數位全像顯微術在照明光源正向入射下所形成的空間頻率響應，係由入射光源的波長，以及光學元件的有限孔徑大小所決定，並且，該空間頻率截止的最大值將會受限於光學繞射極限的二分之一波長，因此，本論文提出數種以合成孔徑方法為基礎的光學多工技術來提供不同角度的斜向入射，這將可拓展光學系統的空間頻率涵蓋範圍，同時實現橫向分辨率的解析度提升，藉以應用於量測奈米結構樣本與未染色的活體生物細胞。 首先，本研究工作在合成孔徑式的數位全像顯微術之中，提出了可調式反切趾窗型函數來抑制不同角度入射光波的頻譜堆疊所引發的低頻擴張，並藉此訊號處理方法達成頻譜歸一化以還原合成頻譜的高頻訊號，相較於使用高速掃瞄振鏡與攝像機的合成孔徑方法，本研究可拍攝少張不同角度入射光波並配合反切趾窗型函數於實現未染色活體生物細胞的解析度提升成像。 接著，為實現光學多工式的合成孔徑數位全像顯微術，我們提出了使用角度-偏振多工的光學定址式解析度提升成像，此方法可透過二值化相位光柵來達成角度多工的入射光波，並配合偏振調制以產生彼此正交的線性偏振態光波，相對於傳統機械式掃瞄振鏡方法，以液晶空間光調制器為主的光學定址式解析度提升成像方法，將可提升全像片的訊息容量以同時記錄兩道光波資訊並可免除機械式的擾動。 再者，為建構緊密的光學掃瞄系統配置，以及探討不同角度入射光波的光學像差對於合成孔徑的解析度提升成像之影響，我們提出了使用液晶空間光調制器來減少遠焦成像系統所需的光學透鏡組，並輸出相位式菲涅耳透鏡與閃耀光柵所結合的電腦全像片來進行光學定址式的角度多工，同時，透過數位全像的波前感測來偵測不同角度入射光波的光學像差種類，最後，該波前感測的光學像差將使用澤尼克多項式繪製，再反饋至液晶空間光調制器以實現光學定址式的光學像差修正。 最後，本研究工作提出使用結構光照明方式以產生相同偏振態、不同角度的入射光波，並配合編碼孔徑實現空間相位移式的結構光成像，同時，使用壓縮感測演算法以恢復該資訊遺失的解碼孔徑區域，以實現單次曝光的解析度提升成像，這將能免除傳統時間多工式結構光照明在相位移上的耗時程序，以及角度-偏振多工方式在量測具非均向性材質與相位延遲樣本的限制。

The spatial frequency response of digital holographic microscopy at central illumination condition is determined by the wavelength of light source and the finite aperture size of optical components, besides, the maximal spatial frequency cutoff is restricted by the optical diffraction limit to one-half of the wavelength. Therefore, this work proposed several of optical-multiplexing techniques based on the synthetic aperture method to provide oblique illumination at different angles, and thus extend the spatial frequency coverage along with realization of the resolution enhancement on the lateral resolution for applications on measure nanostructures and unlabeled biological living cell. First, this research work purposed an adjustable inverse apodization window function to suppress the low-frequency expansion from spectrum overlapping with different angle of incidence waves, and thus perform the spectrum normalization for revealing high-frequency signal of synthetic spectrum in the synthetic aperture digital holographic microscopy. In comparison to high speed galvo-mirror and camera based synthetic aperture method, purposed method is capable of realizing resolution enhanced imaging of label-free living cell by a few different angle of incidence waves with the inverse apodization window function. Then, to realize the optical-multiplexing technique in synthetic aperture digital holographic microscopy, we proposed the angular-polarized multiplexing with optical addressing resolution enhanced imaging. This method employed the binary phase grating to perform the angular-multiplexed illumination wave and the polarization modulation with orthogonally linear polarization state. In comparison to tradition mechanical galvo-mirror based method, the spatial light modulator based optical addressing resolution enhanced imaging method can enlarge the information capacity in the digital hologram and simultaneously record two object wave without mechanical perturbation. In addition, for compacting the optical steering system configuration and analyzing the optical aberration from oblique illumination on influence upon synthetic aperture resolution enhanced imaging. Spatial light modulator is introduced to decrease the usage optical lens set in the 4-f telescope system and display the merged phase Fresnel lens with phase blazed grating for optical addressing angular-multiplexing. In the meantime, through the digital holographic wavefront sensing on different angles of incidence waves, the Zernike polynomial optical aberration model is mapped and display on the spatial light modulator for realizing optical addressing wavefront aberration correction. Finally, we proposed the structured illumination method to generate the same polarization state, different angle of incidence waves and applied the coded aperture to implement the spatial phase shifting structured illumination imaging and the compressive sensing algorithm is used to recover the missing data in the decoded aperture region, and thus perform single-shot resolution enhanced imaging. Then, the time consumed temporally phase shifting structured illumination and the restriction of angular-polarization multiplexing on measure the anisotropic material and phase retardation object can be avoided.

