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Optofluidics for microscopy and sensing Chowdhury, Mohammad Faqrul Alam 2012-03-05

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Opto uidics for Microscopy and Sensing by Md. Faqrul Alam Chowdhury B.Sc., Bangladesh University of Engineering and Technology, 2007 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in The College of Graduate Studies (Electrical Engineering) THE UNIVERSITY OF BRITISH COLUMBIA (Okanagan) February 2012 c Md. Faqrul Alam Chowdhury 2012Abstract Opto uidics describes a relatively new area of research that aims to synergistically combine optics and  uidics technologies. In this work, we ex- amine the application and integration of small  uid volumes into two types of optical devices, yielding improvements in either tunability,  exibility, or cost-e ectiveness. First, we explore a simple methodology to dispense and shape water droplets for use as the magnifying element in a microscope op- erating under either re ection-mode or transmission-mode illumination. A water droplet is created at the end of a syringe and then coated with a thin layer of silicone oil to mitigate evaporation. By applying mechanical pressure to the water droplet using a metal tip, the shape of the droplet is tuned to yield focusing properties amenable for microscopy. Images captured using the microscope demonstrate micron-scale resolution, variable magni - cation, and imaging quality comparable to that obtained by a conventional, laboratory-grade microscope. Next, we develop a surface plasmon resonance (SPR) sensor that exploits the index matching and coating capabilities of  uids. Conventional SPR sensor are implemented using an external light source, optical components to polarize incident light and guide light to and from a metal surface, a coupling device (such as a prism) to convert free- space light into surface plasmons on a metal surface and back into free-space iiAbstract light, and a light detector. Here, we develop a new SPR device architecture by combining several optical components via index matching  uid, which eliminates the need for a prism and integrates light delivery, light polariza- tion control, surface plasmon coupling onto a thin,  exible substrate. We experimentally characterize the SPR device and  nd good agreement be- tween experimental re ectivity measurements and a theoretical re ectivity model based on transfer-matrix formalism. By developing these new meth- ods to integrate  uids for both microscopy and optical sensing applications, this work provides results that highlight both the promise and challenges of creating optical systems based on  uids. iiiTable of Contents Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii Table of Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . xix Dedication . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xx 1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.1 Background . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2 Objective . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2 1.3 Thesis Outline . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2 Basics of Optical Microscopy . . . . . . . . . . . . . . . . . . 5 2.1 Components of a Light Microscope . . . . . . . . . . . . . . . 5 2.1.1 Illuminator . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Condenser . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Objective . . . . . . . . . . . . . . . . . . . . . . . . . 7 ivTable of Contents 2.1.4 Light Microscopy Con gurations . . . . . . . . . . . . 8 2.2 Optical Microscopy Concepts . . . . . . . . . . . . . . . . . . 10 2.2.1 Point Spread Function and Airy Disc . . . . . . . . . 10 2.2.2 Numerical Aperture . . . . . . . . . . . . . . . . . . . 12 2.2.3 Magni cation . . . . . . . . . . . . . . . . . . . . . . 12 2.3 Optical Aberrations . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.1 Spherical Aberration . . . . . . . . . . . . . . . . . . 14 2.3.2 Astigmatism . . . . . . . . . . . . . . . . . . . . . . . 15 2.3.3 Comatic Aberration . . . . . . . . . . . . . . . . . . . 18 2.3.4 Chromatic Aberration . . . . . . . . . . . . . . . . . . 18 2.3.5 Geometrical Distortions . . . . . . . . . . . . . . . . . 18 2.3.6 Field Curvature . . . . . . . . . . . . . . . . . . . . . 21 2.4 Optical Aberrations Correction . . . . . . . . . . . . . . . . . 23 2.4.1 Objective Correction . . . . . . . . . . . . . . . . . . 23 2.4.2 Condenser Correction . . . . . . . . . . . . . . . . . . 26 3 Water Droplet Microscopy . . . . . . . . . . . . . . . . . . . . 28 3.1 Fluidic Lens Microscopy . . . . . . . . . . . . . . . . . . . . 28 3.2 Droplet Lens Dispenser and Actuator . . . . . . . . . . . . . 30 3.3 Re ection-Mode Microscope based on a Droplet Lens . . . . 40 3.4 Transmission-Mode Microscope based on a Droplet Lens . . 44 3.5 Modeling the Optical Properties of the Droplet Lens . . . . . 46 3.6 Limitations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 3.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 vTable of Contents 4 Fibre-Addressable Surface Plasmon Resonance Chip Using Optically Matched Fluid . . . . . . . . . . . . . . . . . . . . . 56 4.1 Surface Plasmon Resonance: Wavevector Matching Condi- tion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.2 Optical Coupling Con gurations to Measure Surface Plasmon Resonance . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.3 Proposed Surface Plasmon Resonance Sensor . . . . . . . . . 65 4.4 Measurement Methodology . . . . . . . . . . . . . . . . . . . 68 4.5 Multi-Layer Re ectivity Model . . . . . . . . . . . . . . . . . 71 4.6 Results and Discussion . . . . . . . . . . . . . . . . . . . . . 77 4.7 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 5 Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84 viList of Tables 2.1 Optical aberration correction for objective lenses . . . . . . . 25 2.2 Optical aberration correction for condenser lenses . . . . . . . 27 4.1 Optical and geometrical parameters of the proposed surface plasmon resonance sensor . . . . . . . . . . . . . . . . . . . . 67 4.2 Resonance wavelength ( res) and corresponding incident an- gle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 viiList of Figures 2.1 Representative image of the internal lens elements inside con- densers of di erent numerical aperture values. . . . . . . . . . 6 2.2 Anatomy of a plan-corrected  uorite objective from ZEISS with 63 magni cation capability, numerical aperture of 1:3 with oil/water/glycerin as the immersion medium, di eren- tial interference contrast (DIC) method, incorporating in n- ity color corrected system, also having adjustable cover glass correction (Korr) suitable for cover glass thickness range of 0:15-0:19 mm. . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 Illustration of trans-illumination optical microscopy using a simple objective and condenser, in a con guration known as an Abbe microscope. The aperture controls the aperture of light entering the condenser. . . . . . . . . . . . . . . . . . . . 9 2.4 Epi-illumination con guration for bright  eld re ection mode microscopy. Light is directed along the optical axis onto the objective lens. The lens focuses the incoming light onto the specimen, collects the re ected light, and projects the image of the specimen. . . . . . . . . . . . . . . . . . . . . . . . . . 10 viiiList of Figures 2.5 Formation of a point spread function (PSF) and resulting Airy pattern. (left) Constructive interference of wavefronts collected by an objective at the point A0 results in a bright central region of the Airy pattern and (right) destructive in- terference at the points A0+1 and A 0  1 results in the dark re- gions of the Airy pattern. . . . . . . . . . . . . . . . . . . . . 11 2.6 Airy pattern resulting from two point sources. The left side illustrates the Airy pattern using an objective with relatively low NA, for three di erent wavelengths, and the right side illustrates the Airy pattern using an objective with relatively high NA, also for three di erent wavelengths. . . . . . . . . . 13 2.7 The e ect of spherical aberration as a function of lens spheric- ity. The plane of observation is at the circle of least confu- sion, P LC. When the sphericity is less, as in (a), maximum intensity is found at the center of the point spread function, yielding a comparatively clear image. . . . . . . . . . . . . . . 16 2.8 Exaggerated representation of the e ect of astigmatism on an imaging system for the case of (a) an object point aligned along the optical axis and an image plane located at the fo- cal plane, (b) an object point located o the optical axis and an image plane located at the sagital focal plane, and (c) an object point located o the optical axis and an image plane located at the tangential focal plane. The point spread func- tion, Airy pattern, ray tracing diagram, and resulting image are shown for each case. . . . . . . . . . . . . . . . . . . . . . 17 ixList of Figures 2.9 Comatic aberration causes smearing of a point source into di erent zones (1, 2, 3, 4) on the image plane. Point spread function, Airy pattern, and overall image for (a) the case of an aligned imaging system without coma and (b) the case of an unaligned imaging system with coma. . . . . . . . . . . . . 19 2.10 Chromatic aberrations with an uncorrected lens, illuminated by a polychromatic (white) point source. The resulting im- age can have a (a) greenish, (b) reddish, or (c) bluish tinge when the position of the image plane is located at focal points corresponding to the green, blue, red portions of the visible spectrum, respectively. . . . . . . . . . . . . . . . . . . . . . . 20 2.11 Demonstration of geometrical distortion of an image of a grid pattern (top row). (a) The transverse magni cation is same for all the image points, irrespective of the distance from the optical axis, yielding an undistorted image. (b) Positive or pin-cushion distortions are evident by larger magni cation of the most distant object points from the optical axis. (c) Negative or barrel distortions are evident. . . . . . . . . . . . 21 2.12 Illustration of the e ect of  eld curvature on an image, with the corresponding alterations of PSF and illumination of grid pattern ( lm plane). At di erent planes of observation, (a) central portion and (b) edges of the image plane come to sharp focus, making it impossible to distinguish minor details of the image at other regions. (c) represents the best compromise between center and edge focus. . . . . . . . . . . . . . . . . . 22 xList of Figures 2.13 Internal lens element combinations ( rst row) and correspond- ing ray tracing diagram demonstrating the chromatic correc- tion (second row) incorporated in an achromat (column one),  uorite (column two) and apochromat (column three) objec- tive of 10 magni cation. . . . . . . . . . . . . . . . . . . . . 24 2.14 (a) Correction for  at- eld curvature for a 10 achromat re- quires insertion of a meniscus lens, a doublet and a triplet lens group into the objective. (b) Correction collar adjustment for di erent coverslip thickness of 0:20 mm and 0:13 mm to cor- rect for aberrations that are introduced due to the variation of the cover glass thickness and dispersion of the medium between the front lens and the cover glass. . . . . . . . . . . . 26 3.1 Droplet size determination by analysis of images taken of the droplet from horizontal and vertical perspectives. The pro- jected area of the droplet measured from the horizontal per- spective as a function of the droplet volume inferred from both perspectives. . . . . . . . . . . . . . . . . . . . . . . . . 31 3.2 Microscope images of a bare water droplet at (a) t = 0 s and (b) t = 15 min. Dispensing a drop of oil over the water droplet results in a thin oil layer surrounding the water droplet. Mi- croscope images of a water droplet with an oil coating at (c) t = 0 s and (d) t = 15 min. (e) The measured projected area of the two types of droplets as a function of time. . . . . . . . 33 xiList of Figures 3.3 (a) Experimental setup to determine the focal distances of the water droplet based on collimation of visible light emitted from an optical  bre. The oil-coated water droplet is attached to a syringe connected to a water reservoir. The focusing properties of the droplet are changed by varying the volume of the droplet. The light emanating from the optical  bre is collimated by the droplet and the far- eld image of the light source is collected by a camera at a far distance (much greater than the focal length) from the lens. Typical far- eld images indicating (b) horizontal collimation, (c) vertical collimation, and (d) full collimation. . . . . . . . . . . . . . . . . . . . . . 34 3.4 (a) and (b) depict images of an oil-coated water droplet at- tached with the syringe where the size and shape of the droplet has been varied by increasing the water volume. The general shape of the droplet is elliptical. The ellipticity of the droplet is larger for smaller droplets due to adhesion to the syringe and larger droplets due to gravity-induced elongation. El- lipticity in the droplet shape yields disparate focal lengths along the horizontal and vertical directions. (c) Horizontal and vertical focal lengths of the droplet as a function of pro- jected droplet area. For this oil-coated water droplet system, there exists only one droplet size where the horizontal and vertical focal lengths are matched. (d) Illustrations demon- strating the changing shape of the water droplet as a function of volume. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36 xiiList of Figures 3.5 Variation of the shape of the oil-coated water droplet system by applying pressure through a bottom tip. A metallic tip is  rst (a) attached to the bottom of a water droplet. A droplet of oil is then dispensed from a syringe, resulting in (b) an oil- coated water droplet connected to a bottom tip. (c) shows a microscope image of the complete  uidic lens system. (d) Sequence of microscope images of the droplet system demon- strating size and shape recon guration by either changing the volume or pressure on the droplet. . . . . . . . . . . . . . . . 