大腦掌控動物的學習與記憶、社交活動、睡眠與生理週期，是生存所不可或缺的器官之一。由過去的一百多年發展的神經科學知識知道，大腦是由數以千萬計的神經細胞組成的複雜三維網絡，因此，要理解大腦運作及功能，研究活體中神經的連結與活動是可行的策略之一。
為了實現此策略，研究大腦的影像工具應具備良好的空間解析度、深層組織穿透能力及高速體積成像等三大特點。以哺乳類動物的腦為例，若以個別神經元為基礎，空間解析度應達到微米等級;而腦的尺寸約為一到數十公分大，所以穿透能力至少也應達到公分等級;再加上神經網絡為三度空間分佈，且反應神經元活動的鈣離子動態約為數百毫秒，因此需要足夠時間解析度的體積成像。在現今各種研究大腦的工具之中，雙光子顯微鏡憑藉其天生的光學切片能力在三度空間中皆具有次微米等級的解析度。然而，即使是目前最先進的雙光子顯微鏡，其最大的穿透深度也僅約1毫米左右，且依舊仰賴緩慢的軸向掃描以進行體積成像。這樣的限制不僅無法用來研究大腦內部1毫米深度以下的區域，也無法捕捉到大腦中三度神經網絡的鈣離子動態。
舉例來說，其中一個受到此技術限制而無法獲得突破性了解的腦功能就是日夜週期。日夜週期影響著我們的睡眠、進食、激素調節，與我們的生活息息相關，但我們對於日夜週期的運作依舊不慎了解。關鍵在於掌管日夜週期的腦區---視交叉上核(suprachiasmatic nucleus)，是一個神經細胞聚集相當濃密的三維網絡，且位於大腦中近乎是最底層的區域。要了解此區域的運作，不僅需要具有良好的空間解析度，更重要的是要能在數公分深的組織取像，以及需要能解析鈣離子動態的體積成像速度。但即使採用小鼠作為替代人類的生物模型，在只有約六到七毫米大小的小鼠腦中，我們依舊困於技術上穿透深度及體積成像速率的限制而無法了解視交叉上核是如何在活體動物中運作的。
為此，我們提出了一個全新的解決方法。在這篇論文中，我們將兩種截然不同的梯度折射率(gradient-index, GRIN)透鏡整合進雙光子顯微鏡中，不只保有原先次微米等級的空間解析度，還可以大大地提高穿透深度以及體積成像速率。更精確地來說，透過採用8毫米長的GRIN透鏡當作內視鏡頭，可以觸及小鼠大腦內部任何想觀察的區域。另外透過可調變的聲學梯度折射率透鏡(tunable acoustic gradient-index, TAG)其百萬赫茲等級的軸向掃描速率，就能達到高速體積成像以解析鈣離子動態。在這篇論文中，我們不只會介紹此技術的基本物理原理，也會詳細的介紹此技術的設計細節，以及最佳化的過程。
此一嶄新的技術將使得研究公分深度腦區的神經活動動態不再遙不可及。不只是視交叉上核，其他的深層腦區如與學習記憶相關的腦區---海馬迴(hippocampus)、與社交功能相關的腦區---杏仁核(amygdala)、以及與睡眠相關的腦區---側背被蓋核(laterodorsal tegmental nucleus)都將受益於此技術。此技術的發展將為構建深層腦區的功能性圖譜開展新的一頁。

Brain governs learning and memory, affects social interaction, regulates sleeping and biological clock. It is one of the most vital organ. After more than 100 years of neuroscience study, we now know a mammal brain is at least centimeter in size, with millions to billions of neurons inside, forming complex three-dimensional (3D) neural networks. To understand functions of brain, studying neural connections and activities in vivo is fundamental .
Given the cm-size brain and three-dimensional neural circuit dynamics, high spatial resolution, deep-tissue, and high-speed volumetric imaging is necessary for brain study. With sub-micrometer spatial resolution, intrinsic optical sectioning, and deep-tissue penetration capability, two-photon microscopy (2PM) has found a special niche in neuroscience. However, current state-of-the-art 2PM typically relies on slow axial scan for volumetric imaging, and the maximal penetration depth is only about 1 mm.
One example impeded by such a limitation is the study of circadian rhythm, or so-called internal biological clock. Circadian rhythm affects our sleeping, eating, and hormone regulation. It is highly related to our life; nevertheless, we know little about how it functions. The problem lies in its related brain region called suprachiasmatic nucleus, SCN, which consists of dense 3D neural networks and locates almost at the bottom of a brain. To understand functions of such a deep and dense brain region, not only high spatial resolution, but also deep-tissue and high-speed volumetric imaging are necessary. However, even adopting mice, whose brain is only 6 ~ 7 mm large, as an alternative animal model, current optical imaging technologies are still not adequate to understand the function of SCN in living animals.
Here, we demonstrate that by integrating two gradient-index (GRIN) lenses into 2PM, both penetration depth and volume-imaging rate can be significantly improved. More specifically, an 8-mm long GRIN lens is adopted, to allow penetration through a whole mouse brain, while a tunable acoustic gradient-index (TAG) lens provides sub-second volume rate via 100 kHz ~ 1 MHz axial scan. In this thesis, we not only introduce physical principles behind such a novel technique, but also explain detail design and optimization of this optical system.
This technique allows, for the first time, the study of calcium dynamics in cm-deep brain regions with sub-cellular and sub-second spatiotemporal resolution. Not only SCN, the study of all the other deep brain regions, such as hippocampus (related to learning and memory), amygdala (related to social interaction), and laterodorsal tegmental nucleus (related to sleep) will also benefit from our technical development. Our novel technique paves the way for construction of deep-brain functional connectome.

