臺灣博碩士論文加值系統

光學同調斷層掃描(OCT)是一種具有微米級的解析度和高速三維成像的重要診斷工具。OCT系統通過測量反射光和背向散射光之間的干涉來獲取訊號，主要應用於眼科、牙科、皮膚病學和血管造影等醫學領域。儘管OCT具有即時和高解析度檢測功能，但整個系統體積龐大且昂貴。隨著矽光子學的發展，光學元件的進一步微小化和積體化可以降低成本並大量生產。
本文於絕緣層上覆矽(SOI)基板上，設計傅立葉域OCT中的被動元件。由於SOI
基板上的OCT元件易受製程誤差影響，因此我們應用了一種稱為色散補償和反相測量(DCOPM)的數位校準程序。此方法可以從重新取樣中的誤差和系統的不平衡色散中，檢測出非線性相位，從而維持OCT訊號的縱向解析度，且可優化DCOPM方法中的校準長度，以在數位的相位檢測法中，獲得最小相位誤差。
為了設計積體化干涉儀，我們使用了串聯型Mach-Zehnder方向耦合器 (TMZDC)配置。與傳統的方向耦合器相比，TMZDC有更多的參數，以優化為具有寬頻且平坦的波長響應。我們比較了採用疊代法和粒子群最佳化演算法(PSO)設計的TMZDC，最佳化之TMZDC可以進一步將耦合器的寬頻平坦響應擴展到 200nm (中心波長為1310nm)。由於OCT中的干涉儀為麥克森配置，因此我們設計了基於PSO的雙向寬頻耦合器，如此可提供平坦的傳輸和反射響應。在類似OCT訊號之雙向寬頻耦合器模擬結果表明，該耦合器的性能優於常規的基於PSO的單向TMDZC。
光譜儀是SD-OCT系統的另一個主要組成部分，SD-OCT系統的縱向解析度、最大成像範圍和訊號衰減皆取決於光譜儀的設計。為了維持SD-OCT的性能，陣列波導光柵(AWG)之FSR需與光源光譜相似且具有較高的波長解析度。直接設計與光源光譜相似之AWG的FSR是不切實際的，因為焦距過長以致超過晶片尺寸，為此，串聯AWG能夠最小化10倍以上的尺寸，同時保持SD-OCT性能。通常基於光柵的輸出強度會因其遠場響應而有類似高斯曲線，此響應會降低SD-OCT之縱向解析度，因此在系統中導入另一種基於PSO的U形頻譜輸出之MZDC耦合器，並置於AWG輸入之前，如此可以補償AWG內部的高斯遠場波長強度，從而保持晶片型SD-OCT之縱向解析度的性能。

Optical Coherence Tomography (OCT) is an important diagnostic tool with micrometer resolution and high-speed three-dimensional imaging. OCT system gets the signal by measuring the interference between reflected light and back-scattered light. OCT is mainly used in medical fields such as ophthalmology, dentistry, dermatology, and angiography. Although OCT has real-time and high-resolution detection functions, the entire system is bulky and expensive. With the development of silicon photonics, the further miniaturization and integration of optical components can reduce costs and support mass production.

In this thesis, passive devices in Fourier-domain OCT are designed to be operated on a SOI (silicon-on-insulator)-platform. Since the SOI-based platform OCT is susceptible to fabrication error, a digital calibration procedure is experimentally demonstrated through dispersion compensation by opposite phase measurement (DCOPM), which could detect the phase non-linearity from error in resample and unbalance dispersion from the system, hence maintaining axial resolution from the OCT signal. The calibration length in the DCOPM method can also be optimized to obtain a minimum phase error in digital phase detection.

To design the integrated interferometer, we used a tandem Mach-Zehnder directional coupler (TMZDC) based configuration. In contrast with the traditional directional coupler, TMZDC has more parameters to be easily optimized to achieve a flat wavelength response in a broadband wavelength region. A TMZDC with the iteration approach is compared with an optimization-based method. The optimization-based TMZDC could further extend the broadband flatness response of the coupler up to 200 nm in a 1310 nm wavelength range. Since the OCT interferometer is using the Michelson configuration, we developed a PSO (particle swarm optimization)-based bidirectional broadband coupler to provide flat transmission and reflection response. The simulation result of OCT-like signal in bidirectional broadband coupler is better than the regular unidirectional PSO-based TMDZC.

