本篇論文將針對晶片型輔助干涉儀對Swept Source - Optical Coherence Tomography (SS-OCT)系統量測結果之影響作探討。首先架設光纖型SS-OCT，量測其縱向解析度，之後用晶片型分光能量器Mach-Zehnder Directional Coupler (MZDC)替代光纖型，量測其縱向解析度。MZDC是以Mach-Zehnder Interferometer為架構，使用延遲長度造成相位差，但延遲長度對製程非常敏感，因此提出用變線寬的方式來做相位延遲，並將變線寬之製程不敏感MZDC加入Lattice Filter，使Lattice Filter之輸出波型能補償Grating Coupler所造成頻寬之不平整，進而恢復SS-OCT的影像解析度。若使用1285-1325 nm波長之SS-OCT系統光源，其理想縱向解析度為21.287 µm，實際量測全光纖型SS-OCT系統，縱向解析度為24.62 µm。為了探討晶片型Grating Coupler的效應，我們將光纖型SS-OCT的主干涉儀中，分別加入兩個Grating Coupler 的晶片型矽直波導，與兩個Grating Coupler晶片型Lattice Filter，其縱向解析度分別為47.2 µm和38.25 µm。實驗結果可以看出兩個Grating Coupler 使SS-OCT系統的縱向解析度劣化近23 µm，而Lattice Filter使縱向解析度恢復近9 µm。
本篇論文也將設計晶片型輔助干涉儀以修正光源之非線性特性，晶片型輔助干涉儀最重要參數就是兩輸出之隔離度以及延遲長度，隔離度將會影響到使用平衡光電偵測器(Balanced Photodetection)的訊雜比，延遲長度則與訊號重採樣有關，同時此晶片型輔助干涉儀必需和主干涉儀同時測量，才能使它們有相同的Time Clock。晶片型輔助干涉儀實驗將會採用Hilbert Transformation，將瞬時相位擷取出來，並透過相位延展(unwrap)使其連續，以修正主干涉儀由非線性組成之干涉波包。
實驗結果顯示非線性掃頻雷射對於SS-OCT系統有顯著的影響，在未使用輔助干涉儀系統所量測之光纖型分光能量器，其點擴散函數約為34.3 µm，使用光纖型輔助干涉儀所量測的點擴散函數約為16.4 µm，而晶片型輔助干涉儀所量測點擴散函數約為16.8 µm，此說明輔助干涉儀設計在晶片上會有相同的效果且還能解決光纖型體積過大的問題。若使用晶片型分光能量器與光纖型輔助干涉儀，點擴散函數約為25.3 µm，此劣化的解析度是從波導之Grating Coupler而來。

This thesis experimentally investigates the effect of a chip-based auxiliary interferometer on the swept source-optical coherence tomography (SS-OCT) system. A fiber-optic SS-OCT is first set up to measure the axial resolution and then followed by a replacement of the chip-based optical power splitter, Mach-Zehnder Directional Coupler (MZDC). The MZDC uses the Mach-Zehnder Interferometer architecture with the delay length for phase differences. However, the delay length is susceptible to process variation. Therefore, utilizing the variable linewidth as the phase delay for process-insensitive MZDC is proposed. Then a lattice filter composed of this MZDC could make the output waveforms compensate for the uneven bandwidth caused by the grating coupler and then restore the SS-OCT image resolution. The ideal axial resolution of the SS-OCT system is 21.3 µm when using a 1285-1325 nm wavelength light source, and the experimental axial resolution of the fiber-type SS-OCT system is 24.62 µm. To investigate the effect of the chip-based grating couplers, we implement two grating couplers-constructed silicon waveguides and lattice filters into the main interferometer of the fiber-type SS-OCT system with axial resolutions of 47.2 µm and 38.25 µm, respectively, in experiments. Two Grating Couplers degraded the axial resolution of the SS-OCT system by nearly 23 µm. In contrast, the lattice filters could restore the axial resolution to about 9 µm.
In this thesis, we will also design a chip-based auxiliary interferometer to correct the light source nonlinearity. The most important parameters of the chip-based auxiliary interferometer are the output isolations and delay length. The isolation will affect the signal-to-noise ratio of the balanced photodetection, and the delay length is related to the signal resampling. The chip-based auxiliary interferometer must be measured simultaneously with the main interferometer to have the same time clock. The chip-based auxiliary interferometer will use Hilbert Transformation to extract the instantaneous phase and make it continuous by unwrapping to correct the nonlinear composition of the interference wave packet of the main interferometer.
The experimental results show that the nonlinear swept-frequency laser significantly affects the SS-OCT system. The point spread function of the fiber-type beam splitter without resampling is about 34.3 µm, which can be resampled and corrected as 16.4 µm and 16.8 µm, respectively, through the fiber-based and chip-based auxiliary interferometers. The chip-based auxiliary interferometer indicates the state-of-the-art resolution and also solves the problem of the large size of the fiber-based OCT. Finally, a chip-based beam splitter is resampled with a fiber-optic auxiliary interferometer. The point spread function is about 25.3 µm, and this degradation in resolution comes from the non-flat Grating Coupler wavelength response.

