摘要
由于在光学、电子衍射和电子显微学、光通讯等方面的重要性,近年来,周期结构衍射成像受到广泛关注,成为当前研究的热点之一。论文将衍射过程看成是光子与衍射物之间的互作用过程,从光子学角度重新审视了衍射现象并对超声光栅、环孔衍射等一般光学问题,运用光子学方法,简洁地给出了与现行文献相同的结论。
在分析现有周期结构衍射成像结果的基础上,提出光子对周期结构信息具有记录和再现的作用,并根据这一假设对Talbot效应进行了深入的研究,引入调节参数q并指出它在正、偏自成像中的作用。
论文还运用光子学方法对莫尔效应进行了综合研究,指出普通云纹是干涉云纹的衍射极限,这样,就将一般云纹技术和干涉云纹技术原理建立在一个统一的框架内,更便于理解。此外,在对周期结构的塔尔博特效应研究中,论文利用维纳分布函数,在空-频域内对周期结构衍射进行了研究,得到了塔尔博特(Talbot)效应的相关结论。
为拓展周期结构成像的应用领域,论文在分析了信号与系统关系的基础上,提出将扩大系统综合孔径实现超分辨成像方法延伸到亚波长段,用Talbot效应和莫尔条纹技术实现亚波长周期结构超分辨成像。这种方法的要点是:光经过透镜准直后照射在亚波长周期结构(如Ronchi光栅)上,在亚波长周期结构物后面,满足塔尔博特公式的位置上,形成Talbot像,在该像位置放置一个编码器,将产生莫尔条纹,由莫尔原理可知,莫尔条纹的空间周期可能大于原亚波长周期结构物光栅的周期,以至于衍射波可通过光学系统传播。再经过恰当的解码,滤掉编码波,就会再现原亚波长周期物的空间信息,取得用传统光学仪器对一维亚波长周期结构的成像,于是用这种新颖的成像技术,便实现了对亚波长周期物的超分辨。一维亚波长周期结构的超分辨结果已经验证了设计的可行性,论文还给出了一般二维亚波长周期结构超分辨的实验设计。
In recent years, since the importance of it in the fields of optics,electronic diffraction, electronic microscopy and optical communication,ones pay their attentions to diffractive characteristic of periodic structure.Diffractive characteristic of period objects were analyzed and generalizedby the photonics method. The photonic Fraunhofer diffraction at a annularaperture or a ultrasonic grating be explained from probability wave inquantum theory, the same conclusion with Huygens-Fresnel principle orFourier transform be obtained.
Talbot effect is explained with the viewpoint of photonics, the sameconclusions to positive self-imaging, negative self-imaging and fractionimaging with Huygens-Fresnel principle or Fourier transform be obtained.The adjustable coefficient q for Talbot-effect is advanced, its actions forpositive self-imaging, negative self-imaging and fraction imaging, as wellas the phase relations between the object and the image be discussed.
The self-imaging process is discussed in spatial-frequency domainwith Wigner transform function. Unified explanation of the effects due toTalbot and Montgomery effect is presented in spatial-frequency domain.
Diffractive characteristic of periodic structure objects were analyzedand generalized by the principle of the recordation and reappearance forspatial information of object by photons. Ordinary Moiréeffect can beregarded as the limit of the coherent Moiréeffect. At the same time, thedirection of Moiréspatial frequency, spatial period of Moiréfringe andthe step of the measuring grating be given with the method used. Being itssimplicity in mathematics, the method suggested is easy to use widely,especially in the fields of information.
