光學同調斷層掃描(Optical Coherence Tomography, OCT)為一種即時高速且為非侵入式之成像技術，透過麥克森干涉儀量測參考端與樣品端之背向散射進行干涉後則可獲得微米等級之解析度影像，目前廣泛運用於牙科、眼科以及血管造影等領域。OCT系統雖具有以上優點，但此系統體積終歸過於龐大且難以微小化，受益於矽光子發展，光學元件得以積體化、降低成本且增加穩定性。目前世界研究之OCT系統積體化時，多數是將光纖寬頻耦合器以晶片型寬頻耦合器取代之，例如DC (Directional Coupler)、MMI (Multimode Interference)以及Bent DC (Bent Directional Coupler)等等，其設計多往優化平坦度、製程不敏感以及高頻寬響應方向邁進，主要原因為OCT系統之影像訊號品質度對於此要求至關重要。
本論文將利用傳輸矩陣設計馬赫詹德爾定向耦合器(Mach-Zehnder Directional Coupler, MZDC)，其中以Mach-Zehnder Interferometer (MZI)為架構且增加延遲長度以累積足夠相位差，如此則可改善DC對波長敏感之缺點且可保留調整耦合長度實現任意分光比之優點，同時擁有更高的頻寬響應。對比於MMI來說，MZDC有較低的光損耗。積體化SD-OCT (Spectral Domain - Optical Coherence Tomography)系統包含分光能量與分光波長器，在理論上，我們提出與製程誤差不敏感之雙向傳輸MZDC，再結合Echelle Grating (EG)輸出頻譜補償，以得到具有64.5 dB 之訊雜比(Signal to Noise Ratio, SNR)。
為驗證光能量耦合器波長平坦度對於OCT系統訊雜比之影響，依照平坦度優到劣依序將晶片型MZDC (Silicon Nitride) 以及MMI (Silicon Nitride) MMI (Silicon)分別搭配反射型光柵、Line CCD進行訊雜比量測。首先在SD-OCT上，計算120 nm寬頻光源之Point Spread Function (PSF)為13.13 μm，以此光源進入具有光柵耦合直波導後，其PSF為17.97 μm。之後再結合三種晶片型光能量耦合器，以反射式光柵與Line CCD，得到的訊雜比分別為 50.02 dB、44.84 dB以及 36.37 dB，此訊雜比之優劣順序與理論值相同，但絕對訊雜比實驗值低於理論計算，其原因為Line CCD之1024個偵測器陣列的Crosstalk。在SS-OCT (Swept-Source OCT)上，從波長1260 nm 至1360 nm之可調光波長雷射之PSF為8.65 μm，以此光源進入具有光柵耦合直波導後，其PSF為15.27 μm。之後再結合三種晶片型光能量耦合器，其訊雜比分別為 44.12 dB、38.6 dB以及 28.23 dB。此SS-OCT訊雜比之優劣順序與絕對訊雜SD-OCT一樣，但其原因可能來自於FMCW之可調光波長雷射之非線性效應。

Optical Coherence Tomography (OCT) is a real-time, high-speed, and non-invasive imaging technique widely used in dentistry, ophthalmology, and angiography through the interference between the reference and sample ends for micron-level resolution images. The OCT system owns the above advantages, but the system size is too large and complex to be minimized. Thanks to the development of silicon photonics, optical components can be integrated, reducing the cost and increasing their stability. Currently, most of the OCT systems studied in the world have replaced optical broadband couplers with wafer-based broadband couplers, such as DC (Directional Coupler), MMI (Multimode Interference), and Bent DC (Bent Directional Coupler). The main design optimizes operation wavelength flatness, process insensitivity, and high bandwidth response, which are essential to the OCT image signal quality.
