相干衍射成像的数学唯一解问题研究  

Underlying Mathematical Mechanism of Coherent Diffraction Imaging Technique

作　　者：吴丽青 昌成成 陶华[1,2] 何小亮[1,2] 刘诚 朱健强[1,2] Wu Liqing;Chang Chengcheng;Tao Hua;He Xiaoliang;Liu Cheng;Zhu Jianqiang(Key Laboratory of High Power Laser and Physics,Shanghai Institute of Optics and Fine Mechanics,Chinese Academy of Sciences,Shanghai 201800,China;National Laboratory on High Power Laser and Physics,China Academy of Engineering Physics,Chinese Academy of Sciences,Shanghai 201800,China;University of Chinese Academy of Sciences,Beijing 100049,China)

机构地区：[1]中国科学院上海光学精密机械研究所中国科学院高功率激光物理重点实验室,上海201800 [2]中国科学院中国工程物理研究院高功率激光物理联合实验室,上海201800 [3]中国科学院大学,北京100049

出　　处：《中国激光》2024年第19期303-331,共29页Chinese Journal of Lasers

基　　金：国家自然科学基金(61827816)。

摘　　要：相干衍射成像(CDI)作为主流的无透镜计算成像迭代技术,一直被广泛地应用于生物成像、波前诊断、光学元件测量等领域。基于CDI和Ptychography技术,Ptychographic Iterative Engine(PIE)技术极大地提高了成像质量和收敛速度。随后,研究人员基于相干衍射成像技术发展了多模态相干调制成像、三维PIE技术、分束编码成像等技术,并将这些技术用于可见光、X射线、紫外光、太赫兹等波段的相位恢复和波前测量。长期以来的相干衍射成像技术缺乏明确的数学解析计算公式和定量的误差分析理论,极大地限制了其作为测量仪器在光学测量和计量等领域的发展和应用。为研究和解决相干衍射成像技术的数学唯一解问题,本课题组建立了一套完备的相干衍射成像系统的底层数学理论模型,计算了CDI、CMI、3PIE、多模态PIE及ePIE等算法的数学解析解,确定了成像中唯一解的条件,为相干衍射成像及其衍生技术的发展和应用奠定了数理基础。Significance Coherent diffraction imaging(CDI),a lensless imaging technique,is mainly developed to reconstruct the complex amplitude of objects with simple optical paths.Combining CDI and Ptychography,Rodenburg proposed a Ptychographic Iterative Engine(PIE)in 2004,which scans the sample through a localized probe light to a raster of positions and records all diffraction intensities formed in a far field.The complex amplitude of the object under observation can be reconstructed accurately and promptly with proper overlapping between two neighboring illuminated regions.As a powerful phase retrieval method,the PIE algorithm has been widely applied in bioimaging,wavefront diagnosis,and optical elements measurement.Presently,the PIE has been successfully realized with a high energy electron beam,X-ray,visible light,and terahertz wave.Applying the multi-slice theory of electron microscopy,three-dimensional(3D)imaging can also be realized with the PIE by regarding a 3D object as a series of 2D infinitely thin layers.In comparison with traditional 3D imaging methods such as optical coherent and magnetic resonant tomography,which generates intensity images,the 3D PIE(3PIE)can provide a high quality 3D phase image for a transparent volume object rapidly.A single-shot 3PIE was also realized by recording a sub-diffraction patterns array with one detector exposure,making 3D phase imaging for dynamic imaging possible.The coherence of synchrotron radiations is not as ideal as that of common laser beams,and a clear reconstruction was not available for the common G-S algorithm,Fienup’s algorithms,standard PIE algorithm,and coherent modulation imaging(CMI)algorithm in most of cases.By treating the recorded incoherent intensity I(x,y)as the summation of several coherent diffraction patterns of different wavelengths as I_(0)(x,y)=Σ_(n) I(λ_(n),x,y),the light field of each wavelength can be reconstructed separately using the synchronized constrainΣ_(n) I'(λ_(n),x,y)/I_(0)(x,y)I'(λ_(n),x,y).This is the principle of multimode PI

关 键 词：光计算 计算成像 相干衍射成像 相位恢复 唯一解 

分 类 号：O438[机械工程—光学工程]