When a periodic object with subwavelength structure be illuminatedby normal incident monochromatic light-beam, evanescent waves canoccur. Bing attenuated quickly, the object with subwavelength structurecan not be imaged by ordinary method. However, one-dimensionalperiodic object with sublambda structure can be corded by a grating sothat homogeneous waves can be obtained. Passing through the optics system designed specially, the well-distributed waves with evanescentwaves be enlarged so that it can be recognized by CCD camera. After that,the homogeneous waves with evanescent waves be decoded by a decodinggrating. By decoding, the information of encoding grating is filtered, theimage of the object with subwavelength structure can be reappeared in theimage plane. The imaging technique based on the conventional opticssetup is a novel technique, by that, superresolution image of object withsubwavelength structure can be obtained. Theoretical analysis of theimaging process for the object with subwavelength structure be given wellby photonics method. It be designed that where the encoding grating andthe decoding grating are placed, so does how to choose the tilt anglesbetween the two gratings and the object. At the same time, it be discussedthat the low pass filters used in the novel technique also. The results ofexperiment demonstrate that the theory which used is valid. Theoreticalanalysis and experimental design for the imaging process oftwo-dimensional object with subwavelength structure be also given byphotonics method.
引文
[1] F. Talbot. Facts relating to optical science [J].Hilos.Mag. 1836,9(4):401~407.
[2] Lord Rayleigh. On copying diffraction-gratings, and on some phenomenon connected therewith," Philos. Mag. 1881, 11, 196~205.
[3] E. A. Hiedemann and M.A. Breazeale. Secondary interference in the Fresnei zone of gratings[J], J. Opt. Soc. Am. 1959, 49(4): 372~375.
[4] John T. Winthrop and C.R. Worthington.Theory of Fresnel Images. Ⅰ. Plane Periodic Objects in Monochromatic Light [J], J. Opt. Soc, Am. 1965, 55(4): 372~381.
[5] M. A. Grimm. Superresolution Image for One-Dimensional Object [J], J. Opt. Soc. Am. 1966, 56 (9): 1151~1156.
[6] W. Duane Montgomery. Self-Imaging objects of infinite aperture [J], J. Opt. Soc. Am. 1967, 57 (6): 772~778.
[7] Zhang Cheng-yi, Tao Chun-kan. A study of talbot effect based on photonic theory[J],Laser&opto-electronics progress, 2006, 43(5): 63~66.
[8] J. R. Leger and M. A. Snyder, Real-time depth measurement and display using Fresnel diffraction and white-light processing," [J]. Appl.Opt, 1984, 23(9): 1655~1670.
[9] J. R. Leger. Lateral mode control of an AIGaAs laser array in a Talbot cavity[J]. Appl. Phys. Lett. 1989, 55, 334~336.
[10] Paul Latimer. Talbot plane patterns: grating imagings or interference effects? [J]. Appl. Opt, 1993, 32 (7): 1078~1083.
[11] Paul Latimer and Randy F. Crouse, Talbot effect reinterpreted.[J]. Appl. Opt, 1992, 31(1): 80~89.
[12] Liao Jiang-Hong and Gu Qu-Wu, Diffraction self-imaging phenomenon of the grating in the optical system: general Talbot effect[J]. Acta Optica Sinica (in Chinese), 1985, 5(4): 331~335.
[13] Xiao-Yi Da. Talbot effect and the array illuminators that are based on it[J]. Appl.Opt, 1992,31 (16): 2983~2986.
[14] Namias. The fractional order Fourier transform and its application to Quantum Mechanics[J]. J. Inst. Math. Appl., 1980, 25, 241~245.
[15] McBride, F. H. Kerr. On Namias' fractional Fourier transforms. IMA J. Appl. Math.,1987,39, 159~175.
[16] David Mendlovic. Image rotation, Wigner rotation, and the fractional Fourier transform[J]. J. Opt. Soc. Am. A, 1993, 10 (10): 2181~2186.
[17] Mendlovic, H. M. Ozaktas. Fractional Fourier transform and their optical implementation[J]. J. Opt. Soc. Am. A. 1993, 10, 1875~1881.
[18] Ozaktas, D. Mendlovic. Fractional Fourier transform and their optical implementation[J]. J. Opt. Soc. Am. A. 1993, 10, 2522~2531.
[19] Ozktas, B. Barshan, D. Mendlovic, et al. Convolution, filtering, and multiplexing in fractional Fourier domains and their relation to chirp and wavelet transforms[J]. J. Opt. Soc. Am. A. 1994, 11, 547~559.
[20] Lohmann., D. Mendlovic. Fractional Fourier transform: photonic implementation[J]. Appl. Opt, 1994, 33, 7661~7664.