37 3.6 Images of a symmetric droplet taken from a vertical perspec- tive (left) and a horizontal perspective (right), where sym- metric circles have been superimposed onto the edge of the droplet in the images. . . . . . . . . . . . . . . . . . . . . . . 38 3.7 (a) Experimental set-up for measuring the focal length of the tip-supported droplet system. By tuning the position of the bottom tip, the shape of the droplet for any volume can be adjusted to achieve complete (horizontal and vertical) colli- mation of the optical  bre light source. (b) Focal length of the droplet system as a function of droplet volume and projected droplet area. . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 3.8 Re ection-mode microscope using a  uidic lens composed of the oil-coated water droplet system. In this con guration, the  uidic lens emulates both the condenser and objective lenses found in a conventional optical microscope. . . . . . . . . . . 41 xiiiList of Figures 3.9 (a) Microscope images of a calibration slide captured at var- ious levels of magni cation using the  uidic lens microscope. The pitch separation between adjacent lines on the slide is 10 m. (b) Field of view and magni cation of the microscope as a function of projected droplet area. . . . . . . . . . . . . . 42 3.10 Focal length of the oil-coated water droplet lens as a function of projected droplet area measured from the lens-sample sep- aration in the microscopy con guration (blue squares) and the  bre-lens separation in the beam collimation con gura- tion (red circles). The error bars in the measurements in the microscopy con guration account for uncertainty in the posi- tion of the sample. . . . . . . . . . . . . . . . . . . . . . . . . 43 3.11 Transmission-mode microscope using a  uidic lens composed of the oil-coated water droplet system. . . . . . . . . . . . . . 44 3.12 Microscope images of spinal cord tissue ( rst row), basswood stem (second row), cardiac muscle tissue (third and fourth row), and Penicillium ( fth row). Column (a) shows the im- ages obtained using the droplet lens in the transmission-mode microscope con guration. Columns (b) and (c) show near- focussed and best-focussed images, respectively, obtained from a conventional laboratory-grade microscope (Zeiss AxioIm- ager) using a 20 objective lens. Column (d) shows cropped images of the highlighted region in the near-focussed images, which matches the region imaged by the droplet lens. . . . . . 45 xivList of Figures 3.13 (a) Image of an oil-coated water droplet (taken from the hor- izontal perspective) adjacent to an optical  bre light source. The separation between the bottom tip and syringe has been tuned to reduce the ellipticity in the droplet shape. (b) de- picts the procedure to extract the geometrical parameters of the lens for theoretical analysis. The two curved surfaces of the droplet are  tted to circles with radii of curvature of R1 and R2. d is the thickness of the lens and 2r is the aperture size of the lens. . . . . . . . . . . . . . . . . . . . . . . . . . . 47 3.14 Schematic of an idealized thick lens constructed using the ge- ometrical parameters of the  uidic lens. (a) Two-dimensional and (b) three-dimensional perspective of the calculated ray trajectories of a collimated beam incident at normal incidence onto the thick lens. . . . . . . . . . . . . . . . . . . . . . . . . 49 3.15 Comparison of focal lengths measured using the beam col- limation con guration to focal lengths calculated using the analytical model under the paraxial approximation and the ray-tracing simulation using (a) 30%, (c) 70%, and (d) 100%  ll factors. The results of the ray tracing simulations using (b) 30%, (d) 70%, and (e) 100%  ll factors. . . . . . . . . . . 52 3.16 (a) Comparison of the focal lengths measured using the mi- croscope con guration to focal lengths calculated using the analytical model under the paraxial approximation and the ray-tracing model using various  ll factors. (b) Tip-syringe separation of the lens versus the droplet size. . . . . . . . . . 53 xvList of Figures 4.1 Dispersion relation diagrams illustrating the wavevector match- ing condition required for light coupling into surface plasmons on a planar air-metal interface. The metal is assumed to be Ag. (a) depicts the real part of surface plasmon wavevector (red line) at an air-Ag interface and the component of the free-space light wavevector (black line) projected onto the in- terface at grazing incidence  = 90 . The gray lines depict the component of the free-space light wavevector projected onto the interface for intermediate incidence angles. (b) de- picts the real part of surface plasmon wavevector (red line) at an air-Ag interface and the component of the light wavevector in a dielectric (cyan line) projected onto the interface. . . . . 60 4.2 Illustration of design parameters tuning in order to achieve required wavevector matched condition. Alteration of the (a) permittivity of higher index dielectric,  d and (b) angle of incidence,  into the dielectric makes surface plasmon exci- tation possible at a desired frequency by shifting the light line. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 4.3 Drop in the intensity of re ected light due to surface plasmon resonance. (a) and (b) demonstrates surface plasmon reso- nance curve for the detection of any slight change in super- strate refractive index through wavelength modulation and angle modulation respectively,   and   depicts the corre- sponding shift in the resonance curve due to the change in superstrate medium. . . . . . . . . . . . . . . . . . . . . . . 62 xviList of Figures 4.4 (a) Kretschemann con guration and (b) optical  bre con g- uration to optically coupling to surface plasmons. In both con gurations, light incident onto a thin metal  lm from an optically denser dielectric medium (labeled the \substrate") couples into surface plasmons on the interface between the metal  lm and the optically rarer dielectric medium (labeled the \superstrate"). . . . . . . . . . . . . . . . . . . . . . . . . 64 4.5 Proposed surface plasmon resonance sensor con guration. A thin metal  lm is deposited onto a clear plastic  lm. The bottom side of the plastic  lm is optically contacted with a linear polarizer sheet. Two optical  bres, one to input light and the other to collect the re ected light with full control over the incident and re ected angle, are then connected to the bottom of the linear polarizer sheet. . . . . . . . . . . . . 67 4.6 Schematic diagrams depicting (a) typical Kretchemann SPR con guration consisting of a thin metal  lm on a prism with two polarizing elements and (b) our integrated SPR con gu- ration consisting of a thin metal  lm on a clear plastic sheet optically contacted to a polarizing sheet with a drop of optical adhesive below. . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.7 Schematic of the experimental surface plasmon resonance chip. The metallic layer on the clear plastic  lm consists of two re- gions: a thin region that is used for surface plasmon coupling and a thicker region that does not enable surface plasmon coupling. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 xviiList of Figures 4.8 (a) Spectral re ection measurements from the 75- nm-thick (blue line) and the 150- nm-thick (red line) portions of an Au  lm for an angle of incidence of  = 45 . A dark measure- ment (black line) illustrates the baseline noise in the spectral measurements and is shown on a magni ed scale in (b). (c) Normalized re ection measurement obtained from the spec- tral re ection measurements. . . . . . . . . . . . . . . . . . . 70 4.9 (left) Three-layer system representing a general multi-layered structure in terms of the re ection and transmission coe - cients at each interface. (right) Model description in terms of the electric  eld, angle of incidence, and wavevector compo- nents. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 4.10 (a) Normalized re ectance measurement for various angles of incidence for transverse-electric incident polarization. Model predictions of the normalized re ectance for the case of (b) imperfect index matching and (c) perfect index matching be- tween the multiple substrate layers. . . . . . . . . . . . . . . . 78 4.11 (a) Normalized re ectance measurement for various angles of incidence for transverse-magnetic incident polarization. Model predictions of the normalized re ectance for the case of (b) imperfect index matching and (c) perfect index matching be- tween the multiple substrate layers. . . . . . . . . . . . . . . . 79 xviiiAcknowledgements This thesis would not have been possible without the help and support of my colleagues, friends, and family. I am heartily thankful to my supervisor, Dr. Kenneth Chau, for both inspiring and teaching me. He has provided constant encouragement, guid- ance and support throughout my thesis. He has introduced me to the art of scienti c research, the beauty of good experimental design, the value of explaining numerical results not only as mathematical constructs, but also through physical interpretation, the subtlety of clear and accessible scien- ti c writing, the rigors of analytical ability and adherence, and the spirit of intellectual integrity. I am indebted to many of my colleagues for their support throughout the work and writing, and owe special thanks to Reyad Mehfuz for his as- sistance in depositing gold layers for the development of a surface plasmon resonance chip. I also give special acknowledgment and thanks to Michael W. Davidson of Molecular Expressions Optical Microscopy Primer for pro- viding permission to use the color plates that accompany second chapter of the thesis. xixTo my family, who, of all that walk on the earth, are most precious to me, for their support in every endeavor. Also to anyone who  nds themselves at a place in life where the question of why seems unanswerable, and to all those who seek and side with the truth. xxChapter 1 Introduction 1.1 Background Optics are ubiquitous in modern technology. Cameras, disc drives, and microscopes all incorporate optical components, such as lenses and prisms, that enable precise control and manipulation of light. Typically, these op- tical components are constructed from solid, transparent materials, such as glass or plastic, which are machined with high precision into speci c shapes with smooth surfaces. While the construction of optical components from solid materials provides mechanical stability, it does not a ord a high de- gree of  exibility and tunability because the shape of the component is  xed. One approach to increase the adaptability of optical systems is to replace solid optical components with analogous components made from  uids [1{4]. This basic endeavor has given rise to the  eld of opto uidics, a general term that refers to optical devices that integrate  uidic components [5{8]. There are several advantages to the use of  uids for optical applications -  uids are deformable, transparent  uids such as water are highly abundant and inex- pensive, and the surface of a  uid is naturally ultra-smooth due to surface tension [9{13]. The main disadvantage to  uid components, however, is the lack of mechanical stability as compared to their solid counterparts. The 11.2. Objective basic challenge in the development of any opto uidic system, therefore, is to design cost-e ective infrastructure that maximizes the tunability conferred by the use of  uid, yet mitigates instability. 1.2 Objective The objective of this work is to introduce, design, build, and test two novel optical systems in which  uids have been used to achieve optical com- ponents that would have otherwise been constructed from solids. We  rst explore an opto uidic microscope in which the objective lens is constructed from a droplet of water attached to the end of a syringe. By varying the shape of the droplet through the application of pressure, the droplet lens achieves tunable focus that can be used for either transmission-mode or re ection-mode imaging with micron-scale resolution. The image quality achieved with the opto uidic microscope is comparable to, but still notice- ably less than, the image quality achieved with conventional laboratory- grade microscopes. Nevertheless, the opto uidic microscope developed here boasts the advantages of simplicity, low-cost of implementation, and tun- ability. We next explore a surface plasmon resonance (SPR) sensor that exploits index matching  uids [1, 2, 14{16] to enable facile coupling between free- space light and surface plasmons. Conventional surface plasmon resonance sensors typically incorporate a prism coupling element to enable free-space light to channel into surface plasmons. Here, we will demonstrate a surface plasmon resonance sensor design in which the prism is e ectively replaced by 21.3. Thesis Outline a drop of index matching  uid, yielding a con guration that is more compact and cost-e ective than the conventional prism con guration. The opto uidic surface plasmon resonance sensor is  bre-addressable and integrates the light delivery and polarization control onto a single  exible substrate. 