In this thesis, the Mach-Zehnder Directional Coupler (MZDC) is designed using a transmission matrix, in which the Mach-Zehnder Interferometer (MZI) is used as the structure. The delay length is increased to accumulate sufficient phase difference to improve the wavelength-sensitive drawback of the DC. The MZDC can retain the advantage of adjusting the coupling length to achieve any splitting ratio while having a higher bandwidth response. Compared to MMI, MZDC also shows a lower optical loss. The integrated SD-OCT (Spectral Domain - Optical Coherence Tomography) system consists of optical power splitters and spectrometers. Theoretically, we present the process of error-insensitive bi-directional transmission MZDC combined with Echelle Grating (EG) output spectrum compensation to get a signal to noise Ratio (SNR) of 64.5 dB.
To verify the effect of wavelength flatness of the optical power coupler on the OCT noise, MZDC (Silicon Nitride), (Silicon Nitride), and MMI (Silicon) were integrated with refractive grating and Line CCD for SNR measurements. The point spread function (PSF) of the 120 nm broadband light source is calculated to be 13.13 μm on a fiber-based SD-OCT and 17.97 μm on an additional grating coupled optical waveguide implementation. After combining three types of chip-based optical couplers with a refractive grating and a Line CCD, the resulting SNR is 50.02 dB, 44.84 dB, and 36.37 dB, respectively. The order of superiority of this SNR is the same as the theoretical value. Still, the absolute SNR is lower than the theoretical calculation because of the 1024 detector arrays of the Line CCD crosstalk. In the swept-source OCT (SS-OCT), the PSF from 1260 nm to 1360 nm is 8.65 μm, and the PSF is 15.27 μm after the light source enters an additional grating coupled optical waveguide implementation. After combining three types of chip-based optical couplers with the balanced photodetector, the resulting SNR is 44.12 dB, 38.6 dB, and 28.23 dB, respectively. The SS-OCT SNR is in the same order as the absolute noise of SD-OCT, but the reason may come from the nonlinear FMCW modulation in the tunable wavelength laser.

[1] W. Drexler and J. G. Fujimoto, “Optical coherence tomography: technology and applications.” Springer Science & Business Media, 2008.
[2] C. F. Beckmann and S. M. Smith, “Probabilistic independent component analysis for functional magnetic resonance imaging,” IEEE Transactions on Medical Imaging, vol. 23, no. 2, pp. 137-52, Feb 2004.
[3] P. J. L. Riviere, P. Vargas, G. Fu, and L. J. Meng, “Accelerating X-ray fluorescence computed tomography,” in 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 3-6 Sept. 2009, pp. 1000-1003, 2009.
[4] V. Daeichin, K. Kooiman, I. Skachkov, J. G. Bosch, A. F. W. v. d. Steen, and N. d. Jong, “Optimization of ultrasound contrast agent for high frequency ultrasound molecular imaging using subharmonic oscillation,” in 2014 IEEE International Ultrasonics Symposium, 3-6 Sept. 2014, pp. 1766-1769, 2014.
[5] J. T. Vaughan, C. Snyder , L. D. Barre, J. Tian , C. Akgun, K. Ugurbil, C. Olson, and A, Gopinah, “Current and Future Trends in Magnetic Resonance Imaging (MRI),” in 2006 IEEE MTT-S International Microwave Symposium Digest, 11-16 June 2006, pp. 211-212, 2006.
[6] S. F. Silva, A. Batista, J. P. Domingues, M. J. Quadrado, and M. Morgado, “Fluorescence lifetime microscope for corneal metabolic imaging,” 2015 IEEE 4th Portuguese Meeting on Bioengineering (ENBENG), 2015.
[7] M. Rajadhyaksha, “Confocal microscopy of skin cancers: translational advances toward clinical utility,” 2009 Annual International Conference of the IEEE Engineering in Medicine and Biology Society, 2009.
[8] D. G. Winters, J. Speirs, E. Block, R. A. Bartels, and J. A. Squier, “High-speed two-dimensional multiphoton microscope using spatial modulation,” Conference on Lasers and Electro-Optics 2012, 2012.
[9] Taiwan Instrument Research Institute Website,
https://www.tiri.narl.org.tw/Publication/InstTdy_Full/2356?PubId=224, September 2020.