The spectrometer is another main component in a spectral-domain OCT (SD-OCT) system. The axial resolution, maximum imaging range, and signal fall-off of the SD- OCT system depend on the spectrometer design. To maintain SD-OCT performance, we need to design an arrayed waveguide grating (AWG) FSR similar to the light source spectrum, and a small wavelength resolution is required. The direct design of AWG is impractical since the focal length size is too long, exceeding the size of the chip. A cascaded AWG can minimize the size more than ten times while maintaining the OCT performance. Typically, a grating-based output intensity has a gaussian-like envelope due to its far-field response, which will degrade the axial resolution performance in SD-OCT. Thus, another PSO-based coupler is introduced. This coupler uses a MZDC configuration with a U-shaped spectrum output. This coupler is implemented right before the AWG and its U-shaped spectrum coupler can compensate the Gaussian far-field wavelength intensity inside the AWG, hence maintaining the performance of axial resolution in on-chip SD-OCT.

Abstract in Chinese . . . . . . . . . . . . . . . . . . . . . . . . . . . i
Abstract in English . . . . . . . . . . . . . . . . . . . . . . . . . . . II
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . ,IV
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . VII
List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XI
List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . XVII
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Silicon-Based OCT System . . . . . . . . . . . . . . . . . . 1
1.2 The goal of the thesis . . . . . . . . . . . . . . . . . . . . . 4
1.3 Organization of the thesis . . . . . . . . . . . . . . . . . . . 6
2 Fourier-Domain Optical Coherence Tomography . . . . . . . . . . 8
2.1 Fourier-domain OCT . . . . . . . . . . . . . . . . . . . . . 8
2.1.1 Spectral-domain OCT . . . . . . . . . . . . . . . . 9
2.1.2 Swept-Source OCT . . . . . . . . . . . . . . . . . . 16
2.2 Axial Resolution . . . . . . . . . . . . . . . . . . . . . . . 19
2.3 Maximum Depth and Sensitivity Fall-OFF . . . . . . . . . . 22
2.4 Sensitivity . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
2.5 OCT Signal Processing . . . . . . . . . . . . . . . . . . . . 24
2.5.1 Background Subtraction . . . . . . . . . . . . . . . 24
2.5.2 Linear Wavenumber Resampling . . . . . . . . . . . 28
2.5.3 Dispersion Compensation . . . . . . . . . . . . . . 36
2.5.4 Digital Phase Detection . . . . . . . . . . . . . . . . 44
2.5.5 Error in Digital Phase Detection . . . . . . . . . . . 48
2.6 Auxiliary Interferometer Design and Optimization . . . . . . 51
2.6.1 Modelling of Non-linearity in laser tuning. . . . . . 51
2.6.2 Experiment of SS-OCT with Different Delay Length
in Auxiliary Interferometer. . . . . . . . . . . . . . 54
3 Silicon Photonics Waveguide . . . . . . . . . . . . . . . . . . . . 57
3.1 Electromagnetic Waveguide Mode . . . . . . . . . . . . . . 57
3.2 Silicon on Insulator Waveguide Mode Simulation . . . . . . 64
3.3 Waveguide Bending Loss . . . . . . . . . . . . . . . . . . . 67
3.4 Waveguide Dispersion . . . . . . . . . . . . . . . . . . . . 69
4 Broadband Coupler Design for FD-OCT on Chip . . . . . . . . . 73
4.1 Directional Coupler . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Non-Flat Coupler Effect on FD-OCT Signal . . . . . . . . . 77
4.3 Mach-Zehnder Directional Coupler . . . . . . . . . . . . . . 80
4.4 Tandem Mach-Zehnder Directional Coupler . . . . . . . . . 84
4.5 Particle Swarm Optimization . . . . . . . . . . . . . . . . . 85
4.6 PSO-based TMZDC . . . . . . . . . . . . . . . . . . . . . . 87
4.7 Bi-Directional PSO-based TMZDC . . . . . . . . . . . . . 89
4.8 Process Variation and Validation with Beam Propagation Method 93
5 Arrayed Waveguide Grating . . . . . . . . . . . . . . . . . . . . . 96
5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . 96
5.2 Working Principle of AWG . . . . . . . . . . . . . . . . . . 97
5.3 AWG Performance for SD-OCT Application . . . . . . . . . 101
5.4 Flat-Top Response AWG with PSO-Based Broadband Coupler 105
6 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . 109
6.2 Future Works . . . . . . . . . . . . . . . . . . . . . . . . . 111
A Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
A.1 Fourier transform of a Gaussian function . . . . . . . . . . . 114
A.2 Convolution and Multiplication . . . . . . . . . . . . . . . . 116
A.3 Fourier transform of a Cosine function . . . . . . . . . . . . 117
A.4 Taylor expansion of non-linear phase from swept-source . . 118
A.5 Coupled mode equation for a symmetry waveguides . . . . . 119
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

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