1.3 Thesis Outline A basic overview of microscopy is given in Chapter 2, which includes an introduction to the physical theory and principles of microscope image for- mation, an overview of common aberrations observed in microscope images and their causes, and a review of state-of-the-art condenser and objective lens designs for correcting these aberrations. The discussion in Chapter 2 will provide the reader with an appreciation of the aberrations observed in the microscope images captured by the opto uidic microscope. Chapter 3 describes a simple, low-cost, and elegant con guration for realizing a tunable microscope system using a water droplet as the objec- tive lens. Starting with a review of contemporary research on  uidic lens microscopy, this chapter demonstrates the application of the droplet lens as an alternative and less-explored approach to realize a  uidic lens. The droplet lens consists of a single droplet of water attached to the end of a micro-liter syringe and possesses large acceptance angles, short focal lengths, and a wide tunability range. The focussing properties of the droplet lens are characterized as a function of the droplet size and modeled as a thick lens using both analytical and ray-tracing methods. We apply the droplet lens as a variable, magnifying component in a microscope and demonstrate 31.3. Thesis Outline microscopic imaging in both re ection-mode and transmission-mode illumi- nation, yielding micron-scale resolution and image quality comparable to that obtained by a conventional laboratory-grade microscope. Chapter 4 begins with an introduction to the theory and principles of SPR and reviews state-of-the-art SPR sensor geometries. We then introduce the design philosophy of a SPR sensor that exploits the index-matching ca- pabilities of  uids. The proposed sensor consists of a thin gold  lm on a multi-layer index-matched  exible substrate, which is then optically at- tached to input and output optical  bres via a drop of index matching  uid. Due to the interconnection between the optical  bre and the substrate via  uid, light transiting from the  bre to the metal  lm is always immersed in a dielectric, precluding the need for a discrete coupling element such as a prism. We build and test a prototype device, detailing the extraction of SPR re ectance curves from the sensor. The performance of the sensor is compared with a multi-layer re ectivity model derived from transfer-matrix formalism. Model predictions of the spectral position and magnitude of the SPR re ectance dip as a function of incidence angle are in good agreement with experimental measurements. The thesis concludes in Chapter 5 with a summary of the key  ndings in the work. 4Chapter 2 Basics of Optical Microscopy A microscope is an instrument that enables visualization of small objects not observable by the naked human eye. The basic optical components of a microscope include an illuminator (a light source and collector lens), a con- denser, objectives lenses, and an eyepiece or camera detector [17]. Di erent combinations of these components are used based on the intended applica- tion and desired magni cation. In this chapter, we will introduce the basic components of a light microscope, detail common aberrations observed in microscope images and their causes, and review state-of-the-art condenser and objective lens designs that correct for these aberrations. 2.1 Components of a Light Microscope 2.1.1 Illuminator Microscope imaging requires a beam of light that is bright, uniform, and constant in amplitude. Common light sources include incandescent  lament lamps and arc lamps [18]. High performance light-emitting diodes (LEDs) are becoming more popular due to their stable output, low energy consumption, low heat generation, low cost and long life span. Laser sources 52.1. Components of a Light Microscope are rarely used due to speckle, caused by interference of light scattered within the illumination  eld. In conjunction with a light source, a collector lens is commonly used to gather the light emanating from the light source. Figure 2.1: Representative image of the internal lens elements inside con- densers of di erent numerical aperture values [19{22]. 2.1.2 Condenser The condenser is an optical element, consisting of multiple lens elements, located between the illuminator and the specimen stage. The role of the condenser is to focus the light from the illuminator onto the imaged region of the specimen. The light cone formed by the beam focussed by the condenser can be adjusted by an adjustable aperture diaphragm. 62.1. Components of a Light Microscope Figure 2.2: Anatomy of a plan-corrected  uorite objective from ZEISS with 63 magni cation capability, numerical aperture of 1:3 with oil/water/g- lycerin as the immersion medium, di erential interference contrast (DIC) method, incorporating in nity color corrected system, also having adjustable cover glass correction (Korr) suitable for cover glass thickness range of 0:15- 0:19 mm [21, 22] 2.1.3 Objective The objective is the most critical component of the light microscope. The role of the objective lens is to collect the light from the imaged region of the specimen and to form a real image that is viewed either by a human eye or a camera. In the simplest realization, the objective can be a large magnifying lens with a short focal length. In more complex realizations, the objective can consist of up to  fteen or more lens elements a xed in a permanent housing, as shown in Figure 2.2 [23]. The multiple lens elements in sophisticated objectives are required to correct for imaging errors and aberrations, which will be discussed later in this chapter. Objectives are primarily classi ed by their numerical aperture and magni cation [24]. The 72.1. Components of a Light Microscope former describes the angle over which the objective can accept light, and the latter describes the enlargement provided by the objective relative to the real imaged region. 2.1.4 Light Microscopy Con gurations The placement of the light source with respect to the other optical components of a microscope depends on the imaging con guration [17, 18, 25]. A microscope intended for light transmission imaging uses the trans- illumination con guration (also known as diascopic illumination), in which the light source and imaging lenses are placed on opposing sides of the specimen. Light emitted from the illumination source is focused onto the specimen by a condenser typically located below the specimen and light transmitted through the specimen is collected by the objective. A condenser aperture diaphragm is a variable aperture placed before the condenser lens. As shown in Figure 2.3, the diaphragm controls the illuminated condenser aperture, enabling adjustment of the angle of the light cone incident onto the specimen. Lighting is optimal when the angle of the light cone matches the numerical aperture of the objective lens on the other side of the specimen. A microscope intended for light re ection imaging uses the epi-illumination con guration (also known as epi-scopic illumination or vertical illumination), in which the light source and imaging lenses are placed on the same side of the specimen. This type of microscope is commonly used for imaging opaque specimen or for metallurgical investigations. Light from the illumination source is directed onto the objective lens. The objective lens focuses the in- cident light onto the sample (like a condenser lens in the trans-illumination 82.1. Components of a Light Microscope Figure 2.3: Illustration of trans-illumination optical microscopy using a sim- ple objective and condenser, in a con guration known as an Abbe micro- scope. The aperture controls the aperture of light entering the condenser [19, 20, 22, 26]. con guration) and collects the light re ected from the sample. Compared to trans-illumination, fewer adjustments are required for epi-illumination be- cause the objective lens acts as both the condenser and objective lens. The re ected light collected by the objective lens is then directed onto an imaging device. Because the illumination source and imaging device are on the same side of the specimen, more than one light path is required, which is achieved by using a partially re ecting surface (a dichroic mirror or beamsplitter), as shown in Figure 2.4. 92.2. Optical Microscopy Concepts Figure 2.4: Epi-illumination con guration for bright  eld re ection mode microscopy. Light is directed along the optical axis onto the objective lens. The lens focuses the incoming light onto the specimen, collects the re ected light, and projects the image of the specimen [19, 20, 22]. 2.2 Optical Microscopy Concepts 2.2.1 Point Spread Function and Airy Disc The response of an imaging system is characterized by its point spread function, a term describing the image produced by an optical element due to an ideal point source of radiation. An axially symmetric lens placed near a point source of radiation produces a point spread function that consists of a circular di raction pattern [25]. Sectioning the di raction pattern in the transverse plane (perpendicular to the axis of the lens) at the focal point yields the classical two-dimensional di raction spectrum, which is charac- 102.2. Optical Microscopy Concepts Figure 2.5: Formation of a point spread function (PSF) and resulting Airy pattern. (left) Constructive interference of wavefronts collected by an ob- jective at the point A0 results in a bright central region of the Airy pattern and (right) destructive interference at the points A0+1 and A 0  1 results in the dark regions of the Airy pattern [19, 21, 22]. terized by a bright circular disc surrounded by an alternating series of bright and dark rings. This di raction spectrum is known as the Airy pattern and the central part of this pattern is called the Airy disc. The radius of this inner disc (known as resolution element or resel) provides a measure of the resolving power of an objective. The relationship between the radius of the inner Airy disc and the resolution of an imaging system is shown in Fig- ure 2.6. The series of images on the left panel of the  gure depicts two Airy patterns, for various wavelengths, resulting from two point sources repre- senting two closely-spaced features on a specimen. The feature separation in the image is de ned by the distance between the centres of the Airy discs. When the Airy discs of the two Airy patterns overlap, it is no longer possi- ble to distinguish the two point sources in the image [26]. The resolution is 112.2. Optical Microscopy Concepts then de ned as the smallest feature separation that is distinguishable in the image plane as two distinct objects. Note that the resolution of an imaging system tends to decrease as the wavelength decreases [24]. 2.2.2 Numerical Aperture Light gathering capacity of a lens is described by a parameter called the numerical aperture (NA), de ned as NA = n sin  ; (2.1) where n is the refractive index of the surrounding medium and  is the most extreme ray in the light cone. The numerical aperture of a lens can be increased by increasing the lens aperture or by using a high refractive index medium surrounding the lens [17, 24, 26]. The relationship between the numerical aperture of a lens and its resolution is shown in the comparative Airy patterns in Figure 2.6. As the acceptance angle of the objective lens increases, the size of the airy pattern diminishes, meaning that the minimum resolution decreases. 2.2.3 Magni cation The magni cation of an imaging system is a dimensionless parameter that describes the relative size of an image of a specimen with respect to its true size. Magni cation is a comparatively less important parameter than the numerical aperture. Increasing the magni cation of an imaging system past a point where the  ne features of a specimen are no longer resolvable 122.2. Optical Microscopy Concepts Figure 2.6: Airy pattern resulting from two point sources. The left side illus- trates the Airy pattern using an objective with relatively low NA, for three di erent wavelengths, and the right side illustrates the Airy pattern using an objective with relatively high NA, also for three di erent wavelengths [19, 21, 22]. 132.3. Optical Aberrations does not increase the image detail, but merely enlarges the image with no new information (known as empty magni cation) [24]. 2.3 Optical Aberrations Optical aberrations describe faults introduced by an imaging system, and are classi ed as either (i) chromatic aberrations or (ii) monochromatic aberrations [27]. The former arises from the variations in the refractive index of materials at visible frequencies, and the latter arises from the non-ideal shape of a lens and the deviation of lens performance from  rst order theory (also known as paraxial or Gaussian optics). Monochromatic aberrations include spherical aberration, astigmatism, and comatic aberration - all of which make an image unclear - and geometrical distortions and Petzval  eld curvature - both of which deform an image. 2.3.1 Spherical Aberration Spherical aberrations are the most common resolution artifact and arise when the sphericity of a lens shape causes light rays incident onto di er- ent parts of a lens to focus at di erent points along the optical axis. The cause of spherical aberrations and its e ect on the image produced by a lens are shown in Figure 2.7, for the case of three lens with di ering degrees of sphericity. Sphericity of the lens shape causes the light rays incident onto di erent portions of the lens aperture to converge at di erent points along the optical axis. Due to the di erent convergence points of the rays, the focal point of the lens is no longer de ned at a single point, but rather de- 142.3. Optical Aberrations  ned at the point where the diameter of the cone formed by the converging rays is minimum, known as the circle of least confusion, P LC [27]. Increas- ing sphericity of the lens shape causes the point spread function and Airy pattern to smear out, resulting in a blurring of the resulting image taken at the position of P LC. Spherical aberration e ects can be reduced by uti- lizing aspherical lens surfaces, or by limiting the periphery of the lens from exposure to incident rays using aperture-stop diaphragms. 2.3.2 Astigmatism Astigmatism describes an imaging error where light rays from orthogonal planes have di erent focal lengths. The point spread function of an imaging system with astigmatism is generally elongated, resulting in an Airy pattern that is elliptical. Because di erent rays are focussed at di erent positions, the shape of the Airy pattern changes as a function of distance from the lens. Astigmatism becomes more pronounced for light rays emerging from a point o the optical axis. Figure 2.8 demonstrates the point spread function, Airy pattern, and resulting image of an imaging system that possesses a large degree of astigmatism. For the case of an object point that is well-aligned with the optical axis, the Airy pattern is approximately symmetrical and the resulting image is well-focussed. As the object point moves away from the optical axis, the Airy pattern becomes elliptical and the resulting image become highly dependent on the position of the image plane. Due to the ellipticity of the Airy pattern, either the vertical or horizontal lines of the image are sharp and focussed, but not both. 152.3. Optical Aberrations Figure 2.7: The e ect of spherical aberration as a function of lens sphericity. The plane of observation is at the circle of least confusion, P LC. When the sphericity is less, as in (a), maximum intensity is found at the center of the point spread function, yielding a comparatively clear image. When the lens become more and more spherical as shown in (b) and (c), contrast and detail of the image is degraded even if the image plane is still at P LC [19, 20, 22]. 