratic programming are proposed.By adopting a positive-negative-positive-negative-positive lens structure with a suitable aberration distribution and setting the reasonable and generally applicable parameters,the Gaussian structure of a full frame zoom lens with zoom range of 30-100 mm,constant F-number of 2.8,field-ofview angle of 24.421°-71.608°is obtained by the proposed three methods.These three optimization methods are analyzed and compared.The actual lens group is used to replace the Gaussian structure obtained by the GLM algorithm.The full spherical design is adopted and the obtained optimal design of the full-frame zoom lens meets the imaging requirements.Three zoom and compensation curves have good linearity,and the average value of the modulation transfer function of system is greater than 0.1 at 50 lp/mm.This full spherical design provides a good initial structure for the later aspheric optimal design.
Three optimization algorithms of generalized Lagrangian multiplier(GLM),interior point and modified sequence quadratic programming are proposed.By adopting a positive-negative-positive-negative-positive lens structure with a suitable aberration distribution and setting the reasonable and generally applicable parameters,the Gaussian structure of a full frame zoom lens with zoom range of 30-100 mm,constant F-number of 2.8,field-ofview angle of 24.421°-71.608°is obtained by the proposed three methods.These three optimization methods are analyzed and compared.The actual lens group is used to replace the Gaussian structure obtained by the GLM algorithm.The full spherical design is adopted and the obtained optimal design of the full-frame zoom lens meets the imaging requirements.Three zoom and compensation curves have good linearity,and the average value of the modulation transfer function of system is greater than 0.1 at 50 lp/mm.This full spherical design provides a good initial structure for the later aspheric optimal design.
引文
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[9] Zhang L Q,Wang Y T,Li L.Method of determining Gaussian parameters for zoom systems with multiple moving lens groups[J].Acta Optica Sinica,2002,22(5):572-576.张丽琴,王涌天,李林.多组元全动型变焦距透镜高斯光学参数的求解方法[J].光学学报,2002,22(5):572-576.
[10] Wang Q,Wang G Y,Cheng X M,et al.Gauss optics of zoom lenses[J].Acta Optica Sinica,2002,22(8):983-988.王琦,王光宇,程雪岷,等.变焦距镜头高斯光学设计的新方法[J].光学学报,2002,22(8):983-988.
[11] Li X T,Cen Z F.Optmization design of zoom lens systems[J].Proceedings of SPIE,2002,4927:44-50.
[12] Li X T,He G X.Research of optimization design for zoom lens Gaussian parameters[J].Journal of Zhejiang University(Natural Science),1993,27(1):122-127.李晓彤,何国雄.变焦距系统高斯解优化的研究[J].浙江大学学报(自然科学版),1993,27(1):122-127.
[13] Song Q,Huang H,Lv X B,et al.An approach for generating the first order structure of multi-movable zoom lens[J].Optics Communications,2016,359:399-404.
[14] Huang H,Li X N,Song Q.New method for all movable zoom lens first order design[J].Acta Optica Sinica,2015,35(s1):s122004.黄浩,李湘宁,宋强.一种全动变焦系统的高斯参数计算方法探究[J].光学学报,2015,35(s1):s122004.
[15] Yuan X C.Optical design[M].Beijing:Beijing Institute of Technology Press,1988:237-238.袁旭沧.光学设计[M].北京:北京理工大学出版社,1988:237-238.
[16] Zhang G D.Computational methods for nonlinear optimization[M].Beijing:Higher Education Press,2005:292-308.张光澄.非线性最优化计算方法[M].北京:高等教育出版社,2005:292-308.
[17] Antoniou A, Lu W S. Practical optimization:algorithms and engineering applications[M].Berlin:Springer,2007:501-529.
[2] TanakaK. Paraxialanalysisofmechanically compensated zoom lenses 3:five-component type[J].Applied Optics,1983,22(4):541-553.
[3] Kryszczyński T,Le'sniewski M,Mikucki J.Use of matrix optics to analyze the complex multi-group zoom systems[J].Proceedings of SPIE,2012,8697:86970I.
[4] Milde T,Zimmermann T.Toward a paraxial predesign of zoom lenses[J].Proceedings of SPIE,2015,9580:958005.
[5] Pal S,Hazra L.Structural design of mechanically compensatedzoomlensesbyevolutionary programming[J].Optical Engineering,2012,51(6):063001.
[6] Pal S, Hazra L. Ab initio synthesis of linearly compensatedzoomlensesbyevolutionary programming[J].Applied Optics,2011,50(10):1434-1441.
[7] Tao C K.Zoomoptical system design[M].Beijing:National Defense Industry Press,1988:33-40,121-135.陶纯堪.变焦距光学系统设计[M].北京:国防工业出版社,1998:33-40,121-135.
[8] Tao C K.Design ofzoom system by the varifocal differential equation I[J].Applied Optics,1992,31(13):2265-2273.
[9] Zhang L Q,Wang Y T,Li L.Method of determining Gaussian parameters for zoom systems with multiple moving lens groups[J].Acta Optica Sinica,2002,22(5):572-576.张丽琴,王涌天,李林.多组元全动型变焦距透镜高斯光学参数的求解方法[J].光学学报,2002,22(5):572-576.
[10] Wang Q,Wang G Y,Cheng X M,et al.Gauss optics of zoom lenses[J].Acta Optica Sinica,2002,22(8):983-988.王琦,王光宇,程雪岷,等.变焦距镜头高斯光学设计的新方法[J].光学学报,2002,22(8):983-988.
[11] Li X T,Cen Z F.Optmization design of zoom lens systems[J].Proceedings of SPIE,2002,4927:44-50.
[12] Li X T,He G X.Research of optimization design for zoom lens Gaussian parameters[J].Journal of Zhejiang University(Natural Science),1993,27(1):122-127.李晓彤,何国雄.变焦距系统高斯解优化的研究[J].浙江大学学报(自然科学版),1993,27(1):122-127.
[13] Song Q,Huang H,Lv X B,et al.An approach for generating the first order structure of multi-movable zoom lens[J].Optics Communications,2016,359:399-404.
[14] Huang H,Li X N,Song Q.New method for all movable zoom lens first order design[J].Acta Optica Sinica,2015,35(s1):s122004.黄浩,李湘宁,宋强.一种全动变焦系统的高斯参数计算方法探究[J].光学学报,2015,35(s1):s122004.
[15] Yuan X C.Optical design[M].Beijing:Beijing Institute of Technology Press,1988:237-238.袁旭沧.光学设计[M].北京:北京理工大学出版社,1988:237-238.
[16] Zhang G D.Computational methods for nonlinear optimization[M].Beijing:Higher Education Press,2005:292-308.张光澄.非线性最优化计算方法[M].北京:高等教育出版社,2005:292-308.
[17] Antoniou A, Lu W S. Practical optimization:algorithms and engineering applications[M].Berlin:Springer,2007:501-529.
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