摘要
光波通过随机介质传播和成像是诸如激光通信、航空测绘、卫星遥感等领域湍流大气环境中运行的光学系统的设计和使用中必然要考虑到的问题,同时也是激光医学、生物工程等领域中运用光学工具进行病情诊断与治疗、生物特性测量和研究的科技人员经常会涉及到的基础知识。
在处理随机介质中的光传输问题时,我们采用了光线光学的方法,结合物理光学中关于波面变形的计算,得到了一系列直观的像质评价指标。由于光线追迹的过程中,会随时调用随机介质内的折射率及其梯度信息,如何在内存中存储海量的折射率信息是该研究中遇到的最大问题。本文提出了自适应网格的方法,有效地描述了随机介质内的非均匀折射率分布,在保证光线追迹精度的前提下,实现了内存空间的最大使用效率。
本文首先介绍了随机流场介质与光波传输特征之间的关系及其应用背景;重点分析了光线在不均匀介质中传输的基本原理和实现方法。然后,详细介绍了自适应网格法的数据结构,具体算法,最终实现了在折射率变化较大,即梯度较大的区域,网格自动划分为较小的小网格,实现了存储空间的最大化利用和模拟精度的大幅提升。在本论文中,结合自适应网格的方法,还提出了自动变步长光线追迹的方法,实现了折射率变化缓慢的区域采用大步长,而折射率变化剧烈的区域采用小步长光追的最优化光追模型。同时,针对光线光学在变折射率介质中的应用,列出了多种常用的光学像质评价参量的具体实现方法,如传递函数(MTF)、点列图、中心点亮度(PSF)和斯特列尔比(Strehl)等。
为了验证自适应网格算法及光追程序的正确性,本文选用了一种可以由公式表达的折射率分布介质作为分析对象,离散化地得到若干采样点的折射率值,作为原始折射率数据文件输入自适应网格程序,并基于此进行光线追迹的运算;计算结果与商用光学设计软件ZEMAX相比较,结果显示自适应网格方法具有非常高的精度,并且在合理的折射率梯度阈值条件下,自适应网格能够非常有效地节省内存占用量,使大尺寸的高精度随机介质的折射率特性的模拟成为可能。同时,本文还以某随机介质为例,验证了变步长光追的效果,结果显示,采用变步长的光线追迹方法,能有效地节省光线追迹的时间,大大提高光传输模拟的效率。
In the application fields like laser communication, aerial photo-mapping and remote sensed imaging, how dose an optical wave be transmitted through the random medium is a critical problem. Meanwhile, in other industries like laser medicine, and biological engineering, the imaging through a random medium is also a basic knowledge for the researchers and scientists.
In solving the problem of imaging through the random medium, this paper mainly applies the method of ray tracing, combined with the technology of wavefront calculations in the field of physical optics, so as to obtain a series of image evaluation results. During the ray trace process, the refractive index and its gradient information of the random medium are frequently used, how to storage the mass refractive information is one of the biggest problems in the research. This paper presented the method, namely self-adaptive grid, effectively describing the arbitrary refractive distribution in the random medium. By applying the local-subdivision algorithm, the storage volume can get its full usage under the circumstances that the ray trace accuracy is guaranteed.
This paper firstly overviews the relationship between the random medium and optical wave transmission, and its application background, emphasizing on the principle and realization method of ray tracing through the inhomogeneous medium. Secondly, the data structure and the corresponding algorithm of self-adaptive grid is explained in detail, so as to achieve the optimum situation that the grid is divided into smaller ones in the area where the refractive index changes vastly, and the grid size is larger in the area where the refractive index changes smoothly. And then, the paper also presented the method of vary-step ray trace method, that combining the ray trace step with the local adaptive grid size, so as to achieve an optimum ray trace model. In addition, this paper also describes various image evaluation methods concerning the application of ray trace through random medium, such as MTF, spot diagram, PSF and Strehl, etc..
In order to verify the correctness of self-adaptive grid algorithm and the corresponding ray trace codes, one simple model is taken as an example, or say, the refractive index distribution of GRIN lens can be described by a sort of equations, so that numerous refractive index information at discrete sample locations can be obtained, and input into the self-adaptive grid software. The ray trace calculations based on such an algorithm can be easily compared with that from the commercially available software Zemax. The results illustrate that the algorithm of self-adaptive grid has very high accuracy, and such a method can greatly reduce the storage consumption under a reasonable threshold setting, so as to make the high-accuracy image simulation through the random medium come possible. Meanwhile, this paper also takes a real random medium as an example, and the results show that the vary-step ray trace method can effectively reduce the ray tracing time and greatly improve the image simulation efficiency.