162.3. Optical Aberrations Figure 2.8: Exaggerated representation of the e ect of astigmatism on an imaging system for the case of (a) an object point aligned along the optical axis and an image plane located at the focal plane, (b) an object point located o the optical axis and an image plane located at the sagital focal plane, and (c) an object point located o the optical axis and an image plane located at the tangential focal plane. The point spread function, Airy pattern, ray tracing diagram, and resulting image are shown for each case [19, 20, 22]. 172.3. Optical Aberrations 2.3.3 Comatic Aberration Comatic aberration or coma is an optical aberration that arises from imperfections in the lens shape, causing incident rays obliquely incident onto a lens to focus at di erent positions in the image plane. The intensity distribution of the point spread function  ares out, creating an asymmetrical comet-like shape. The tail of the comet-like point spread function may be pointing away or towards the center of the image  eld of view, depending on whether the coma is positive or negative, respectively. Coma can be neutralized using a combination of di erent lenses with positive and negative coma or can be negated by using an aperture-stop at the proper location. 2.3.4 Chromatic Aberration Chromatic aberration arises when a lens focuses rays of di erent color into di erent focal points. This type of aberration occurs because the re- fractive index of the lens medium varies as a function of frequency, a phe- nomenon known as dispersion. Figure 2.10 illustrates an example of chro- matic aberration in an imaging system and its e ect on the resulting image. Blue, green, and red light are focussed at di erent positions by the objective lens, and as a result, the microscope image can have a reddish, greenish, or bluish tinge depending on the position of the image plane. 2.3.5 Geometrical Distortions Geometrical distortions describe aberrations that arise when the trans- verse magni cation, MT , of a lens varies as a function of o -axis position, 182.3. Optical Aberrations Figure 2.9: Comatic aberration causes smearing of a point source into dif- ferent zones (1, 2, 3, 4) on the image plane. Point spread function, Airy pattern, and overall image for (a) the case of an aligned imaging system without coma and (b) the case of an unaligned imaging system with coma [19, 20, 22]. yielding distortions in the overall image. Di erent types of geometrical dis- tortions are illustrated in Figure 2.11. Positive (pin-cushion) distortions are characterized by MT that increases as a function of axial position, and negative (barrel) distortions are characterized by MT that decreases as a function of axial position. Simple thick lenses and compound lens systems are prone to geometrical distortions, whereas thin lenses are generally im- 192.3. Optical Aberrations Figure 2.10: Chromatic aberrations with an uncorrected lens, illuminated by a polychromatic (white) point source. The resulting image can have a (a) greenish, (b) reddish, or (c) bluish tinge when the position of the image plane is located at focal points corresponding to the green, blue, red portions of the visible spectrum, respectively [19, 20, 22]. 202.3. Optical Aberrations mune to distortions. One method to eliminate geometrical distortions is to cascade positive and negative lenses with respect to a symmetrical aperture stop. Figure 2.11: Demonstration of geometrical distortion of an image of a grid pattern (top row). (a) The transverse magni cation is same for all the image points, irrespective of the distance from the optical axis, yielding an undistorted image. (b) Positive or pin-cushion distortions are evident by larger magni cation of the most distant object points from the optical axis. (c) Negative or barrel distortions are evident by the smaller magni cation of the most distant object points from the optical axis [19, 20, 22, 27]. 2.3.6 Field Curvature A lens with a curved surface produces an image plane that is also curved. Simple objective lenses fail to simultaneously focus the paraxial (near the centre) and peripheral (near the edge) regions of the object within the  eld of view. The resulting image is sharp and crisp in either the centre or on the edges, but not both. Inward curvature of the objective lens can be e ectively 212.3. Optical Aberrations Figure 2.12: Illustration of the e ect of  eld curvature on an image, with the corresponding alterations of PSF and illumination of grid pattern ( lm plane). At di erent planes of observation, (a) central portion and (b) edges of the image plane come to sharp focus, making it impossible to distin- guish minor details of the image at other regions. (c) represents the best compromise between center and edge focus [19, 20, 22]. 222.4. Optical Aberrations Correction nulli ed by placing a negative  eld  attener lens near the focal plane, which has little e ect on other aberrations. Modern ‘plan’ or ‘plano’ objectives are capable of producing sharp image detail from the centre to the edges, but these objective lenses are typically very expensive. 2.4 Optical Aberrations Correction Advances in glass formation, grinding and manufacturing techniques have resulted in highly complex objective and condenser lens designs, which have nearly eliminated all the aberrations discussed above [17, 25{28]. In this section, we will detail some of the distinguishing features of commer- cially available objective lens and condensers and review some of the aber- ration correction features. 2.4.1 Objective Correction Table 2.1 lists di erent types of objectives with their corrections for opti- cal aberrations. Achromats, the least expensive, are only partially corrected for chromatic aberration. Fluorites or semi-apochromats are greatly im- proved over achromats, with better chromatic aberration correction, higher numerical aperture, better resolving power and higher degree of contrast. Apochromats are the best choice for color photomicrography in white light conditions. Achromats,  uorites, and apochromats, however, all su er from pronounced  eld curvature [17]. Objectives with correction for  at- eld are named ‘plan’ or ‘plano’, and are considerably more di cult to fabricate due to the increased number of lenses. For example, typical achromats consists 232.4. Optical Aberrations Correction of  ve lenses (two lens doublets and a hemispherical lens) in comparison to more complex plan-achromats consisting of nine lens elements (three dou- blets and three single lenses). Top-of-the-line ‘plan-apochromats’, corrected for spherical, chromatic and  eld-curvature aberrations, may contain eigh- teen to twenty lens elements with proportional increase in cost (upwards to $3000 to $5000 for a single objective), depending on magni cation and numerical aperture [26]. Figure 2.13: Internal lens element combinations ( rst row) and correspond- ing ray tracing diagram demonstrating the chromatic correction (second row) incorporated in an achromat (column one),  uorite (column two) and apochromat (column three) objective of 10 magni cation [19{22, 28]. 242.4. Optical Aberrations Correction Table 2.1: Optical aberration correction for objective lenses Achromats  Axial chromatic correction for red and blue  Corrected for spherical aberration in green  Green halo appears in the images for focus cho- sen in red-blue region  Lack of correction for  atness of  eld curvature Fluorites or semi-apochromats  Improved correction of optical aberration  Corrected chromatically for red and blue, with green focused at a much closer distance  Spherical aberration is corrected for two colors  Su er from lack of  eld curvature correction Apochromats  Corrected chromatically for three colors (red, green and blue)  Spherical correction for two colors  Su er from pronounced  eld curvature Plan-achromats, Plan- uorites, Plan-apochromats  These are achromats,  uorites and apochromats respectively provided with  at- eld correction along with other corrections mentioned above  Plan correction is achieved at the cost of signif- icant increase in the number of lens elements 252.4. Optical Aberrations Correction Figure 2.14: (a) Correction for  at- eld curvature for a 10 achromat re- quires insertion of a meniscus lens, a doublet and a triplet lens group into the objective. (b) Correction collar adjustment for di erent coverslip thickness of 0:20 mm and 0:13 mm to correct for aberrations that are introduced due to the variation of the cover glass thickness and dispersion of the medium between the front lens and the cover glass [19, 21, 22, 28]. 2.4.2 Condenser Correction Di erent types of condenser corrections are listed in Table 2.2. Abbe condensers possess a wide cone of illumination and are the simplest and least-corrected condenser. Aplanatic and achromatic condensers boast a slightly higher degree of correction. Aplanatic-achromatic condensers have the highest level of correction. 262.4. Optical Aberrations Correction Table 2.2: Optical aberration correction for condenser lenses Abbe  Consists of two optical lens elements  Image produced is not sharp and is surrounded by blue and red color at the edges Achromatic  Corrected exclusively for chromatic aberration, not for spherical aberration  Typically contains four lens elements  Provides highest attainable numerical aperture of 0:95 without immersion oil Aplanatic  Well corrected for spherical aberration in green, but not for chromatic aberration  Featured with  ve lens elements  Capable of focusing light in a single plane Aplanatic- Achromatic  Provides with highest level of correction for both chro- matic and spherical aberration  Featured with eight internal lens elements, cemented into two doublets and four single lenses  Best choice for color photomicrography 27Chapter 3 Water Droplet Microscopy Water droplets are an attractive medium to realize lensing elements. Water is transparent over the visible frequency range, ultra-smooth surfaces of a droplet are naturally created through surface tension, and the droplet shape is recon gurable by either applying pressure or electric  elds. Here, we use a water droplet as the magnifying component in a simple microscope operating under either re ection-mode or transmission-mode illumination. A water droplet is created at the end of syringe and then coated with a thin layer of oil to mitigate evaporation. By applying pressure to the water droplet using a metal tip, the shape of the droplet is tuned to yield focusing properties amenable for microscopy. Images captured using the microscope show micron-scale resolution and tunable magni cation. The results demon- strate a simple, low-cost, and elegant con guration for realizing a tunable microscope system based on a droplet of water. 3.1 Fluidic Lens Microscopy A lens is a discrete optical element that causes an incoming beam of light to either converge or diverge. The e ect that a lens imparts onto an incident light beam is determined, in large part, by the curvature of the surfaces of 283.1. Fluidic Lens Microscopy the lens, which then sets its focal length. For a lens constructed from a transparent solid, such as glass, crystal, or plastic, the curvature of the lens surfaces is rigid and its focal length is  xed. Tunability of the focal length then requires a system of lenses, where the e ective focal length of the lens system is adjusted by varying the relative positions of the constituent lenses. There has been growing interest in the development of lenses constructed from  uids [29{32]. The advantage of a  uidic lens, as opposed to a solid lens, is that the curvature of the lens can be easily deformed, meaning that a tunable focal length can be achieved using a single element, and the surfaces of the lens are naturally smooth due to surface tension. The use of a  uid, however, introduces the requirement of systems to provide mechanical sta- bility, prevent evaporation, and manipulate the  uid. To date,  uidic lenses have been implemented in the form of discrete optical elements, consisting of a housing structure to store the constituent  uid and an actuation method to adjust the shape of the  uid. The actuation method is commonly based on the application of mechanical pressure or an electric  eld to the  uid vol- ume. Fluidic lenses based on the application of electric  elds exploit either the electro-wetting e ect [31, 33] or dielectrophoresis force [34{38]. Fluidic lenses based on the application of mechanical pressure, on the other hand, exploit the natural deformation of  uids in pressurized environments. Pres- sure lenses are tuned by either applying a hydraulic or ambient pressure to a  xed  uid volume [32, 39{42] or by changing the volume of  uid [43{50]. Current implementations of  uidic lenses have demonstrated a high de- gree of stability and control over the shape of the  uid, but require elabo- rate housing structures [36, 41, 43, 45, 49, 51], in many cases constructed 293.2. Droplet Lens Dispenser and Actuator using multiple micro- or nano-fabrication steps [43, 44]. An alternative and less-explored approach to realizing a  uidic lens is to exploit the existing low-technology methods available to controllably dispense and shape small volumes of  uids. In this work, we explore a  uidic lens constructed from a water droplet attached to a syringe. To mitigate evaporation, the water droplet is encased in a transparent and immiscible silicone oil layer, which also forms the exterior portion of the lens. The droplet is actuated by both applying a pressure with an external tip and varying the volume of the droplet directly through the syringe. The resulting droplet lens possesses large acceptance angles, short focal lengths, and a wide tunability range. A potentially useful feature of this implementation is that the droplet lens can created on demand and discarded after use. We demonstrate the applica- tion of the droplet lens as a variable, magnifying component in a microscope operating under both re ection-mode and transmission-mode illumination. Although the droplet lens does not possess the same degree of stability and control as other  uidic lens implementations, it may  nd usefulness due to the low-cost of implementation, wide availability of requisite equipment, and simplicity of operation. 