1 Introduction: Why two-photon volumetric endoscopy 1
1.1 Brain study: current knowledge and challenge . . . . . . . . . . . . . . . 1
1.1.1 Features of brain . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1.2 From human to model animals — advantage of mouse . . . . . . 2
1.1.3 Challenges for mouse brain study — SCN for example . . . . . . 4
1.2 Comparison and development of brain study techniques . . . . . . . . . . 5
1.2.1 Common techniques for brain study . . . . . . . . . . . . . . . . 6
1.2.2 Optical microscopy for brain study . . . . . . . . . . . . . . . . . 8
1.2.3 Optical microscopy with invasiveness for deep brain regions . . . 9
1.2.4 Two-photon volumetric endoscopic imaging . . . . . . . . . . . . 11
1.2.5 Aim and structure of thesis . . . . . . . . . . . . . . . . . . . . . 12
2 General Principle: Physics behind two-photon volumetric endoscopy 13
2.1 Two-photon laser-scanning microscopy . . . . . . . . . . . . . . . . . . 13
2.2 GRIN lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.3 TAG lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
2.4 Two-photon volumetric endoscopy . . . . . . . . . . . . . . . . . . . . . 21
3 Designing system: How to achieve two-photon volumetric endoscopy 23
3.1 Optical system setup: figure and list . . . . . . . . . . . . . . . . . . . . 23
3.2 Contrast agent and excitation laser wavelength . . . . . . . . . . . . . . . 25
3.3 Selection of GRIN lens . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
3.4 Selection of objective lens . . . . . . . . . . . . . . . . . . . . . . . . . 28
3.5 Selection of TAG lens . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
3.6 Expected performance . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6.1 Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6.2 FOV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
3.6.3 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.6.4 DOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
3.6.5 Volume imaging rate . . . . . . . . . . . . . . . . . . . . . . . . 37
3.7 The speed of galvo scanners . . . . . . . . . . . . . . . . . . . . . . . . 39
3.8 Selections of scan lens, tube lens, and dichroic beamsplitter . . . . . . . . 40
3.9 Beam size consideration . . . . . . . . . . . . . . . . . . . . . . . . . . 44
3.10 Detector: Photomultiplier tube, PMT . . . . . . . . . . . . . . . . . . . . 46
3.11 Data streaming and 3D image reconstruction . . . . . . . . . . . . . . . . 50
3.12 Selection of AMP . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
3.13 Selection and function of DAQ . . . . . . . . . . . . . . . . . . . . . . . 53
3.13.1 Starting data acquisition . . . . . . . . . . . . . . . . . . . . . . 53
3.13.2 Sampling strategy . . . . . . . . . . . . . . . . . . . . . . . . . . 54
3.13.3 Packing data and 3D Image reconstruction . . . . . . . . . . . . 55
4 Sample preparation and experimental protocols 58
4.1 Test sample: fluorescent beads preparation . . . . . . . . . . . . . . . . . 58
4.2 Mouse sample: GRIN lens implantation . . . . . . . . . . . . . . . . . . 59
4.3 Experimental protocols . . . . . . . . . . . . . . . . . . . . . . . . . . . 60
5 Results and Discussion 68
5.1 System performance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.1.1 Depth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
5.1.2 Spatial resolution . . . . . . . . . . . . . . . . . . . . . . . . . . 69
5.1.3 FOV . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
5.1.4 DOF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
5.1.5 Acquisition speed . . . . . . . . . . . . . . . . . . . . . . . . . . 74
5.2 In vivo images of deep brain regions . . . . . . . . . . . . . . . . . . . . 77
5.2.1 Estimation of system signal loss . . . . . . . . . . . . . . . . . . 78
5.2.2 In vivo deep brain images of different mice and dates . . . . . . . . . 79
6 Conclusion and future outlooks 82
6.1 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
6.2 Future outlooks . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
References 84

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