[21] Bernardo, O.D.D.soares. Fractional Fourier transform and imaging[J]. J. Opt. Soc. Am. A. 1994, 11, 2622~2676.
[22] Rainner G. Dorsch, Adof W. Lohmann. Fractional Fourier transform used for a lens-design problem[J]. Appl. Opt, 1995, 34: 4111~4112.
[23] Liren Liu, Xiaoben Liu, Lianguang Ye. Joint Talbot effect and logic-operated moire patterns[J]. J. Opt. Soc. Am. A. 1990, 7,970~976.
[24] A.W.Lohmann, J.Schwider, N. streibl, et,al. An array illuminator based on phase contrast[J]. Appl. Opt, 1988, 27: 2915~2921.
[25] Adolf W. Lohmann and James A. Thomas, making an array illuminator based on the Talbot effect[J]. Appl. Opt, 1990, 29(29): 4337~4340.
[26] Adolf W. Lohmann. An array illuminator based on the Talbot effect[J]. Optik, 1988, 79, 41~45.
[27] Kalestynski A. Imaging in spatially periodic light fields. Opt. Eng,199232, 465~469.
[28] Fan Xizhi. Discuss of Talbot effect basing on Young's double-slit interference[J]. Acta Photonica Sinica (in Chinese), 2005, 34(4): 621~623.
[29] Paul Latimer, Talbot effect and Cornu's spiral [J]. Appl. Opt, 1994, 33 (22): 4983~4987.
[30] K.Patorski and P. Szwaykowski. Light intensity distribution in the Fresnel diffraction region of a non-sinusoidal phase grating[J]. Appl. Opt, 1981, 11, 627~631.
[31] K. Patorski, S. Yokozeki and T. Suzuki. Collimation test by double grating sheafing interfero--meter[J]. Appl. Opt, 1976, 15(4): 1234~1240.
[32] J.M. Cowley and A. F. moodie. Fourier images; Ⅰ. The point source. 1957, Proc.R.Soc.London Ser. B70, 486~496.
[33] J.T. Winthrop and C.R. Worthington. Theory of Fresnel images, plane periodic objects in monochromatic light[J]. J. Opt. Soc. Am. 1966, 55, 373~381.
[34] L. deng, E. w. Hagley, J.E. Simsarian, Mark Edwards, Charles W. Vlark, et al. Temproal, Matter-Wave-Dispersion Talbot effect[J]. Phys. Rev. lett. 1999, 83(26): 5407~5411.
[35] A. G. Rojo, J. L. cohen, and P.R. Berman. Talbot oscilation and periodic focusing in a onedimen- -sional condensate[J].Phys.Rev.A. 1999,60(2): 1482~1490.
[36] Tao Jing-guang, Liao Zhaoshu, Yang Kuntao. Analysis of Talbot image symmetry about Fourier spectrum plane and measurement of focal length[J]. Acta Optica Sinica (in Chinese),1994, 14(1): 50~54.
[37] Zu Jifeng, Zhou Changhe Xi Peng, et, al. Wavelength-Division and Beam Splitting Element Based on the Talbot Effect[J]. Acta Optica Sinica (in Chinese),2003, 23(4):431~433.
[38] A.W.Lohmann and F. Sauer. Holographic telescope arrays[J]. Appl. Opt, 1988,27:3003~3007.
[39] Norbert Streibl. Review paper: Beam shaping with optical array generators[J]. Journal of modern optics, 1989,36(12): 1559~1573.
[40] Piotr Szwaykowski and Victor Arrizon. Talbot array illuminator with multilexel phase gratings[J]. Appl. Opt, 1993, 32(7): 1109~1114.
[41] Huaisheng Wang, Changhe Zhou, Liren Liu. Simple Fresnel diffraction equations of a grating for Talbot arry illumination[J]. Opt. Commun, 2000, 173, 17~22.
[42] Changhe Zhou, Svetomir Stankovic, and Theo Tschudi. Analytic phase-factor equations for Talbot array illuminations[J]. Appl. Opt, 1999,38(2): 284~290.
[43] Huaisheng Wang. To measure chirped ultrashort laser pulse by the Talbot effect of a grating[J]. Opt. Commun, 2006, 259, 107~109.
