周期结构成像理论及其应用研究
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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.
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
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