[10] M. Pircher, “Development and Application of Optical Coherence Tomography,” MDPI AG 2018- Multidisciplinary Digital Publishing Institute: Basel, Switzerland, 2018
[11] M. Rajarajan, B. M. A. Rahman, and K. T. V. Grattan, “A rigorous comparison of the performance of directional couplers with multimode interference devices,” Journal of lightwave technology, vol. 17, no. 2, p. 243, 1999.
[12] Z. Lu, H. Yun, Y. Wang, Z. Chen, F. Zhang, N. A. F. Jaeger, and L. Chrostowski “Broadband silicon photonic directional coupler using asymmetric-waveguide based phase control,” Opt. Exp., vol. 23, no. 3, pp. 3795–3808, Feb. 2015.
[13] B. E. Little and T. Murphy, “Design rules for maximally flat wavelength-insensitive optical power dividers using Mach-Zehnder structures,” IEEE Photonics Technology Letters, vol. 9, no. 12, pp. 1607-1609, 1997.
[14] S.-H. Hsu, “Signal power tapped with low polarization dependence and insensitive wavelength on silicon-on-insulator platforms,” JOSA B, vol. 27, no. 5, pp. 941-947, 2010.
[15] M. K. Smit and C. V. Dam, “PHASAR-based WDM-devices: Principles, design and applications,” IEEE Journal of selected topics in quantum electronics, vol. 2, no. 2, pp. 236-250, 1996.
[16] F. Horst, W. M. J. Green, B. J. Offrein, and Y. Vlasov, “Echelle grating WDM demultiplexers in SOI technology, based on a design with two stigmatic points,” Proc. SPIE 6996, 69960R, 69960R-8, 2008.
[17] B. I. Akca and C. R. Doerr, “Interleaved silicon nitride AWG spectrometers,” IEEE Photonics Technology Letters, vol. 31, no. 1, pp. 90-93, 2018.
[18] A. Leinse, L. Wevers, D. Marchenko, R. Dekker, R. G. Heideman, R. M. Ruis, D. J. Faber, Ton G. van Leeuwen, K. B. Kim, and K. Kim, “Spectral domain, common path OCT in a handheld PIC based system,” in Optical Coherence Tomography and Coherence Domain Optical Methods in Biomedicine XXII, 2018, vol. 10483: International Society for Optics and Photonics, p. 104831J.
[19] B. I. Akca, V. D. Nguyen, J. Kalkman, N. Ismail, G. Sengo, F. Sun, A. Driessen, Ton G. van Leeuwen, M. Pollnau, K. Wörhoff, and Rene M. de Ridder, “Toward spectral-domain optical coherence tomography on a chip,” IEEE journal of selected topics in quantum electronics, vol. 18, no. 3, pp. 1223-1233, 2011.
[20] L. Chen, C. R. Doerr, L. Buhl, Y. Baeyens, and R. A. Aroca, “Monolithically integrated 40-wavelength demultiplexer and photodetector array on silicon,” IEEE Photonics Technology Letters, vol. 23, no. 13, pp. 869-871, 2011.
[21] S. k. Selvaraja and P. Sethi, “Review on Optical Waveguides,” Emerging Waveguide Technology, 2018.
[22] R. A. Soref, J. Schmidtchen and K. Petermann, ”Large Single-Mode Rib Waveguides in GeSi-Si and Si-on-SO2,” IEEE Journal of Quantum Electronics, vol. 27, no. 8, pp. 1971-1974, 1991.
[23] Seong Phun Chan, Ching Eng Png, Soon Thor Lim, G. Reed, and V. Passaro, “Single-mode and polarization-independent silicon-on-insulator waveguides with small cross section,” Journal of Lightwave Technology, vol. 23, no. 6, pp. 2103-2111, 2005.
[24] T. Aalto, “Microphotonic silicon waveguide components,” VTT Technical Research Centre of Finland, 2004.
[25] H. Takahashi, “Wavelength multiplexer/demultiplexer (MUX/DEMUX in WDM),” in Encyclopedic handbook of integrated optics, Boca Raton, Taylor & Francis Group, pp. 483-486, 2006.