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Journal Papers
1. Y.-C. Lin, Y.-T. Lee, X.-J. Lai, C.-J. Cheng, and H.-Y. Tu “In situ Mapping of Light-induced Refractive Index Gratings by Digital Holographic Microscopy,” Jpn. J. Appl. Phys 49, 10251 (2010).
2. H.-Y. Tu, X.-J. Lai, C.-J. Cheng, and L.-C. Lin, “Color Reproduction of Multi-wavelength digital holography using a color correction algorithm,” Jpn. J. Appl. Phys. 50, 060207 (2011).
3. L.-C. Lin, H.-Y. Tu, X.-J. Lai, Y.-L. Huang, and C.-J. Cheng, “Color correction for chromatic distortion in a multi-wavelength digital holographic system,” J. Opt. 13, 055401 (2011).
4. L.-C. Lin, H.-Y. Tu, X.-J. Lai, S.-S. Wang, and C.-J. Cheng, “Fluid surface compensation in digital holographic microscopy for topography measurement,” J. Mod. Optic 59(11), 992-1001 (2012).
5. C.-J. Cheng, W.-J. Hwang, C.-T. Chen, and X.-J. Lai, “Efficient FPGA-based Fresnel transform architecture for digital holography,” J. Disp. Technol. 10(4), 272-281 (2014).
6. C.-H. Wu, X.-J. Lai, C.-J. Cheng, Y.-C. Yu, and C.-Y. Chang, “Novel applications of digital holographic microscopy in therapeutic evaluation of Chinese herbal medicines,” Appl. Opt. 53(27), G192-G197 (2014).
7. X.-J. Lai, H.-Y. Tu, C.-H. Wu, Y.-C. Lin, and C.-J. Cheng, “Resolution enhancement of spectrum normalization in synthetic aperture digital holographic microscopy,” Appl. Opt. 54(1), A51-A58 (2015).
8. X.-J. Lai, C.-J. Cheng, Y.-C. Lin, and H.-Y. Tu, “Angular-polarization multiplexing with spatial light modulators for resolution enhancement in digital holographic microscopy,” J. Opt. 19, 055607 (2017).
9. H.-Y. Tu, W.-J. Hsiao, X.-J. Lai, Y.-C. Lin, and C.-J. Cheng, “Synthetic aperture common-path digital holographic microscopy with spiral phase filter,” J. Opt. 19, 065604 (2017).
10. X.-J. Lai, H.-Y. Tu, Y.-C. Lin, and C.-J. Cheng, “Coded aperture structured illumination digital holographic microscopy for superresolution imaging,” Opt. Lett. 43(5), 1143-1146 (2018).
11. Vinoth B., X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Integrated dual-tomography for refractive index analysis of free-floating single living cell with isotropic superresolution,” Scientific Reports 8, 5943 (2018).