[44] Christian Cuadrado-Labord, Pablo A. Costanzo-Caso, Ricardo Duchowicz, et,al. Temporal Talbot effect applied to determine dispersion parameters[J]. Opt. Commun, 2006, 260, 528~534.
[45] L. Praxmeyer, K. Wodkiewicz. Talbot effect in cylindrical waveguides[J]. Opt. Commun, 2006, 268, 215~225.
[46] Ding Jiansheng. measurement of long focal length by using the Talbot effect and Moire technique[J].Opto-Electronie Engineering(in Chinese), 1994, 21(1): 53~57.
[47] Hou Chang-lun, Bai Jian, Hou Xi-gun, et,al. The accurate measurement of angle based on Talbot effect of Ronchi grating[J] Optical Instruments(in Chinese), 2004, 26 (1): 11~14.
[48] Gao Kan, ZHU Qin, C. Paul, et al. Experimental Study of Long Period Moire Gratings[J]. Chinese Journal of Lasers(in Chinese), 2006, 33(7): 933~936.
[49] Wang Shifan. Theory and Practice on Information Optics [M], Beijing. Beijing University of posts and Telecommunications Press, 2004, 73-75.
[50] K. Patorski. The self-imaging phenomenon and its applications[J]. Prog. Opt, 1989, 27: 1-108.
[51] A. W. Lohmann, H. Knuppertz, J. Jahns. Fractional Montgomery effect: a self-imaging phenomenon [J]. J. Opt. Soc. Am. A, 2005, 22(8): 1500-1508.
[52] Wenjian Cai, Timothy D. Gerke, Theodore J.Reber, et al. Computer-generated volume holograms optimize degrees of freedom in 3d aperiodic structures[J]. OPN.2006, 17(12): 26.
[53] M. J. Bastiaans. The Wigner distribution function applied to optical signals and systems[J]. Opt. Comm. 1978, 25 (1): 26-30.
[54] W. Lukosz.Optical System with Resolving Powers Exceeding the Classical Limit[J]. J. Opt. Soc. Am. 1966,56 (11): 1463~1472
[55] Yan Yuan, Chen Hui, Zhu Wenyong. A Vector Modal Theory for Perfectly-Conducting Rectangular Aperture Grating[J]. Acta Optica Sinica (in Chinese), 1994, 14 (6): 622-625.
[56] Zeng Jinyan. Quantum Mechanics[M]. Beijing: Science Press(in China), 2000(3), 1-55.
[57] Mei Zhenlin, Sui Chenghua. Research of the ultrasonic grating and the sound speed[J]. Physical experiment of college (in Chinese), 2004, 17 (1): 28~31.
[58] Zhang Chengyi. A quantitative study for the measure of sound-speed by the ultrasonic grating[J]. Physical experiment of college (in Chinese), 2006, 19 (1): 17~19.
[59] Hal Huan, Osami Sasaki, Takamasa Suzuki. Movement measurement with a grating interferometer using sinusoidal phase-modulation[J]. Opt. Commun, 2006,267,341~346.
[60] Jamshidi-Ghaleh Kazem, Mansour Nastaran. Nonlinear refraction measurements of materials using the moire deflectometry[J]. Opt. Commun, 2004,234,419~425.
[61] Zhang Cheng-yi, Tao Chun-kan, Chen Mei-hong.A simple study method for experiment of ultrasonic grating and its frequency shift of Doppler[J].Physics experimentation,2006,26(12): 35~37.
[62] Zhang Cheng-yi, Tao Chun-kan, Gao Wan-rong. Recordation and reappearance for spatial information by photons[J].Opto-electronic engineering, 2006, 33(5):57~61.
[63] I.Glatt,O. Kafri.Beam direction determination by Moire deflectometry using circular gratings[J]. Appl. Opt, 1987, 26(19): 4051~4057.
[64] Hou Chang-lun, Bai Jian, Hou Xi-gun,et,al. The accurate measurement of angle based on Talbot effect of Ronchi grating[J]. Optical Instruments (in Chinese),2004, 26(1): 11~14.