3.2 Droplet Lens Dispenser and Actuator We design a  uidic lens based on water droplets controllably dispensed from and attached to the end of a micro-liter syringe (Hamilton 701RN 10 L syringe). We establish a coordinate system where the axis of the syringe is oriented along the x-axis (horizontal), gravity is directed along 303.2. Droplet Lens Dispenser and Actuator Figure 3.1: Droplet size determination by analysis of images taken of the droplet from horizontal and vertical perspectives. The projected area of the droplet measured from the horizontal perspective as a function of the droplet volume inferred from both perspectives. the z-axis (vertical), and the optical axis of the lens is oriented along the y-axis. In general, the droplet can be modeled as an ellipsoid with three principle axes a, b, and c, corresponding to the diameters of the droplet along the x, y, and z axes, respectively. The parameters a, b, and c are measured from images of the droplet taken from vertical and horizontal perspectives, where b and c are extracted from the horizontal perspective (yz plane) and a and b from the vertical perspective (xy plane). The volume, V , and horizontal projected area, A, are then given by V =  abc=6 and A =  bc=4, respectively. Either the volume or the area can be used as a metric for the droplet size. As shown in Figure 3.1, a positive, monotonic 313.2. Droplet Lens Dispenser and Actuator correlation between the volume and projected area indicates that increases in the droplet volume yield proportional increases of the droplet size in terms of projected area. Throughout the remainder of this paper, the droplet size will be discussed primarily in terms of the horizontal projected area. A water droplet directly exposed to atmosphere is prone to rapid evapo- ration which results in shape distortions. To mitigate evaporation, we coat the water droplet in a thin layer of silicone oil. The oil coating is applied by simply dispensing an oil droplet above the attached water droplet. As the oil droplet whisks past the water droplet, a thin protective layer of oil evenly and completely surrounds both the water droplet and a portion of the syringe. As shown in the images in Figure 3.2, addition of the oil coat- ing does not signi cantly change the overall shape of the water droplet or its transparency, but reduces the evaporation rate of the water droplet by  ve-fold, from 0:072 mm2= min to 0:014 mm2=min [Figure 3.2(e)]. Although the oil coating does not completely eliminate evaporation, it does enable a single, millimeter-scale water droplet to last for over an hour. Because the droplet is still attached to the syringe, gradual reduction in the size of the oil-coated water droplet can be compensated by controllably dispensing water from the syringe. We next study the focussing properties of an oil-coated water droplet as a function of water volume using the con guration depicted in Figure 3.3(a). Light diverging from a single-mode  bre having a 5 m core diameter is collimated by the droplet lens and then recorded by a camera placed a distance much greater than the focal length away from the coated droplet. 323.2. Droplet Lens Dispenser and Actuator Figure 3.2: Microscope images of a bare water droplet at (a) t = 0 s and (b) t = 15 min. Dispensing a drop of oil over the water droplet results in a thin oil layer surrounding the water droplet. Microscope images of a water droplet with an oil coating at (c) t = 0 s and (d) t = 15 min. (e) The measured projected area of the two types of droplets as a function of time. The bare water droplet has an evaporation rate of 0:072 mm2=min and the oil-coated water droplet has an evaporation rate of 0:014 mm2= min. The evaporation rate depends on the relative humidity and can be further reduced by encasing the setup in a high-humidity chamber. Oil coating the water droplet yields a greater than 5 times decrease in the evaporation rate. 333.2. Droplet Lens Dispenser and Actuator Figure 3.3: (a) Experimental setup to determine the focal distances of the water droplet based on collimation of visible light emitted from an optical  bre. The oil-coated water droplet is attached to a syringe connected to a water reservoir. The focusing properties of the droplet are changed by varying the volume of the droplet. The light emanating from the optical  bre is collimated by the droplet and the far- eld image of the light source is collected by a camera at a far distance (much greater than the focal length) from the lens. Typical far- eld images indicating (b) horizontal collimation, (c) vertical collimation, and (d) full collimation. The beam shapes are insensitive to the screen position. 343.2. Droplet Lens Dispenser and Actuator The  bre is aligned along the y-axis (optical axis) of the lens to miti- gate astigmatism e ects. For a given volume, we measure two focal lengths of the lens: a \horizontal" focal length corresponding to the distance from the center of the lens to the  bre tip resulting in a horizontally-collimated beam shape [Figure 3.3(b)] and a \vertical" focal length corresponding to the distance resulting in a vertically-collimated beam shape [Figure 3.3(c)]. The horizontal and vertical focal lengths are generally unequal because the transverse shape of the lens is not symmetric [Figure 3.4(c)]. This asym- metry arises from two competing e ects, illustrated in Figure 3.4(d). For smaller droplet volumes, attachment of the droplet along the shaft of the syringe causes elongation of the horizontal diameter a relative to vertical diameter c, yielding an oblate ellipsoidal shape. For larger droplet volumes, the increasing e ect of gravity on the droplet causes concurrent elongation of the diameter c and reduction in a, yielding a prolate ellipsoidal shape. As a result, the vertical focal length monotonically increases and the horizontal focal length decreases and plateaus as a function of the increasing droplet size [Figure 3.4(c)]. Due to the competing e ects of droplet attachment and gravity, there is only one droplet volume that yields a symmetric transverse shape. When a symmetric transverse shape is achieved, the horizontal and vertical focal lengths are matched, resulting in a beam shape that is fully collimated [Figure 3.3(d)]. To enable greater control over the shape of the droplet for any droplet volume, we incorporate a metallic tip below the end of the syringe that attaches onto the dispensed water droplet. The metallic tip is actuated in three-dimensions, with positioning accuracy on the order of ’ 1 m, using 353.2. Droplet Lens Dispenser and Actuator Figure 3.4: (a) and (b) depict images of an oil-coated water droplet attached with the syringe where the size and shape of the droplet has been varied by increasing the water volume. The general shape of the droplet is elliptical. The ellipticity of the droplet is larger for smaller droplets due to adhesion to the syringe and larger droplets due to gravity-induced elongation. Ellipticity in the droplet shape yields disparate focal lengths along the horizontal and vertical directions. (c) Horizontal and vertical focal lengths of the droplet as a function of projected droplet area. For this oil-coated water droplet system, there exists only one droplet size where the horizontal and vertical focal lengths are matched. (d) Illustrations demonstrating the changing shape of the water droplet as a function of volume. 363.2. Droplet Lens Dispenser and Actuator Figure 3.5: Variation of the shape of the oil-coated water droplet system by applying pressure through a bottom tip. A metallic tip is  rst (a) attached to the bottom of a water droplet. A droplet of oil is then dispensed from a syringe, resulting in (b) an oil-coated water droplet connected to a bottom tip. (c) shows a microscope image of the complete  uidic lens system. (d) Sequence of microscope images of the droplet system demonstrating size and shape recon guration by either changing the volume or pressure on the droplet. 373.2. Droplet Lens Dispenser and Actuator Figure 3.6: Images of a symmetric droplet taken from a vertical perspective (left) and a horizontal perspective (right), where symmetric circles have been superimposed onto the edge of the droplet in the images. the three-axis mechanical linear stage (Newport ULTRAlign). Inclusion of the bottom tip provides physical support for the weight of the droplet (per- mitting larger droplet sizes than previously possible without the tip) and enables tuning of the lens curvature, particularly along the vertical direc- tion, by varying the separation distance between the tip and the syringe. An image of a typical  uidic lens resulting from this con guration is shown in Figure 3.5 (c). The sequence of images in Figure 3.5 (d) highlights con- trollable and reversible alterations of the droplet shape by either changing the droplet volume or varying the tip-syringe separation. In particular, for 383.2. Droplet Lens Dispenser and Actuator Figure 3.7: (a) Experimental set-up for measuring the focal length of the tip-supported droplet system. By tuning the position of the bottom tip, the shape of the droplet for any volume can be adjusted to achieve complete (horizontal and vertical) collimation of the optical  bre light source. (b) Focal length of the droplet system as a function of droplet volume and projected droplet area. 393.3. Re ection-Mode Microscope based on a Droplet Lens a given droplet volume, the tip-syringe separation can be varied until a highly symmetric droplet shape is realized (Figure 3.6). The symmetric droplet shape possesses matching vertical and horizontal focal lengths, a basic requirement for application as an imaging lens. Figure 3.7(b) summa- rizes the focal lengths of a series of droplets, possessing symmetric transverse shapes, created using the modi ed dispensing and droplet shaping con gu- ration. 3.3 Re ection-Mode Microscope based on a Droplet Lens We next build a re ection-mode microscope where the oil-coated droplet dispensed from the syringe acts as both the condenser and objective lenses. The microscope con guration is depicted in Figure 3.8. Visible light from a light-emitting diode is directed along the optical axis onto the lens. The lens focuses the incoming light onto a sample and then collects and colli- mates the re ected light. The collimated beam goes through an aperture with a diameter of 1:38 mm and is then captured by a CMOS camera. The magni cation of the microscope is varied by changing the volume of the wa- ter droplet and then adjusting the tip-syringe separation until the resulting image is free of distortions. Figure 3.9 (a) depicts representative images of a calibration slide captured by the microscope at various magni cation levels. The calibration slide consists of a series of parallel lines, where the pitch spacing between successive lines is 10 m. The magni cation values are measured by comparing the actual size of the sample and the size of the 403.3. Re ection-Mode Microscope based on a Droplet Lens Figure 3.8: Re ection-mode microscope using a  uidic lens composed of the oil-coated water droplet system. In this con guration, the  uidic lens emulates both the condenser and objective lenses found in a conventional optical microscope. A light-emitting diode emits visible light into a beam- splitter, which re-directs the light onto the  uidic lens. The lens focuses the light onto a sample and then collects and collimates the back-scattered light. An image of the focal region is captured using a CMOS camera sensor (Logitech C160 with lens removed). image of the sample projected onto the CMOS sensor. We position the cal- ibration slide diagonally at an angle of 35 with respect to the horizontal. The diagonal position of the sample enables visualization of barrel [34, 44], pin-cushion [31], or mustache distortions along both the vertical or horizon- tal directions based on smearing of the lines. Slight overall blurriness of the entire image at larger magni cations (at 43X and 46X) is due to spher- ical aberrations introduced by the spherical shape of the lens surfaces. As shown in Figure 3.9(b), this particular microscope con guration is capable of magni cation values from 37X to 47X, with a corresponding  eld of view that ranges from 170 m to 120 m. It should be noted higher magni cation values are possible by using droplets of smaller sizes and lower magni cation 413.3. Re ection-Mode Microscope based on a Droplet Lens Figure 3.9: (a) Microscope images of a calibration slide captured at various levels of magni cation using the  uidic lens microscope. The pitch sepa- ration between adjacent lines on the slide is 10 m. (b) Field of view and magni cation of the microscope as a function of projected droplet area. 423.3. Re ection-Mode Microscope based on a Droplet Lens values are possible by using a larger tip size capable of sustaining larger droplet sizes. One of the reasons for using water as the lens material rather than using a droplet of the non-volatile oil as the lens itself is the high surface tension of water droplet which allows a relatively large sized droplet to remain attached. The focal length of the lens, measured by recording the lens-sample separation yielding the sharpest image, follows the same trend as the focal lengths previously measured using the beam collimation con guration (Figure 3.10). Larger droplet sizes are used in the microscope con guration to accommodate the larger beam size from the light-emitting diode. Figure 3.10: Focal length of the oil-coated water droplet lens as a function of projected droplet area measured from the lens-sample separation in the microscopy con guration (blue squares) and the  bre-lens separation in the beam collimation con guration (red circles). The error bars in the mea- surements in the microscopy con guration account for uncertainty in the position of the sample. 