[26] A. F. Fercher, C. K. Hitzenberger, G. Kamp, and S. Y. El-Zaiat, “Measurement of intraocular distances by backscattering spectral interferometry,” Optics Communications, vol. 117, no. 1-2, pp. 43-48, 1995.
[27] W. Drexler, J. G. Fujimoto, “Optical Coherence Tomography: Technology and Applications,” Springer International Publishing AG: Berlin/Heidelberg, Germany, 2015
[28] P. Li, Y. He, and H. Ma, “Spectral-domain optical coherence tomography and applications for biological imaging,” in 2006 International Symposium on Biophotonics, Nanophotonics and Metamaterials, pp. 222-225, 2006.
[29] Z. Chen, “Fourier domain functional optical coherence tomography,” in Frontiers in Optics, 2005: Optical Society of America, p. FWA1. 2005.
[30] T. Latychevskaia, “Lateral and axial resolution criteria in incoherent and coherent optics and holography, near- and far-field regimes,” Applied Optics, vol. 58, no. 13, p. 3597, 2019.
[31] H. Imam, “Microscopy/ophthalmology/supercontinuum lasers: supercontinuum light empowers research, biomedicine,” Biooptics world, 2014.
[32] B. Bouma and G.Tearney, “Handbook of optical coherence tomography,” Marcel Dekker Inc. (New York, USA), 2002.
[33] H. M. Subhash, “Full-field and single-shot full-field optical coherence tomography: a novel technique for biomedical imaging applications,” Advances in Optical Technologies, vol. 1, pp. 1-26, 2012.
[34] A. Agrawal, T. J. Pfefer, P. D. Woolliams, P. H. Tomlins, and G. Nehmetallah, “Methods to assess sensitivity of optical coherence tomography systems,” Biomedical optics express, vol. 8, no. 2, pp. 902-917, 2017.
[35] M. Smit, “New focusing and dispersive planar component based on an optical phased array,” Electronics Letters, vol. 24, no. 7, p. 385, 1988.
[36] H. Takahashi, S. Suzuki, K. Kato, and I. Nishi, “Arrayed-waveguide grating for wavelength division multi/demultiplexer with nanometre resolution,” Electronics Letters, vol. 26, no. 2, p. 87, 1990.
[37] R. Adar, C. Henry, C. Dragone, R. Kistler, and M. Milbrodt, “Broad-band array multiplexers made with silica waveguides on silicon,” J. Lightw. Technol., vol. 11, no. 2, pp. 212–219, Feb. 1993.
[38] H. Bissessur, F. Gaborit, B. Martin, P. Pagnod Rossiaux, J.-L Peyre, and M. Renaud, “16 channel phased array wavelength demultiplexer on InP with low polarization sensitivity,” Electron. Letters, vol. 30, no. 4, pp. 336–337, Feb. 1994.
[39] A. Malik, M. Muneeb, S. Pathak, Y. Shimura, J. V. Campenhout, and R. Loo, “Germanium-on-silicon mid-infrared arrayed waveguide grating multiplexers,” IEEE Photon. Technol. Lett., vol. 25, no. 18, pp. 1805–1808, Sep. 2013.
[40] S. Cheung, T. Su, K. Okamoto, and S. J. B. Yoo, “Ultra-Compact Silicon Photonic 512 × 512 25 GHz Arrayed Waveguide Grating Router,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 20, no. 4, pp. 310-316, 2014.
[41] D. Seyringer, M. Sagmeister, A. Maese-Novo, M. Eggeling, E. Rank, P. Muellner, R. Hainberger, W. Drexler, M. Vlaskovic, H. Zimmermann, G. Meinhardt, and J. Kraft, “Technological verification of size-optimized 160-channel silicon nitride-based AWG-spectrometer for medical applications,” Appl. Phys. B 125(6), 88, 2019.