[65] Gao Kan, Zhu Qin, C.Paul, et al. Experimental Study of Long Period Moire Gratings[J].Chinese Journal of lasers (in Chinese), 2006, 33(7): 33~36.
[66] Gao Kan, Zhou Ying-wu, Qu Rong-hui et. al. Theoretical Analysis of Long-Period Moire Gratings[J]. Chinese Journal of Lasers (in Chinese), 2005, 32(3): 427~430.
[67] Sun Chen, Shen Yibing, Bai Jian, et,al. The Precision Limit Analysis of Long Focal Length Testing Based on Talbot effect of Ronchi Grating[J]. Acta Photonica Sinica (in Chinese),2004,33 (10): 1214~1217.
[68] P.S.Carney, D.G. Fischer, J.T.Foley, et al. Comment: Evanescent waves do contribute to the far field[J]. J. Mod. Optics, 2000, 47(4): 757~758.
[69] Akhlesh Lakhtakia, Werner S. Weiglhofer. Evanescent plane wave and the far field: resolution of a controversy[J]. J. Mod. Optics, 2000, 47(4): 759~763.
[70] C.J.R.Sheppard, F. Aguilar. Comment: Evanescent fields do contribute to the far field(1999, J. mod. optics,46,729) [J]. J. Mod. Optics, 2001, 48(1): 177~180.
[71] Nikolai 1. Petrov. Evanescent and propagating fields of a strongly focused beam[J]. J. Opt. Soc. Am. A.2003,20 (12): 2385~2389.
[72] Mufei Xiao. Evanescent and propagating electromagnetic fields in scattering from point-dipole structures: comment[J]. J. Opt. Soc. Am. A.2002,19 (7): 1447~1451.
[73] D.C.Bertilone. The contributions of homogeneous and evanescent plane waves to the scalar optical field: exact diffraction formulae [J]. J. Mod. Optics, 1991, 38(5): 865~875.
[74] Zhang Cheng-yi. A generalized study of Doppler Effect[J].J. Liaocheng university.(Nature Science Edition), 2003:110-114. (in China)
[75] Adolf W. Lohmann and D.P. Paris. Supperresolution for nonbirefringement objects[J]. Appl. Opt, 1964, 3: 1037~1043.
[76] W. Lukosz. Optical System with Resolving Powers Exceeding the Classical Limit Ⅱ[J]. J. Opt. Soc. Am. 1967, 57 (7): 932~941.
[77] Adolf W. Lohmann. Space-bandwidth product of optical signals and systems[J].J. Opt. Soc. Am. A. 1996,13 (3): 470~473.
[78] David Mendlovic. Space-bandwidth product adaptation and its application to superresolution: examples[J]. J. Opt. Soc. Am. A. 1997, 14 (3): 563~567.
[79] David Mendlovic Space-bandwidth product adaptation and its application to superresolution: fundamentals[J]. J. Opt. Soc. Am. A. 1997, 14 (3): 558~562.
[80] M. J. Bastiaans. Wiger distribution function and its application to first-order optics[J]. J. Opt. Soc. Am. 1979,69 (12): 1710~1716.
[81] Max Born and Emil Wolf. Principles of Optics[M]. London: Printed in the United Kingdom at the University Press, Cambridge. 1999, chapter 8.
[82] Martin J. Bastiaans. Moments of the Wigner distribution of rotationally symmetric partially coherent light[J]. Optics Letters, 2003, 28 (24): 2443~2445.
[83] Adolf W. Lohmann. Image rotation, wigner rotation, and the fractional Fourier transform[J]. J. Opt. Soc. Am. A. 1997,14 (3): 558~562.
[84] Kurt Bernardo Wolf. Wigner functions for Helmholtz wave fields[J]. J. Opt. Soc. Am. A. 1999, 16 (10): 2476~2487.
[85] David Mendlovic, Adof W. Lohmann, Naim konforti, et al. One-dimensional superresolution optical system for temporally restricted objects[J]. Appl. Opt, 1997, 36(11): 2353~2359.
[86] Amir Shemer. Superresolving optical system with time mutiplexing and computer decoding[J]. Appl. Opt,1999,38 (35): 7245~7251.