433.4. Transmission-Mode Microscope based on a Droplet Lens 3.4 Transmission-Mode Microscope based on a Droplet Lens The oil-coated droplet lens is next used as the objective lens in a micro- scope con guration using transmission-mode illumination. The microscope con guration is depicted in Figure 3.11. Visible light from a light-emitting diode passes through a condenser lens and is focussed onto a sample. Light transmitted through the sample is collected and collimated by the droplet lens. The collimated beam is then captured by a CMOS camera. Figure 3.12 (a) depicts images of various semi-transparent biological samples captured by the microscope at di erent levels of magni cation. Figure 3.11: Transmission-mode microscope using a  uidic lens composed of the oil-coated water droplet system. In this con guration, a separate lens is used as a condenser lens to illuminate the sample, and the  uidic lens acts as an objective lens. A light-emitting diode emits visible light into the condenser lens, which focuses the light onto the sample. The objective lens collects and collimates the light transmitting through the sample. An image of the focal region is captured using a CMOS camera. 443.4. Transmission-Mode Microscope based on a Droplet Lens Figure 3.12: Microscope images of spinal cord tissue ( rst row), basswood stem (second row), cardiac muscle tissue (third and fourth row), and Peni- cillium ( fth row). Column (a) shows the images obtained using the droplet lens in the transmission-mode microscope con guration. Columns (b) and (c) show near-focussed and best-focussed images, respectively, obtained from a conventional laboratory-grade microscope (Zeiss AxioImager) using a 20 objective lens. Column (d) shows cropped images of the highlighted region in the near-focussed images, which matches the region imaged by the droplet lens. 453.5. Modeling the Optical Properties of the Droplet Lens Slight blurriness near the edges of the images are attributed to Petz- val  eld curvature e ects [27] (as opposed to spherical aberration e ects observed in the re ection-mode images in Figure 3.9). To qualitatively ac- cess the performance of the droplet lens, two sets of microscope images are captured by a conventional laboratory-grade microscope (Zeiss AxioImager) using a 20 objective lens: best-focussed images in which the sample is positioned at the focal plane and near-focussed images in which is sample is positioned slightly outside of the focal plane [Figures 3.12 (c) and (d)]. Images captured using the droplet lens have comparable micron-scale reso- lution and image quality to those obtained by the conventional microscope. The level of detail captured by the droplet lens does not match that of the best-focussed images, but is more comparable to that of the near-focussed images. Nonetheless, the imaging capabilities of the droplet are impressive considering the relative simplicity of our implementation. 3.5 Modeling the Optical Properties of the Droplet Lens We model the droplet as a thick lens with geometrical parameters ex- tracted from the images of the droplet [Figure 3.13]. The thickness of the lens, d, is the droplet diameter b along the optical axis and the height of the lens (or total aperture size) is 2r, which is approximately half of the total tip-syringe separation. We extract the radii of curvature by  tting the shape of the front and back surfaces of the droplet, captured in images of the droplet taken from a horizontal perspective, with circles of radii R1 and 463.5. Modeling the Optical Properties of the Droplet Lens Figure 3.13: (a) Image of an oil-coated water droplet (taken from the hori- zontal perspective) adjacent to an optical  bre light source. The separation between the bottom tip and syringe has been tuned to reduce the ellipticity in the droplet shape. (b) depicts the procedure to extract the geometrical parameters of the lens for theoretical analysis. The two curved surfaces of the droplet are  tted to circles with radii of curvature of R1 and R2. d is the thickness of the lens and 2r is the aperture size of the lens. R2, respectively, and then scaling the pixel sizes in the image to real dimen- sions. The transverse shape of the lens is symmetric (as observed from the images of the droplet taken from both horizontal and vertical perspectives [Figure 3.6] and further supported by observations of full beam collimation 473.5. Modeling the Optical Properties of the Droplet Lens and distortion-free imaging), meaning that the parameters d, 2r, R1, and R2 are the same regardless of the direction that the lens is viewed. The focal length is measured with respect to the center of the lens. Figure 3.14 (a) illustrates an idealized biconvex thick lens created using geometrical parameters extracted from images of the water droplet. The e ective focal length, fh, of the thick lens for paraxial approximation can be calculated [27] as 1 fh = (nl  1)  1 R1  1 R2 + (nl  1) d nlR1R2  : (3.1) Values of fh are determined with respect to the principal planes of the lens (as shown in Figure 3.14), which are located at distances h1 =  fh (nl  1) d R2nl (3.2) and h2 =  fh (nl  1) d R1nl (3.3) from the vertices of the front and back surfaces, respectively. Given the symmetric biconvex lens shape in our experiments where jR1j = jR2j = R and hence jh1j = jh2j = h, fh is related to the focal length measured from the center of the lens fp by fp = fh +  d 2  h  : (3.4) 483.5. Modeling the Optical Properties of the Droplet Lens Figure 3.14: Schematic of an idealized thick lens constructed using the geo- metrical parameters of the  uidic lens. (a) Two-dimensional and (b) three- dimensional perspective of the calculated ray trajectories of a collimated beam incident at normal incidence onto the thick lens. The focal length corresponds to the distance from the center of the lens to the convergence point of the rays. 493.5. Modeling the Optical Properties of the Droplet Lens For each droplet size, we extract the geometrical lens parameters d, 2r, R1, and R2 from the images taken of the droplet from the vertical and horizontal perspectives. The focal length of the droplet is determined by analytical calculations under the paraxial approximation (Eqs. 3.1 and 3.4) and a ray tracing simulation based on the transfer-matrix method. Fig- ures 3.14(a) and (b) show ray tracing simulation results of a collimated input beam incident onto a lens created using realistic parameters extracted from images of a droplet lens. The ray tracing simulations are conducted for collimated illumination where the aperture  ll factors (corresponding to the ratio of the illuminated aperture to the total lens aperture) are 30%, 70% and 100%. The results of the ray tracing simulations for the three  ll- factor test cases are depicted in Figures 3.15 (b), (d), and (f). For 30%  ll factor, the focal length measured from the ray tracing simulations simply corresponds to the distance from the center of the lens to the well-de ned convergence point of the rays with the optical axis. For 70% and 100%  ll factors, the rays no longer converge at a single point due to the strongly refracted rays incident at distances further from the optical axis and the fo- cal length instead corresponds to the distance from the center of the lens to point where the diameter of the cone formed by the rays is minimum, known as the circle of least confusion, P LC. Figures 3.15 (a), (c), and (e) compare the focal lengths calculated under the paraxial approximation and simulated with the ray tracing simulation with the focal lengths measured via beam collimation. Analytical calculations using the paraxial approximation and the ray tracing simulations for 30%  ll factor consistently over-estimate the experimentally-measured focal lengths for all droplet sizes. Increasing the 503.5. Modeling the Optical Properties of the Droplet Lens  ll factor decreases the focal length values extracted from the ray tracing simulations. Ray tracing simulations using a 70%  ll factor yield focal length values most closely matching the experiment. We next compare the calculated focal lengths to the focal lengths mea- sured using the microscope con guration [Figure 3.16]. The microscope in- cludes an aperture stop that restricts the beam size to a diameter of 1:38 mm. When the droplet size exceeds the aperture stop dimension, the focal length measurements more closely match those calculated under the paraxial ap- proximation. As the droplet size decreases to less than the aperture stop dimension, the paraxial approximation fails and the focal lengths are bet- ter modeled using ray tracing simulations with high  ll factor. Spherical aberrations are thus expected to be lower for larger droplets and higher for smaller droplets, a trend consistent with the microscope images shown in Figure 3.9. The sharpest images are obtained at lower magni cations (using larger droplets) and the blurriness increases at higher magni cations (us- ing smaller droplets). It should be noted that the focal lengths measured using the beam collimation con guration for all droplet volumes are consis- tent with ray-tracing simulations using a 70%  ll factor. Assuming that the beam emanating from the  bre has a small divergence angle, proportionality between the droplet aperture size and focal length yields an approximately constant  ll factor. Overall consistency between the focal lengths measured using the beam collimation and microscopy con gurations and the calculated focal lengths suggests that refraction due to the thin oil coating surrounding the water droplet does not signi cantly in uence the focussing properties of the lens. 513.5. Modeling the Optical Properties of the Droplet Lens Figure 3.15: Comparison of focal lengths measured using the beam colli- mation con guration to focal lengths calculated using the analytical model under the paraxial approximation and the ray-tracing simulation using (a) 30%, (c) 70%, and (d) 100%  ll factors. The results of the ray tracing simulations using (b) 30%, (d) 70%, and (e) 100%  ll factors. 523.5. Modeling the Optical Properties of the Droplet Lens Figure 3.16: (a) Comparison of the focal lengths measured using the micro- scope con guration to focal lengths calculated using the analytical model under the paraxial approximation and the ray-tracing model using various  ll factors. (b) Tip-syringe separation of the lens versus the droplet size. The size of the aperture stop is shown by the dotted grey line. For tip- syringe separations exceeding the aperture size, the corresponding images have reduced spherical aberrations (denoted as SA in the plot), and for tip-syringe separations less than the aperture size, the images have greater spherical aberrations. The magni cation provided by various droplet sizes are labeled, corresponding to the microscope images shown in Figure 3.8. 533.6. Limitations 3.6 Limitations The most signi cant limitation of building an imaging system based on a suspended droplet is lack of mechanical stability. Changes in the shape of the droplet due to ambient vibrations and gradual reduction of the droplet size due to evaporation both cause distortions in the captured image. Ambient vibrations can be reduced by using vibration dampening stages. Evaporation has been mitigated, but not eliminated, by coating the droplet with a thin layer of silicone oil. Further reduction in the evaporation rate of the droplet can be achieved by housing the system in a sealed and humidity-controlled environment, or housing the entire syringe and droplet system in an im- miscible  uidic environment. Another limitation of our implementation is alignment sensitivity due to  uctuations in the optical axis as the droplet size changes. This e ect has been mitigated by using a light-emitting diode with a wide emission angle and a CMOS sensor area larger than droplet size, both of which reduces the sensitivity of the image to the optical axis location, but could be further reduced by developing an alignment system that automatically adjusts the position of optical elements with respect to the size of the droplet. 3.7 Summary In conclusion, we have explored a novel, low-technology method to imple- ment a  uidic lens using low-cost and widely available techniques to dispense and shape small volumes of  uids. The  uid lens consists of a single droplet of water attached to the end of a micro-liter syringe. The water droplet is 543.7. Summary coated with a layer of silicone oil which forms the outer portion of the lens and mitigates rapid evaporation of the droplet. The shape and size of the droplet are tuned by applying an external pressure to the droplet through a tip and directly injecting water into the droplet through the syringe. A unique feature of this  uidic lens implementation is that the lens can be created on demand and can be discarded after use with little waste of ma- terials. We have characterized the focussing properties of the droplet lens as a function of the droplet size and used the droplet as the objective lens in both re ection-mode and transmission-mode microscope con gurations. The droplet lens is capable of micron-scale resolution imaging, wide tunabil- ity by varying the droplet volume, and image quality comparable to, but noticeably less than, that obtained by conventional laboratory-grade micro- scopes. Although our low-technology implementation lacks the mechanical stability and degree of control of recently explored  uidic lens implemen- tations, it may be useful in resource-limited regions due to the low cost of implementation, wide accessibility of the requisite materials, and relative simplicity of operation. 55Chapter 4 Fibre-Addressable Surface Plasmon Resonance Chip Using Optically Matched Fluid Surface plasmons are transverse-magnetic (TM) polarized electromag- netic waves that are coupled with free electron density oscillations at the interface of a metal and a dielectric medium [52{54]. Surface plasmon reso- nance (SPR) describes a condition where light couples e ciently into surface plasmons, light waves that propagate along the surface of a metal. A SPR device is a type of optical sensor that exploits the sensitivity of surface- plasmon coupling to the dielectric environment adjacent to a metal surface. A common SPR device con guration consists of a substrate with a metallic layer, an external light source, optical components to polarize and guide light, a coupling device (typically a prism) to convert light into surface plas- mons, and a light detector. SPR devices have found niche application as non-destructive, label-free biochemical sensors [55, 56]. 