內嵌光鉗差動共焦顯微鏡的架設與特性量測

Construction and Characterization of Optical Tweezer Embedded Differential Confocal Microscope

詹益鑑(I-Chien Jan)

指導教授 ： 詹國禎

共同指導教授 ： 管傑雄

國立臺灣大學/電機資訊學院/電機工程學研究所/博士(2004年)

https://doi.org/10.6342/NTU.2004.02409

摘要

本論文基於差動共焦顯微術與光鉗技術的原理，建立了內嵌光鉗差動共焦顯微鏡的實驗系統，並對系統進行測試、校正、改進與特性量測。

差動共焦顯微術具有縱向解析率高、動態範圍大、工作距離長、量測速度高等特點。其縱向解析率的限制主要來自系統的雜訊，以本論文建構的系統來說，其縱向解析率可達 2奈米；而動態量測範圍達數微米，由光波波長與物鏡的數值孔徑決定。由於差動共焦顯微術是以光波在遠場進行偵測，因此不需要閉迴路鎖定樣品的高度，而具有高速的表面高度量測能力。差動式共焦顯微鏡的長工作距離與大動態範圍，對於高週期性的微小結構量測有特別的優勢。而搭配高解析率的橫向位移檢測元件，可以得到十奈米等級的三度空間定位能力。

本論文以正立式的架構搭建一套差動共焦顯微鏡，詳細描述了系統的架構與元件規格與光路設計。針對系統的雜訊進行分析，排除了機械震動、光學雜訊、電性擾動與其他環境影響因素，得到75 dB 的差動共焦訊躁比。在縱向解析率的測試中，以波長633 nm 的光源，60X, NA = 0.85 物鏡量測得到了 2 nm 的結果。以此差動共焦顯微鏡的原型架構，進行半導體蝕刻樣本與微流道晶片中的微柱狀樣本的觀測，並與光學顯微鏡與電子顯微鏡的影像作比較。

光鉗是單一光束所造成的光學嵌住現象，利用光子動量轉移所造成的作用力來抓取微小物體，可用來操控微米級甚至奈米級的微小物體。其主要優點是非接觸性與非侵入性。光鉗以和顯微鏡結合成內嵌式光鉗，賦予顯微鏡對於觀察目標的操控能力。而光鉗理論模型分為幾何光學模型與電磁波模型，本論文針對幾何光學模型，推導數學理論與進行數值模擬。

本論文架構了正立式與倒立式的兩種內嵌光鉗差動共焦顯微鏡，詳細描述了系統的架構與元件規格與光路設計。在正立式光鉗架構中，量得了光鉗的Q值，並進行了位移偵測的實驗，計算出光鉗的彈力常數k。在倒立式光鉗差動共焦顯微鏡的架構中，使用了四象限二極體進行橫向位移偵測，結合差動共焦顯微鏡的縱向解析率，得到了小球三度空間的定位能力。校正結果顯示X、Y、Z三軸的解析率分別為為8 nm 、10 nm 與5 nm，同時各具有 1 μm 的動態範圍。而量測小球在光鉗中同時受布朗運動擾動的頻譜訊號，由勞倫茲分佈的擬合曲線截止頻率可推估水的黏滯係數，並與一般標準值誤差約在1%左右，驗證了本系統可以小球的動態頻譜分析，得到相當精準的黏滯度估算。

內嵌光鉗差動共焦顯微鏡系統，以差動共焦顯微鏡的架構，配合配合高靈敏度的位移檢測器以及光鉗裝置，可以量測光鉗的力學特性，並作為以動態散射頻譜術為基礎的微觀黏滯度量測系統。由系統測試與量測結果，本論文建立的內嵌光鉗差動共焦顯微鏡，具備了在微流變學研究上的應用潛力。

關鍵字

光鉗 ； 差動共焦顯微術

並列摘要

In this thesis, an optical tweezer embedded differential confocal microscope system is developed. Base on the principle of differential confocal microscope and optical tweezer theory, the system is constructed and characterized. Some experimental results are carried out by the system and discussed.

The main features of differential confocal microscopy include high depth resolution, large dynamic range, long working distance and high acquisition rate. The depth resolution of differential confocal microscopy in only limited by system noise. In the system build in this thesis, a depth resolution of 2 nm has been achieved. The dynamic range is as large as several micrometers, determined by wavelength of light source and numerical aperture of objective lens. Since probing the sample with far-field optical wave and without closed-loop locking the height of sample surface, differential confocal microscopy has advantage of high acquisition rate. The long working distance and large dynamic range features are suitable to measure the surface profile of high periodic structures. By collaborating with lateral detection element, resolution of ten nanometers in three-dimensional positioning has also been verified in the system.

A homemade differential confocal microscope in upright configuration is constructed. The setup of the systems, specifications of elements and instruments, optical beam path configurations are also described in this thesis. The system noises, including mechanical vibration, optical background and electrical noise, are well analyzed and excluded. The signal to noise ratio of differential confocal signal is measured as high as 75 dB. If the wavelength is 633 nm, using the objective lens of 0.85 numerical aperture, the depth resolution is two nanometers. By the differential confocal microscope, wet-etched semi-conductor sample and the micro-cylinders in microfluidic channels are observed and compared with images taken with optical microscope and scanning electron microscope.
Optical tweezer, as known as single beam optical tarp, grabs small particles of micrometer-size even nanometer-size by the force from photo momentum transfer. The main features of optical tweezer are non-contact and non-invasive. By combining optical tweezer and optical microscopes, one can manipulate the observed object in the microscopic scale. Ray optics model and electromagnetics model describe the model of optical trap, and the mathematical theory and simulation of ray optics model are introduced in this thesis.

Upright and inverted configurations of optical tweezer embedded differential confocal microscopes are constructed. The Q value and the spring constant k of optical tweezer are characterized in the upright configuration system. In the setup constructed with inverted microscope, a quadrant photodiode is used to perform detection of lateral displacement. Combining with the depth resolution power of differential confocal microscope, three-dimensional positioning of a microsphere has been verified. Within 1-μm dynamic range in three axes, the resolutions of X, Y, and Z axes are 8 nm, 10 nm, 5 nm, respectively. By measuring the power spectrum density of silica bead trapped in optical tweezer, the cut-off frequency of Lorentz distribution is fitted. With the cut-off frequency and the spring constant k, the coefficient of viscosity of water is estimated in the experiment, of the error within 1% from the standard value.

Combining the configuration of differential confocal microscopy and the optical tweezer, with sensitive lateral displacement detector, the system shows good potential on microrheology studies from the characterization in this thesis.

並列關鍵字

optical tweezer ； differential confocal microscope

參考文獻

[1] G. Binnig, C. F. Quate, and Ch. Gerber, “Atomic force microscope,” Phys. Rev. Lett. 12, 930 (1986).

[2] E. Betzig and J. K. Trautman, “Near-field optics: microscopy, spectroscopy, and surface modification beyond the diffraction limit,” Science 257, 189 (1992).

[3] P. Davidovits and M. D. Egger, “Scanning laser microscope,” Nature 223, 831 (1969).

[4] W. Denk, J. H. Strickler, and W. W. Webb, “Two-photon laser scanning fluorescence microscopy,” Science 248, 73 (1990).

[5] C. H. Lee and J. Wang, “Noninterferometric differential confocal microscopy with 2-nm depth resolution,” Opt. Commun. 135, 233 (1997).