引文
[1]Daniel Malacara,and Zacarias Malacara,Handbook of optical design,Marcel Dekker,Inc.,2004,Chap 1.
[2]E.W.Marchand,Gradient index optics.Academic Press,1978.
[3]刘德森,变折射率介质理论及其技术实践,西南师范大学出版社,2005,前言
[4]乔亚夫.梯度折射率光学[M].北京:科学出版社,1991
[5]R.Siegel,J.R.Howell,Thermal radiation heat transfer,4th Edition,New York:Taylor &Francis,2002.
[6]J.C.Maxwell,Cambridge and Dublin,Math.J.,1854,8:88
[7]R.K.Lunenburg,Mathematical theory of optics,University of California Press,1964
[8]R.W.Wood,Physical optics,McMillan,1905
[9]S.Kawakami and J.Nishizawa,An optical waveguide with the optimum distribution of the refractive index with reference to wavefront distortion.IEEE J.,1968,16(10):814
[10]M.S.Sodha,A.K.Ghatak,Inhomogeneous optics waveguides,Plenum Press,1977
[11]G.I.Greisukh,S.T.Bobrov,S.A.Stepanov,Optics of diffractive and gradient-index elements and systems,SPIE Optical Engineering Press,1997
[12]K.Iga,Y.Kokubun,M.Oikawa,Fundamentals of micro-optics,Academic Press,1984
[13]K.Kobayashi,R.Ishikawa,K.Minemura,S.Sugimoto,Fiber and integrated optics,1979,2:1
[14]J.F.Goldenberg,J.J.Miceli,D.T.Moore,Applied optics,1985,24(4):288
[15]刘德森等,变折射率透镜的研究和发展现状,物理,1988,11(3):143
[16]Zemax Manual,Focus Software.Inc.,2002.
[17]李桂春等,气动光学,国防工业出版社,2006,绪论:2
[18]殷兴良等,气动光学原理,中国宇航出版社,2003,前言
[19]H.W.Liepmann,Deflection and diffusion of a light ray passing through a boundary layer.Report No.SM- 14397,1952.
[20]A.E.Fuhs,Overview of aero-optical phenomena,1981,SPIE Vol.293
[21]L.H.Liu,Descrete curved ray-tracing method for radiative transfer in an absorbing-emitting semitransparent slab with variable spatial refractive index,Journal of Quantitative Spectroscopy and Radiative Transfer,2004,83(3-4):333-344
[22]A.Sharma,D.V.Kumar,and A.K.Ghatak,Tracing rays through graded-index medium:a new method,Applied Optics,1982,A21,984-987.
[23]W.Hou,R.Thalmann.Accurate measurement of the refractive index of air.Measurement,1994,13:307-314.
[24]P.C.Ariessohn,Two wavelength laser transmissometer for measurement of the mean size and concentration of coal ash droplets in combustion flows,Appl.Opt.,1980,Vol.19:22.
[25]E.R.Peck,Precise measurements of optical dispersion using a new interferometric technique:comment.Appl.Opt.,1986,25:3597-3598.
[26]Guangping Xie,Youjin Wang,L.J.Reiter.High-accuracy absolute measurement of the refractive index of air,Opt.Eng.,2004,43(4):950-953.
[27]Ichiro Fujima,Shige Iwasaki,Guangping Xie,Precise measurement of the difference of the air-refractive indices between visible and near-infrared wavelengths using two-color interferometer.Proc.SPIE,1999,3897:767-772.
[28]柳春郁,余有龙,高应俊,基于菲涅尔原理的光纤型折射率测量装置,光电子·激光,2004,15(12):1464-1466.
[29]J.H.Gladstone and T.P.Dale,Researches on the refraction,dispersion and sensitiveness of liquids,Philos.Trans.R.Soc,1863,153,317-343.
[30]H.Barrell,J.E.Sears,The Refraction and Dispersion of Air for the Visible Spectrum,Phil.Trans.Roy.Soc.A.,1939:238.