564.1. Surface Plasmon Resonance: Wavevector Matching Condition There are a couple of limitations with existing SPR device architectures. First, the requirement of many external components restricts the minia- turization of SPR devices. Second, SPR devices require expensive optical elements, such as prisms, which drives up the cost and makes single-use ap- plication infeasible. In an e ort to overcome these limitations, we design, fabricate, and test a SPR device architecture that is  bre-addressable, does not require a discrete coupling structure, and integrates the light delivery and polarization control onto the a single  exible substrate. Our SPR device consists of a thin gold layer deposited on a clear plastic sheet, which is then optically connected from the bottom surface onto a plastic linear polarizer sheet. Two cleaved  bres, one to collect the input light and the other to collect the output light, are then optically attached to the SPR chip. The angles of the collection  bres are tuned so that visible light incident onto the gold  lm from the bottom of the chip couples to surface plasmons on the other side of the gold  lm. Because the SPR device is constructed entirely from widely-available and inexpensive components, it has the advantages of low-cost and amenability to single-use applications. 4.1 Surface Plasmon Resonance: Wavevector Matching Condition Surface plasmon resonance occurs when the wavevector of light matches the surface plasmon wavevector [57]. For an interface between a dielectric medium, characterized by a permittivity  1, and metallic medium, charac- 574.1. Surface Plasmon Resonance: Wavevector Matching Condition terized by a permittivity  2, the surface plasmon wavevector is given by kSPP (!) = ! c s  1(!)  2(!)  1(!) +  2(!) (4.1) where ! is the frequency and c is the speed of light in vacuum. The wavevec- tor of light in the dielectric medium, on the other hand, is given by kd = ! c p  1(!); (4.2) which, for  1  1, is always less than kSPP . Inequality between the surface plasmon wavevector and the light wavevector precludes wavevector match- ing. This is shown in Figure 4.1(a), which plots the surface plasmon wavevec- tor for the representative case of an air-Ag interface and the wavevector of free-space light at grazing incidence (  = 90 ) on the interface. The free- space light wavevector forms a straight line and is commonly known as the \free-space light line". At low frequencies, the surface plasmon wavevector is similar to the free-space light line, but as the frequency increases, the wavevector departs from the free-space light line and increases towards an asymptotic limit. In general, the wavevector matching condition cannot be achieved because the surface plasmon wavevector lies to the right of the light line, for any incidence angle up to the limiting case of grazing incidence. Surface plasmon resonance via wavevector matching requires either an increase in the light wavevector with respect to a  xed surface plasmon wavevector or a decrease in the surface plasmon wavevector with respect to a  xed light line, both of which shift the relative positions of the light 584.1. Surface Plasmon Resonance: Wavevector Matching Condition wavevector and surface plasmon wavevector so that regions of overlap are possible. This requires at least three distinct media: a metallic medium, a dielectric medium of lower refractive index and another dielectric medium of higher refractive index. In the simplest con guration where a metallic medium is sandwiched on both sides by the two types of dielectric media, there are at least four types of waves that are possible: two light waves, one in each dielectric media, and two surface plasmon waves, one at each of the two interfaces of the metallic medium. Figure 4.1(b) plots dispersion diagrams of the possible light and surface plasmons waves for the representative case of an Ag medium sandwiched by air and glass. Although wavevector matching is not possible between light and surface plasmons associated with the same dielectric medium, wavevector matching is possible between light in glass and surface plasmons at the air-Ag interface [53]. Wavevector matching between light incident onto a metal surface from an optically denser medium and surface plasmons at the interface between a metal and an optically rarer medium can be achieved by either tuning the incidence angle (known as angle modulation) or tuning the wavelength of light (known as wavelength modulation). Both angle modulation and wave- length modulation provide a means to shift the incident light wavevector until it matches with the surface plasmon wavevector, and are highlighted in Figure 4.2. Wavevector matching results in a drop in the re ectivity from the metal surface, which can be mapped as a function of angle or wavelength. Representative SPR re ectivity curves are shown in Figure 4.3, for the case of a silver medium sandwiched by a denser dielectric medium (substrate) of 594.1. Surface Plasmon Resonance: Wavevector Matching Condition Figure 4.1: Dispersion relation diagrams illustrating the wavevector match- ing condition required for light coupling into surface plasmons on a planar air-metal interface. The metal is assumed to be Ag. (a) depicts the real part of surface plasmon wavevector (red line) at an air-Ag interface and the component of the free-space light wavevector (black line) projected onto the interface at grazing incidence  = 90 . The gray lines depict the component of the free-space light wavevector projected onto the interface for intermedi- ate incidence angles. (b) depicts the real part of surface plasmon wavevector (red line) at an air-Ag interface and the component of the light wavevector in a dielectric (cyan line) projected onto the interface at grazing incidence  = 90 . The gray lines depict the component of the light wavevector in a dielectric projected onto the interface for intermediate incidence angles. Note that wavevector matching is possible between the surface plasmon at an air-metal interface and the light wavevector in a dielectric. 604.1. Surface Plasmon Resonance: Wavevector Matching Condition Figure 4.2: Illustration of design parameters tuning in order to achieve required wavevector matched condition. Alteration of the (a) permittivity of higher index dielectric,  d and (b) angle of incidence,  into the dielectric makes surface plasmon excitation possible at a desired frequency by shifting the light line. Wavevector matching condition can also be satis ed by (c) tuning frequency of incident light, f along a particular light line. 614.1. Surface Plasmon Resonance: Wavevector Matching Condition Figure 4.3: Drop in the intensity of re ected light due to surface plasmon resonance. (a) and (b) demonstrates surface plasmon resonance curve for the detection of any slight change in superstrate refractive index through wavelength modulation and angle modulation respectively,   and   de- picts the corresponding shift in the resonance curve due to the change in superstrate medium. 624.2. Optical Coupling Con gurations to Measure Surface Plasmon Resonance refractive index 1.5 and a rarer dielectric medium (superstrate) of variable refractive index ranging from 1.0 to 1.1. SPR sensors exploit the sensitivity of the position of the re ectivity dip on the dielectric environment adjacent to the metal surface. As the dielectric constant of the superstrate is changed from 1:0 to 1:1, the position of the re ectivity dip shifts to higher angles for the case of angle modulation and longer wavelengths for the case of wavelength modulation. 4.2 Optical Coupling Con gurations to Measure Surface Plasmon Resonance A common method to optically couple to surface plasmons uses the Kretschemann con guration [58, 59]. As shown in Figure 4.4(a), the Kretsche- mann con guration consists of a thin metal  lm deposited on a high-refractive- index prism. Light, typically from a laser source, is polarized and directed onto the metal  lm from the prism side. The prism region below the metal  lm is known as the substrate, and the region above the metal  lm is known as the superstrate. For a su ciently thin metal  lm, light incident onto the  lm from the prism side evanescently tunnels through the  lm, enabling light on the prism side to couple to surface plasmons on the superstrate side. When the incidence angle is tuned so that wavevector matching is achieved between incident light and surface plasmons on the superstrate side, e cient surface plasmon coupling is achieved and the intensity of the light re ected from the  lm diminishes. The external angle (measured with respect to the 634.2. Optical Coupling Con gurations to Measure Surface Plasmon Resonance Figure 4.4: (a) Kretschemann con guration and (b) optical  bre con gura- tion to optically coupling to surface plasmons. In both con gurations, light incident onto a thin metal  lm from an optically denser dielectric medium (labeled the \substrate") couples into surface plasmons on the interface be- tween the metal  lm and the optically rarer dielectric medium (labeled the \superstrate"). 644.3. Proposed Surface Plasmon Resonance Sensor normal to the prism face) is related to the internal incidence angle by  int = arcsin  na np sin  ext  +  p; (4.3) where  p is the angle from the prism/metal interface to adjacent side, np and na are the refractive index of the prism material and free space respectively. Another widely-used method to optically couple to surface plasmons uses a coated optical  bre [60, 61]. As shown in Figure 4.4(b), the optical  bre con guration consists of a thin metal  lm deposited onto the exposed core of an optical  bre. In the region of the exposed core, light guided within the optical  bre interacts with the thin metal  lm. Optical coupling to surface plasmons from the  bre core to the other side of the metal  lm occurs at frequencies where wavevector matching is achieved, which, for a broadband light input, results in characteristic spectral dips in the light output. One of the advantages of the optical  bre con guration is that the incident light is always immersed in a dielectric, meaning that discrete coupling elements such as prisms are not required. However, both the polarization and inci- dence angle of light in the optical  bre core are not well de ned, meaning that the e ciency of coupling is less than that achieved by the Kretschemann con guration. 4.3 Proposed Surface Plasmon Resonance Sensor The proposed surface plasmon resonance sensor is depicted in Figure 4.5. Similar to other SPR device con gurations, a thin metal  lm is used to en- 654.3. Proposed Surface Plasmon Resonance Sensor able light incident from an optically denser dielectric medium to couple to surface plasmons on the other side of the  lm. The  lm is deposited onto a clear polymer sheet, and the bottom of the polymer sheet is connected to a linear polarizing sheet using an optically transparent adhesive. A single- mode optical  bre is used to guide light towards to the metal  lm, and a multi-mode optical  bre is used to collect light re ected from the metal  lm. The light collected by the multi-mode  bre is analyzed by a spectrometer. A multi-mode  bre is used for light collection, as opposed to a single-mode  bre, due to its larger acceptance angle. The excitation and collection  - bres are then connected to the bottom of the polarizer sheet using a drop of optical adhesive. The drop of optical adhesive connects the end of the exci- tation  bre to the bottom of the polarizer sheet, ensuring that light incident onto the metal  lm is always immersed in a dielectric. Complete immersion of the incident light in a dielectric precludes the requirement of a discrete coupling element, similar to optical- bre-based SPR con gurations. Optical and geometrical parameters related to di erent layers of the SPR con guration is given in Table 4.1. Due to the similar refractive index values of the  bre, optical adhesive, polarizer sheet, and polymer sheet, little light is re ected from the dielectric interfaces of the sensor. One of the advantages of this con guration is that it integrates light delivery, polarization control, and surface plasmon coupling onto a single  exible substrate and enables interrogation of surface plasmon resonance by either angle tuning or wave- length tuning. An additional bene t is that the components are inexpensive and easily assembled, paving the way for disposable and commercially viable SPR sensors for single-use applications. 664.3. Proposed Surface Plasmon Resonance Sensor Figure 4.5: Proposed surface plasmon resonance sensor con guration. A thin metal  lm is deposited onto a clear plastic  lm. The bottom side of the plastic  lm is optically contacted with a linear polarizer sheet. Two optical  bres, one to input light and the other to collect the re ected light with full control over the incident and re ected angle, are then connected to the bottom of the linear polarizer sheet. Table 4.1: Optical and geometrical parameters of the proposed surface plas- mon resonance sensor Layer material Layer thickness Material refractive index Au 75 nm, 150 nm Published data [62] Polymer sheet 130 m 1.5 - 1.6 Optical adhesive (thin) 30 m 1.56 Polarizer sheet 110 m 1.5 Optical adhesive (thick) | 1.56 Optical  bre | 1.49 - 1.5 674.4. Measurement Methodology Figure 4.6: Schematic diagrams depicting (a) typical Kretchemann SPR con guration consisting of a thin metal  lm on a prism with two polarizing elements and (b) our integrated SPR con guration consisting of a thin metal  lm on a clear plastic sheet optically contacted to a polarizing sheet with a drop of optical adhesive below. 