12. Y.-C. Lin, H.-Y. Tu, X.-R. Wu, X.-J. Lai, and C-J Cheng, “One-shot synthetic aperture digital holographic microscopy with non-coplanar angular-multiplexing and coherence gating,” Opt. Express 26(10), 12620-12631 (2018).
 
Conference Papers
1. X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Coded structured illumination with compressive sensing for resolution enhancement in digital holographic microscopy,” Optics & Photonics Taiwan International Conference 2017 (OPTIC2017), Kaohsiung, Taiwan, 2017.
2. X.-J. Lai, Y.-C. Lin, and C.-J. Cheng, “Low-frequency moiré fringes synthesize by mutual correlation for resolution enhancement in structured illumination digital holographic microscopy,” Digital Holography & 3-D Imaging (DH2017), Jeju Island, South Korea, 2017.
3. X.-J. Lai, W.-J. Hsiao, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Synthetic aperture common-path digital holographic microscopy based on spiral phase filter,” International Workshop on Holography and related technologies (IWH2016), Jiaoxi, Yilan, Taiwan. [Student Paper Award]
4. X.-J. Lai, H.-Y. Tu, and C.-J. Cheng, “Resolution enhancement of digital holographic microscopy based on structured-illumination induced moiré fringes,” International Workshop on Holography and related technologies (IWH2016), Jiaoxi, Yilan, Taiwan.
5. X.-J. Lai, H.-Y. Tu, Y.-C. Lin, and C.-J. Cheng, “Structured illumination induced moiré fringes for resolution enhancement in digital holographic microscopy,” Digital Holography & 3-D Imaging (DH2016), Heidelberg, Germany, 2016.
6. X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Resolution enhancement by structured-illumination induced moiré effect in digital holographic microscopy,” Optics & Photonics Taiwan International Conference 2015 (OPTIC2015), Hsinchu, Taiwan, 2015.
7. X.-J. Lai, H.-Y. Tu, Y.-C. Lin, and C.-J. Cheng, “Angular- and polarization-multiplexing with spatial light modulators in digital holographic microscopy,” Optics & Photonics Taiwan, International Conference Taiwan 2014 (OPTIC2014), Taipei, Taiwan, 2014. X.-J. Lai, C.-J. Cheng, H.-Y. Tu, and L.-C. Lin, “Resolution enhancement in synthetic aperture digital holographic microscopy,” OSA Imaging and Applied Optics Congress: Topical Meeting on Digital Holography and Three-dimensional Imaging (DH2014), Seattle, USA, 2014.
8. X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Superresolution Imaging in Scanning Synthetic Aperture Digital Holographic Microscopy,” Optics & Photonics Taiwan International Conference 2013 (OPTIC2013), Chung-Li, Taiwan, 2013. [Student Paper Award]
9. X.-J. Lai, Y.-L. Lee, H.-Y. Tu, and C.-J. Cheng, “Scanning synthetic aperture for all-in-one digital holographic microscopy,” Optics & Photonics Taiwan, International Conference (OPTIC2012), Taipei, Taiwan, 2012.
10. X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Beam-rotation tomographic imaging of digital holographic microscopy,” International Photonics Conference (IPC2011), Tainan, Taiwan, 2011.
11. X.-J. Lai, Y.-C. Lin, H.-Y. Tu, and C.-J. Cheng, “Multimodality imaging of digital holographic microscopy,” The 30th Progress In Electromagnetics Research Symposium (PIERS2011), Suzhuo, China, 2011.
 
Patents
1. 鄭超仁，林昱志，賴信吉，影像處理方法，中華民國發明專利：證書號I537876（2016年06月11日）。
2. 鄭超仁，劉晉宇，賴信吉，透明基板之瑕疵檢測方法與裝置，中華民國發明專利：申請號106100291（2017年01月05日）。