參考文獻
[1] 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.
[2] J. T. Vaughan., C. Snyder, L. DelaBarre, J. Tian, C. Akgun, K. Ugurbil, C. Olson, and A. Gopinath, “Current and Future Trends in Magnetic Resonance Imaging (MRI),” in 2006 IEEE MTT-S International Microwave Symposium Digest, 11-16 June , pp. 211-212,2006.
[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, 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] D. G. Winters, J. Speirs, E. Block, R. A. Bartels, and J. A. Squier, “High-Speed Two-Dimensional Multiphoton Microscope using Spatial Modulation,” in Conference on Lasers and Electro-Optics 2012, San Jose, California, 2012/05/06: Optical Society of America, in OSA Technical Digest,JW3G.1,2012.
[6] M. Rajadhyaksha, “Confocal microscopy of skin cancers: translational advances toward clinical utility,” (in eng), Annual International Conference of the IEEE Engineering in Medicine and Biology Society, vol. pp. 3231-3, 2009.
[7] S. F. Silva, A. Batista, J. P. Domingues, M. J. Quadrado, and M. Morgado, “Fluorescence lifetime microscope for corneal metabolic imaging,” in 2015 IEEE 4th Portuguese Meeting on Bioengineering (ENBENG), 26-28 Feb., pp. 1-5, 2015.
[8] Taiwan Instrument Research Institute Website,
https://www.tiri.narl.org.tw/Publication/InstTdy_Full/2356?PubId=224, September 2020.
[9] A. F. Fercher, W. Drexler, C. K. Hitzenberger, and T. Lasser, “Optical coherence tomography-principles and applications,” Reports on Pogress in Pysics, vol. 66, no. 2, p. 239, 2003.
[10] S. Jiang, et al. "Absolute distance measurement using frequency-scanning interferometry based on hilbert phase subdivision," Sensors, 19, 23, 5132, 2019.
[11] B. Shao, , Q. Tan, , W. Zhang, , D. Liang, , X. Deng, , B. Zhang, , & W. Zhang. Chip-based microwave-photonic LiDAR for high-sp eed ranging and velocimetry. In Advanced Sensor Systems and Applications XII (Vol. 12321, pp. 38-43). SPIE,2022.
[12] 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.
[13] M. E. Brezinski, Optical coherence tomography: principles and applications. Elsevier, 2006.
[14] T. Latychevskaia, "Lateral and axial resolution criteria in incoherent and coherent optics and holography, near-and far-field regimes," Applied Otics, vol. 58, no. 13, pp. 3597-3603, 2019.
[15] T. Fountoukidou, P. Raisin, D. Kaufmann, J. Justiz, R. Sznitman, and S. Wolf, “Motion-invariant SRT treatment detection from direct M-scan OCT imaging,” International Journal of Computer Asisted Rdiology and Srgery, vol. 13, no. 5, pp. 683-691, 2018.
[16] H. Imam, “Microscopy/ophthalmology/supercontinuum lasers: supercontinuum light empowers research, biomedicine,” Biooptics world, 2014.
[17] W. Drexler, ,& J. G. Fujimoto, (Eds.). Optical coherence tomography: Tchnology and Aplications. Springer Science & Business Media 2008.
[18] S. k. Selvaraja and P. Sethi, “Review on Optical Waveguides,” Emerging Waveguide Technology, 2018.
[19] 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.
[20] C.S. Phun ,P.E. Ching , L.T. Soon , 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.
[21] T. Aalto, “Microphotonic silicon waveguide components,” VTT Technical Research Centre of Finland, 2004.
[22] A. Dewanjee , J. N. Caspers , J. S. Aitchison, & M. Mojahedi, “ Demonstration of a compact bilayer inverse taper coupler for Si-photonics with enhanced polarization insensitivity. Optics express, 24(25), 28194-28203,2016.
[23] H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, “Optical directional coupler based on Si-wire waveguides,” IEEE Photonics Technology Letters, vol. 17, no. 3, pp. 585-587, 2005.
[24] D Taillaert,, P. Bienstman, , & R. Baets, Compact efficient broadband grating coupler for silicon-on-insulator waveguides. Optics letters, 29(23), 2749-2751,2004.
[25] 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.
[26] H. Yamada, T. Chu, S. Ishida, and Y. Arakawa, "Optical directional coupler based on Si-wire waveguides," IEEE Photonics Technology Letters, vol. 17, no. 3, pp. 585-587, 2005.
[27] S. Bidnyk, , D. Feng, A. Balakrishnan, M. Pearson, M. Gao , H. Liang, ... & M. Asghari,. Silicon-on-insulator-based planar circuit for passive optical network applications. IEEE Photonics Technology Letters, vol. 18, no. 22, 2392-2394,2006.
[28] [Online]. Available: https://www.thorlabs.com/thorproduct.cfm?partnumber= PDB450C-AC.
[29] B. E. Little and Murphy, “Design rule for maximally flat wavelength-insensitive optical power dividers using Mach-Zehnder structures,” IEEE Photonics Technology Letters, vol. 9, no. 12, pp.1607-1609, 1997.