[42] Y. Hibino, “Recent advances in high-density and large-scale AWG multi/demultiplexers with higher index-contrast silica-based PLCs,” IEEE Journal of Selected Topics in Quantum Electronics, vol. 8, no. 6, pp. 1090-1101, 2002.
[43] H. Talahashi, K. Oda, H. Toba, and Y. Inoue, “Transmission characteristics of arrayed waveguide N×N wavelength multiplexer,” Journal of Lightwave Technology, vol. 13, no. 3, pp. 447-455, 1995.
[44] S. Pathak, P. Dumon, D. Van Thourhout, and W. Bogaerts, “Comparison of AWGs and Echelle Gratings for Wavelength Division Multiplexing on Silicon-on-Insulator,” IEEE Photonics Journal, vol. 6, no. 5, pp. 1-9, 2014.
[45] J. B. D. Soole, M. R. Amersfoort, H. P. LeBlanc, N. C. Andreadakis, A. Rajhel, C. Caneau, R. Bhat, M. A. Koza, C. Youtsey, and I. Adesida, “Use of Multimode Interference Coupler to Broaden The Passband of Wavelength-Dispersive Intergrated WDM Filters,” IEEE Photonics Technology Letters, vol. 8, no. 10, pp. 1340-1342, 1996.
[46] K. Takada, Y. Inoue, H. Yamada, and M. Horiguchi, “Measurement of phase error distributions in silica-based arrayed-waveguide grating multiplexers by using Fourier transform spectroscopy,” Electronics Letters, vol. 30, no. 20, pp. 1671-1672, 1994.
[47] H. Yamada, “Crosstalk reduction in a 10-GHz spacing arrayed-waveguide grating by phase-error compensation,” Journal of lightwave technology, vol. 16, no. 3, p. 364, 1998.
[48] J. Brouckaert , W. Bogaerts, P. Dumon, D. V. Thourhout, and R. Baets, “Planar concave grating demultiplexer fabricated on a nanophotonic silcon-on-insulator platform,” Journal of Lightwave Technology, vol. 25, no. 5, pp. 1269-1275, 2007.
[49] J. Chen, Y. Yang, and N. Zhu, “Echelle grating based mode demultipexer for vertical mode-division multiplexing,” Opt. Express 24, pp. 24509-24516, 2016.
[50] D. Melati, P. G. Verly, A. Delage, S. Wang, J. Lapointe, P. Cheben, J. H. Schmid, S. Janz, and D.-X. Xu, “Compact and low crosstalk echelle grating demultiplexer on silicon-on-insulator technology,” Electronics 8, 687, 2019.
[51] E. F. Schibert, Light-emitting diodes, 2nd ed., New York: Cambridge University Press, 2006.
[52] J.-m. Liu, Photonic Devices, New York: Cambridge University Press, 2005.
[53] B.I. Akca, “Spectral-domain optical coherence tomography on a silicon chip,” Ph. D. thesis, Universiteit Twente, 12, 2012.
[54] J.-M. Liu, Photonic devices. Cambridge University Press, 2009.
[55] K. Jinguji, N. Takato, A. Sugita, and M. Kawachi, “Mach-Zehnder interferometer type optical waveguide coupler with wavelength-flattened coupling ratio,” Electronics Letters, vol. 26, no. 17, pp. 1326-1327, 1990.
[56] Y. P. Li and C. Henry, “Silica-based optical integrated circuits,” IEE Proceedings-Optoelectronics, vol. 143, no. 5, pp. 263-280, 1996.
[57] H.-Y. Zheng, B.-L. Cheng, H.-Y. Lu, S.-H Hsu, and M. Takabayashi, “Bidirectional Coupler Study for Chip-Based Spectral-Domain Optical Coherence Tomography,” Micromachines, vol. 13, no. 3, pp. 4-5, 2022.
[58] H. Li, Y. Bai, X. Dong, E. Li, Y. Li, W. Zhou, and Y. Liu, “Practical fabrication and analysis of an optimized compact 8-channel silicon arrayed waveguide grating,” Optical Engineering, 52(6), 064602, 2013.