[87] Michael S.Patterson. Time resolved reflectance and transmittance for the noninvasive measureement of tissue optical properties[J]. Appl.Opt.1989, 28 (12): 2331~2336.
[88] Kyu Yoshimori. Effects of a linear edge on optical imaging[J]. J. Opt. Soc.Am. A. 1995,12 (5): 981~990.
[89] Kyu Yoshimori. Effects of a linear edge on optical imaging:errata[J], J. Opt. Soc.Am. A, 1995,12 (11) 2540~2541.
[90] Dobryna Zalvidea. Quality parameters analysis of optical imaging systems with enhanced focal depth using the Wigner distribution function[J].J. Opt. Soc. Am. A.2000,17 (5): 867~873.
[91] Dobryna Zalvidea. Phase mask for spatial and temporal control of ultrashort light pulses focused by lenses[J]. J. Opt. Soc. Am. A. 2003,20 (10): 1981~1986.
[92] David Mendlovic. High-frequency enhancement by an optical system for superresolution of temporally restricted objects[J]. Opt. Lett, 1998,23 (10): 801~803.
[93] Edmund Y. Lam. Noise in superresolution reconstruction [J]Opt. Lett, 2003, 28 (22):2234~2237.
[94] Martin J. Bastiaans Moments of the Wigner distribution of rotationally symmetric partially coherent light[J]. Opt.Lett, 2003, 28 (24): 2443~2445.
[95] Tan Chunkan, Tao Chunkuang. Information Theory in Optics [M]. Beijing: Science Press (in China), 2005(1):
[96] Zhang Shulin. Scanning near-field optical microscope & its application [M].Beijing, Science Press (in China), 2003: 13~32.
[97] Fan Weijun, Zhou Bifang, Wang Haitao et al. Research of Fourier Phase in Optical Synthetic-Aperture Imaging Technique [J]. Acta Optica Sinica, 2004, 24 (3): 408~412.
[98] Zhang Cheng-yi, Tao Chun-kan. Photonics Study on Imaging Of One-Dimensional Periodic Object with Subwavelength Structure[J]. Acta Optica Sinica (in Chinese), 2006, 26 (11): 1651~1656.
[99] Daniele Contini. Photon migration through a turbid slab described by a model based on difussion approximation.1[J].theory Appl. Opt. 1997, 36 (19): 4587~4599.
[100] Miguel Moscoso. Depolarization and blurring of optical images by biological tissue[J].JOpt. Soc.Am. A. 2001, 18 (4) 948~960.
[102] Liu Songhao, Li chunfei. Photonics technology and application[M].Guangdong science & Technology Press(in Chinese), 2006(1): 625~709.
[103] Anthony J. Devaney and Pengyi Guo. Superresolution imaging from limited-aperture optical diffracted field data [J]. J. Opt. Soc. Am. A, 2005, 22 (6): 1086-1092.
[105] Wang Hu. Method for Testing Laser Collimation Using Talbot Effect[J].Optics & Optoelectronic Technology(in China),2004,2(3):25~27.
[106] Zhao Kang, Cheng Huai Xin. Methods for measuring the long focal length of lens based on Talbot effect and moire technique[J]. China Measurement Technology(in China),2004,30(6):24~26.
[107] Hu Han-hui, Liao Zhao-shu. A approach to the moire fringe with double frequency grating[J].J. Huazhong Univ. of Sci. & Tech.(Nature Science Edition) 2005, 33(3): 72~74.
[108] Vardit Eckhouse. Subwavelength structure imaging[J].Opt. Eng, 2004,43 (10): 2462~2468.
[109] A. Gammal, A.M. Kamchatnov. Temporal Talbot effect in interference of matter waves from arrays of Bose-Einstein condensates and trasition to Fraunhofer diffraction[J]. Phys. Lett. A, 2004, 324: 227~234.
[110] Laura Chantada, Carlos R. Fernandez-Pousa, Carlos Gomez-Reino.Theory of the partially coherent temporal Talbot effect[J]. Opt. Commun, 2006, 266, 393~398.