4.4 Measurement Methodology Surface plasmon resonance is interrogated by measuring the re ectance of an Au  lm that has two regions of di erent thicknesses: a thin region that is 75- nm thick and a thick region that is 150- nm thick (Figure 4.7). The thicknesses of the two regions of the gold  lm are measured using a Dek Tak scanning pro lometer. The thin region is optically semi-transparent and 684.4. Measurement Methodology permits light tunneling across the  lm, whereas the thick region is optically opaque and does not permit light tunneling across the  lm. Thus, light incident onto the thin portion of the  lm can couple to surface plasmons on the other side of the  lm, whereas light incident onto the thick portion of the  lm cannot couple to surface plasmons on the other side. We thus quantify a normalized re ectance by R(!) = Is(!) Id(!) Ic(!) Id(!) ; (4.4) where Is is the intensity of light re ected from the thin region, Ic is the intensity of light re ected from the thick region, and Id is the dark spectrum (corresponding to spectrometer noise recorded in the absence of light input). Figure 4.7: Schematic of the experimental surface plasmon resonance chip. The metallic layer on the clear plastic  lm consists of two regions: a thin region that is used for surface plasmon coupling and a thicker region that does not enable surface plasmon coupling. Re ection measurements from the thicker region are used to normalize re ection measurements from the thinner region. 694.4. Measurement Methodology The spectral intensities and resulting normalized re ectance are shown in Figure 4.8 for a representative case of  = 45 . The dip in the re ectance at  = 578 nm is indicative of surface plasmon resonance. Figure 4.8: (a) Spectral re ection measurements from the 75- nm-thick (blue line) and the 150- nm-thick (red line) portions of an Au  lm for an angle of incidence of  = 45 . A dark measurement (black line) illustrates the base- line noise in the spectral measurements and is shown on a magni ed scale in (b). (c) Normalized re ection measurement obtained from the spectral re ection measurements. 704.5. Multi-Layer Re ectivity Model 4.5 Multi-Layer Re ectivity Model We model the re ectivity of a multi-layered system using transfer-matrix formalism [63{65]. Let’s  rst consider a three layered system composed of regions m, n and k, as shown in Figure 4.9 (left). We label the regions 1 and 2 as the left and right sides of the interface m-n, respectively, and the regions 3 and 4 as the left and right sides of interface n-k, respectively. Figure 4.9: (left) Three-layer system representing a general multi-layered structure in terms of the re ection and transmission coe cients at each interface. (right) Model description in terms of the electric  eld, angle of incidence, and wavevector components. As shown in Figure 4.9 (right), the electric  eld components and re ec- tion and transmission coe cients are denoted by Ei1mn = Incident electric  eld from layer m to n at region 1; 714.5. Multi-Layer Re ectivity Model Et2mn = Transmitted electric  eld from layer m to n at region 2; Er3nk = Re ected electric  eld from layer n to k at region 3;  mn = Re ection coe cient for re ection from m-n interface to m;  mn = Transmission coe cient for transmission from layer m to n: For a transverse-magnetic polarized incident wave, the re ection and transmission coe cients [64] are given by  mn = 1 bmn 1 + bmn ; (4.5)  mn = 2  q  m  n  1 + bmn ; (4.6) where  m and  n represent the complex permittivities of layer m and layer n, respectively, kz;m and kz;n are the normal components of the wavevector corresponding to layer m and n, respectively, and the parameter bmn is given by bmn =   m  n   kz;n kz;m  : (4.7) The transmission and re ection coe cients pertaining to a two-layer inter- face are related by  mn =   nm; (4.8)  2mn = 1  mn  nm: (4.9) The tangential component of the wavevector can be calculated at the inter- face using the boundary condition as kx;m = kx;n; =  2   p  m sin  inc = k0 p  m sin  inc; (4.10) 724.5. Multi-Layer Re ectivity Model where  is the free space wavelength of incident electric  eld. The normal components at each layer can be calculated using Snell’s law as kz;m = q k02  m  kx;m2; (4.11) kx;n = q k02  n  kx;n2: (4.12) Incorporating multiple re ections at layer n, as shown in Figure 4.6 (left), the incident  eld at region 1 can be related to the  elds at region 2 by Et2mn =  mnE i1 mn +  mnE i2 nm " 1 +   nm nke  j   +   nm nke  j   2 +    # ; =  mnE i1 mn +  nm 1  nm nke j  Ei2nm: (4.13) Equation 4.13 can be rearranged as Ei1mn = 1  mn Et2mn  1  mn   nm 1  nm nke j   Ei2nm; = 1  mn  Et2mn +   mn 1 +  mn nke j   Ei2nm  ; (4.14) where   = 2 n and  n = kz;ndn are the parameters associated with prop- agation over 2dn and dn, respectively. Er1mn, which consists of contributions from the re ected and transmitted  eld at region 1, can also be expressed as a function of  elds at region 2 Er1mn =  mnE i1 mn +  nmE i2 nm " 1 +   nm nke  j   +   nm nke  j   2 +    # : (4.15) 734.5. Multi-Layer Re ectivity Model Replacing Eqn. 4.14 into Eqn. 4.15 and simplifying the series, we get Er1mn =  mn  1  mn Et2mn  1  mn   nm 1  nm nke j   Ei2nm  +  nm 1  nm nke j  Ei2nm: (4.16) Rearranging Eqn. 4.16 Er1mn =  mn  mn Et2mn +   nm  mn +  mn  nm  mn(1  nm nke j  ) Ei2nm; =  mn  mn Et2mn + (  mn)2 +  mn  nm  mn(1 +  mn nke j  ) Ei2nm: (4.17) Equation 4.17 can be re-arranged into the form Er1mn =  mn  mn Et2mn + 1  mn(1 +  mn nke j  ) Ei2nm; = 1  mn   mnE t2 mn + 1 1 +  mn nke j  Ei2nm  : (4.18) Comparing Eqns. 4.14 and 4.18, a matrix equation can be derived 2 6 4 Ei1mn Er1mn 3 7 5 = 1  mn 2 6 4 1  mn1+  mn nke j   mn 11+  mn nke j  3 7 5 2 6 4 Et2mn Ei2nm 3 7 5 ; = 1  mn 2 6 4 1 M  mn  mn M 3 7 5 2 6 4 Et2mn Ei2nm 3 7 5 ; (4.19) where M = 1 1 +  mn nke j  : (4.20) Equation 4.19 relates the electric  elds at region 1 and 2. Fields at region 2 744.5. Multi-Layer Re ectivity Model and region 3 can be related using the relationship Ei3nk = E t2 mne  j kz;ndn ; (4.21) Er3nk = E i2 nme j kz;ndn ; (4.22) which can be rearranged as Et2mn = E i3 nke j kz;ndn ; (4.23) Ei2nm = E r3 nke  j kz;ndn : (4.24) Writing the above equations in matrix form yields 2 6 4 Et2mn Ei2nm 3 7 5 = 2 6 4 ej  n 0 0 e j  n 3 7 5 2 6 4 Ei3nk Er3nk 3 7 5 : (4.25) Combining Eqns. 4.19 and 4.25, we get 2 6 4 Ei1mn Er1mn 3 7 5 = 1  mn 2 6 4 1 M  mn  mn M 3 7 5 2 6 4 ej  n 0 0 e j  n 3 7 5 2 6 4 Ei3nk Er3nk 3 7 5 : (4.26) Fields at region 1 and 3 can now be related by a transmission matrix, T = 1  mn 2 6 4 1 M  mn  mn M 3 7 5 ; (4.27) and a propagation matrix, P = 2 6 4 ej  n 0 0 e j  n 3 7 5 : (4.28) 754.5. Multi-Layer Re ectivity Model The system matrix, S, for a three-layer unit can be achieved by cascading T and P, written as S = T  P = 2 6 4 S11 S12 S21 S22 3 7 5 : (4.29) Re ectance of the three layer stack can now be calculated as a ratio of Er1mn and Ei1mn, which are related through the elements in the system matrix. To model the re ectance of the multilayered SPR sensor, which consists of a thick layer of optical adhesive, a polarizer sheet, a thin layer of optical adhe- sive, a polymer substrate, an Au layer, and the superstrate region (which in this case is air), we derive the system matrix for a six-layered system given by S = T1  P1  T2  P2  T3  P3  T4  P4  T5; = 2 6 4 S11 S12 S21 S22 3 7 5 ; (4.30) where T1 and P1 correspond to the polarizer sheet, T2 and P2 correspond to the thin optical adhesive layer, T3 and P3 correspond to the polymer substrate, T4 and P4 correspond to the Au layer, and T5 corresponds to the superstrate region. The re ectance of the six-layered system can be calculated from the system matrix as R =    S21 S11    2 : (4.31) Normalized re ectance is obtained by calculating re ectance values for the thin Au layer and normalizing by re ectance values for the thick Au layer. 764.6. Results and Discussion 4.6 Results and Discussion We  rst measure the normalized re ectance of the SPR sensor for an incident wave that is transverse electric polarized. Figure 4.10(a) plots the normalized re ectance spectra for incidence angles from 41 to 49 , where, notably, no resonance dip is measured. The measurements are corroborated by the model calculations, performed for the case of index mismatch [Ta- ble 4.1] between the dielectric layers [Figure 4.10(b)] and the case of perfect index matching between the dielectric layers [Figure 4.10(c)]. Both the ex- periment and model calculations suggest the absence of surface plasmon resonance for transverse electric incidence polarization. We next measure the normalized re ectance for an incident wave that is transverse magnetic polarized. Figure 4.11(a) plots the normalized re-  ectance spectra for incidence angles from 42 to 47 . A pronounced dip is observed in the normalized re ectance spectra for all incidence angles. As the incidence angle increases, the position of the dip shifts towards smaller wavelengths which is in good agreement with the dispersion curve of surface plasmon. As seen in Figures 4.11(b) and (c), the model also predicts dips in the normalized re ectance, which have a similar magnitude to those ob- served in the experiment. Model predictions of the spectral position of the dip as a function of incidence angle agree well with experimental measure- ments, as highlighted in Table 4.2. The approximately 1 o set between the model calculations and experiment may arise from a small tilt in the sensor position. 774.6. Results and Discussion Figure 4.10: (a) Normalized re ectance measurement for various angles of incidence for transverse-electric incident polarization. Model predictions of the normalized re ectance for the case of (b) imperfect index matching and (c) perfect index matching between the multiple substrate layers. 784.6. Results and Discussion Figure 4.11: (a) Normalized re ectance measurement for various angles of incidence for transverse-magnetic incident polarization. Model predictions of the normalized re ectance for the case of (b) imperfect index matching and (c) perfect index matching between the multiple substrate layers. 794.7. Summary Table 4.2: Resonance wavelength ( res) and corresponding incident angle Experiment Model  inc ( degree)  res ( nm)  inc ( degree)  res ( nm) 47 551.322 46 551.97 46 568.29 45 568.11 45 578.11 44 579.34 44 589.05 43 589.16 43 606.72 42 602.49 42 616.75 41 613.01 4.7 Summary We have presented a new SPR device architecture that exploits the wide availability of guided optics and index-matched  uids. The device consists of a thin metal  lm on a polymer sheet, which is connected to a linear polarizer sheet. Optical  bres are used to guide light to and from the metal  lm. The resulting SPR device has the advantages of low cost, compactness, and amenability for single-use applications. We have characterized the device for both transverse-magnetic and transverse-electric polarization and have found good agreement with a transfer-matrix model. 80Chapter 5 Conclusions Optical components constructed from  uids have several advantages over those constructed from solid materials, including increased tunability, lower cost of fabrication, and naturally smooth surfaces. In this thesis, we have explored two optical systems in which small volumes of  uids have been used to manipulate and control the  ow of light, and have highlighted both the advantages and disadvantages of this approach. In one application, we have constructed a  uidic lens based on a water droplet attached to the end of a syringe. The droplet shape can be tuned by both applying an external pressure and manipulating the droplet volume through the injection or withdrawal of  uid to achieve variable focus and magni cation. We have characterized the focussing properties of the droplet lens as a function of the droplet size and used the droplet as the objective lens in both re ection-mode and transmission-mode microscope con gurations. The images captured by the droplet microscope show micron-scale resolution and quality comparable to that obtained by a conventional laboratory-grade microscope. As opposed to other liquid lens implementation methods that require elaborate housing structures and multiple micro- or nano-fabrication steps, the droplet lens developed in Chapter 3 exploits low-cost and widely- 81Chapter 5. Conclusions available techniques to dispense and shape small volumes of  uids. A  uidic coating technique has been discovered which yields a highly stable water droplet structure in ambient air that is addressable by free-space illumina- tion. A key feature of the droplet lens is that the lens can be created on demand and can be discarded after use with little waste of materials. The low cost of implementation, wide accessibility of the requisite materials, rel- ative simplicity of operation, and good quality of images obtained suggests that microscopy using water droplets may be viable for resource-limited re- gions. In the second application, we have constructed a new surface plasmon resonance (SPR) sensor based on  bre optics and index-matched  uids. Con- ventional SPR sensors require discrete optical coupling elements, such as a prism and a polarizer, to enable free-space light to couple to surface plas- mons on a metal  lm. We have circumvented this requirement by designing a SPR sensor in which light delivered to the surface plasmon substrate is always immersed in a dielectric. This was achieved by optically attaching input and output optical  bres, a polarizer, and a surface plasmon substrate using index matching  uid. The  uid physically binds the di erent compo- nents of the sensor and provides an unimpeded pathway for light incident onto the metal  lm. We have demonstrated the working principle of the SPR sensor, experimentally characterized the performance of a prototype device, and compared our experimental  ndings with theoretical predictions based on a re ectivity model. The new SPR sensor con guration is more compact and cost-e ective than the conventional prism con guration. An additional bene t is that the components used are inexpensive and easily 82Chapter 5. Conclusions assembled, which paves the way for disposable and commercially-viable SPR sensors that can be used for single-use applications. 83Bibliography [1] P. Mach, M. Dolinski. K. W. Baldwin, J. A. Rogers, C. Kerbage, R. S. Windeler and B. J. Eggleton, \Tunable micro uidic optical  ber," Appl. Phys. Lett., vol. 80, no. 23, pp. 4294{4296, 2002. [2] F. Cattaneo, K. Baldwin, Shu Yang, T. Krupenkine, S. Ramachandran and J.A. 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