[31]J.M.Rueger,Refractive Indices of Light,Infrared and Radio Waves in the Atmosphere,Report of the Ad-Hoc Working Party of the IAG Special Commission SC3 on Fundamental Parameters(SCFC),1999-2003,23rd General Assembly of IUGG,Sapporo,Japan,30 June-11July 2003,6 pages.
[32]D.C.Wilcox,Turbulence Modeling for CFD,2nd ed.DCW Industries,Inc.,1998.
[33]E.Frumker,O Pade,Generic method for aero-optic evaluations,Appl.Opt.,2004,Vol.43(16):3224-3228
[34]R.J.Renka,Multivariate interpolation of large sets of scattered data,ACM_Assoc.Comput.Mach.Trans.Math.Software,1988,14_2:139-148.
[35]G.R.Liu,Mesh free methods,Boca Raton,CRC Press,2003
[36]G.R.Liu,Y.T.Gu,An introduction to meshifree methods and their programming.New York:Springer,2005
[37]Kazuhiro Nakahashi,George S.Deiwertt.Self-Adaptive-Grid Method with Application to Airfoil Flow.AIAA Journal.1987,25(4):513-515.
[38]G.S.Deiwen,E.Venkatapathy,C.avies,J.Djomehri,K.Abrahamson.Application of a self-adaptive grid method to complex flows,NASA Technical Memorandum 102223,1989:1-5.
[39]Davies,C.B,Venkatapathy,E.The Multidimensional Self-Adaptive Grid Code,SAGE,1992,NASA TM-103905.
[40]Liu F,Ji SH,Liao GJ.An adaptive grid method and its application to steady Euler flow calculations.SIAM Journal on Scientific Computing.1998,20(3):811-825.
[41]D.Marcuse,Light transmission optics,Van Nostrand Reinhold Company,1982.
[42]M.Born and E.Wolf,Principle of Optics,Cambridge U.Press,1999
[43]刘德森,变折射率介质理论及其技术实践,西南师范大学出版社,2005,第一章。
[44]孟繁斌,张静波,刘铁安等,应用程涵方法研究光线方程和费马原理,沈阳大学学报,2002,14(2):37-38
[45]A.K.Ghatak and K.Thyagarajan,Contemporary Optics(Plenum,New York,1978),Chap.1.
[46]P.Ben Abdallah,V.Le Dez,Thermal emission of a semitransparent slab with variable spatial refractive index,J.Quant.Spectrosc.Radiat.Transfer,67 185-98
[47]吴健,乐时晓,随机介质中的光传播理论,成都电讯工程学院出版社,1988:103-188.
[48]黄战华,程红飞,变折射率介质中光线追迹通用算法的研究,光学学报.2005,25(5).
[49]L.H.Liu,K.Kudo,B.X.Li,Comparison of ray-tracing methods for semitransprent slab with variable spatial refractive index,Journal of Quantitavie Spectroscopy and Radiative Transfer,2004,85(2):125-133
[50]H.A.Buchdahl,Rays in Gradient Index Media:Separable Systems,J.Opt.Soc.Am.1973,63:46.
[51]易大义,沈云宝,李有法,计算方法,浙江大学出版社,1989:120
[52]A.Sharma,Computing optical path length in gradient-index media:a fast and accurate method,Appl.Opt.24,1985,4367-4370.
[53]M.A.Alonso and G.W.Forbes,Using rays better.Ⅱ.Ray families for simple wavefields,2001,J.Opt.Soc.Am.A 18,1146-1159.
[54]J.L.Devore,Probability and statistics for engineering and the sciences,Brooks/Cole Pub.Co.,1991
[55]Barakat,R.,Rayleigh Wavefront Criterion,J.Opt.Soc.Am.,1965,55,641-649.
[56]J.W.Goodman,Introduction to Fourier Optics 2nd ed.McGraw-Hill,New York,1996
[57] Baker, L, ed., Selected Papers on Optical Transfer Function: Foundation and Theory, SPIE Optical Engineering Press, Bellingham, WA, 1992.
[58] Malacara, D., Diffraction and Scattering, Chap. IV in Methods of Experimental Physics, Physical Optics and Light Measurements, Vol. 26, D. Malacara, ed., Academic Press, San Diego, CA, 1988.