Variable Focus Microscopy Using a Suspended Water Droplet

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Variable focus microscopy using a suspended water droplet

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Please note that terms and conditions apply. IOP PUBLISHING JOURNAL OF OPTICS A: PURE AND APPLIED OPTICS J. Opt. 14 (2012) 055501 (12pp) doi:10.1088/2040-8978/14/5/055501 Variable focus microscopy using a suspended water droplet

F A Chowdhury and K J Chau

School of Engineering, University of British Columbia, Kelowna, BC, Canada V1V 1V7

E-mail: [email protected]

Received 3 December 2011, accepted for publication 23 March 2012 Published 18 April 2012 Online at stacks.iop.org/JOpt/14/055501 Abstract We explore a low-technology methodology to dispense and shape water droplets for application as the magnifying element in a microscope using either reﬂection-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 magniﬁcation and imaging quality comparable to that obtained by a conventional, laboratory-grade microscope.

Keywords: opto-ﬂuidics, microscopy (Some ﬁgures may appear in colour only in the online journal)

1. Introduction

A lens is a discrete optical element that causes an incoming beam of light to either converge or diverge. The effect that a lens imparts onto an incident light beam is determined, in large part, by the curvature of the surfaces of 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 fixed. Tunability of the focal length then requires a system of lenses, where the effective 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 fluids [1–9]. The advantage of a fluidic 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 Figure 1. Droplet size determination by analysis of images taken of surface tension. The use of a fluid, however, introduces the droplet from horizontal and vertical perspectives. The projected the requirement of systems to provide mechanical stability, area of the droplet is measured from the horizontal perspective as a function of the droplet volume inferred from both perspectives. prevent evaporation and manipulate the fluid. To date, fluidic lenses have been implemented in the form of discrete optical elements, consisting of a housing structure to store the the application of mechanical pressure or an electric field to constituent fluid and an actuation method to adjust the shape the fluid volume. Fluidic lenses based on the application of of the fluid. The actuation method is commonly based on electric fields exploit either the electro-wetting effect [3, 10]

+12$33.00 12040-8978/12/055501 c 2012 IOP Publishing Ltd Printed in the UK & the USA J. Opt. 14 (2012) 055501 F A Chowdhury and K J Chau

Figure 3. (a) Experimental set-up to determine the focal distances of the water droplet based on collimation of visible light emitted from an optical fiber. The oil-coated water droplet is attached to a Figure 2. Microscope images of a bare water droplet at (a) t = 0 s syringe connected to a water reservoir. The focusing properties of and (b) t = 15 min. Dispensing a drop of oil over the water droplet the droplet are changed by varying the volume of the droplet. The results in a thin oil layer surrounding the water droplet. Microscope light emanating from the optical fiber is collimated by the droplet images of a water droplet with an oil coating at (c) t = 0 s and and the far-field image of the light source is collected by a camera at (d) t = 15 min. (e) The measured projected area of the two types of a far distance (much greater than the focal length) from the lens. droplets as a function of time. The bare water droplet has an Typical far-field images indicating (b) horizontal collimation, (c) evaporation rate of 0.072 mm2 min−1 and the oil-coated water vertical collimation and (d) full collimation. The beam shapes are droplet has an evaporation rate of 0.014 mm2 min−1. The insensitive to the screen position. evaporation rate depends on the relative humidity and can be further reduced by encasing the set-up in a high-humidity chamber. Oil coating the water droplet yields a greater than five times decrease in attached to a syringe. To mitigate evaporation, the water the evaporation rate. droplet is encased in a transparent and immiscible silicone oil layer, which also forms the exterior portion of the lens. or dielectrophoresis force [11–15]. Fluidic lenses based on the The droplet is actuated by both applying a pressure with an application of mechanical pressure, on the other hand, exploit external tip and varying the volume of the droplet directly the natural deformation of fluids in pressurized environments. through the syringe. The resulting droplet lens possesses large Pressure lenses are tuned by either applying a hydraulic or acceptance angles, short focal lengths and a wide tunability ambient pressure to a fixed fluid volume [4, 16–19] or by range. A potentially useful feature of this implementation is changing the volume of fluid [20–26,9]. that the droplet lens can be created on demand and discarded Current implementations of fluidic lenses have demon- after use. We demonstrate the application of the droplet strated a high degree of stability and control over the shape lens as a variable, magnifying component in a microscope of the fluid, but require elaborate housing structures [13, 20, operating under both reflection-mode and transmission-mode 17, 22, 26, 27], in many cases constructed using multiple illumination. Images captured using the microscope show micro- or nanofabrication steps [20, 21]. An alternative and micron-scale resolution, variable magnification and imaging less-explored approach to realizing a fluidic lens is to exploit quality comparable to that obtained by a conventional the existing low-technology methods available to controllably microscope. Although the droplet lens does not possess the dispense and shape small volumes of fluids. In this work, same degree of stability and control as other fluidic lens we explore a fluidic lens constructed from a water droplet implementations, it may find usefulness due to the low cost of

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Figure 4. (a), (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 is 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. implementation, wide availability of the requisite equipment dimensions measured using this technique is of the order of and simplicity of operation. 1%. The volume, V, and horizontal projected area, A, are then given by V = πabc/6 and A = πbc/4, respectively. Either the 2. Droplet lens dispenser and actuator volume or the area can be used as a metric for the droplet size. As shown in figure1, a positive, linear correlation between We design a fluidic lens based on water droplets controllably the volume and projected area indicates that increases in the dispensed from and attached to the end of a microliter syringe droplet volume yield proportional increases of the droplet size (Hamilton 701RN 10 µl syringe). The needle length is 51 mm along all three dimensions. Throughout the remainder of this and the needle outer and inner diameters are 0.47 mm and paper, the droplet size will be discussed primarily in terms of 0.13 mm, respectively. The end of the syringe is a sharp, the horizontal projected area. beveled, non-coring needle point (point style 2), mounted A water droplet directly exposed to the atmosphere is so that the beveled opening faces down. The accuracy of prone to rapid evaporation which results in shape distortions. the volume dispensed by the syringe is within ±0.1 µl. We To mitigate evaporation, we coat the water droplet in a thin establish a coordinate system where the axis of the syringe is layer of silicone oil. The oil coating is applied by simply oriented along the x axis (horizontal), gravity is directed along dispensing an oil droplet above the attached water droplet. the z axis (vertical) and the optical axis of the lens is oriented As the oil droplet whisks past the water droplet, a thin along the y axis. In general, the droplet can be modeled as an protective layer of oil completely surrounds both the water ellipsoid with three principal axes a, b and c, corresponding droplet and a portion of the syringe. Due to the similar to the diameters of the droplet along the x, y and z axes, refractive index values of silicone oil (n = 1.4034) and water respectively. The parameters a, b and c are measured from (n = 1.33), we initially assume that the refractive effects of microscope images of the droplet taken from both vertical the oil layer are negligible and later confirm this assumption and horizontal perspectives, where b and c are extracted by comparing experimental measurements of the optical from the horizontal perspective (yz plane) and a and b from properties of the oil-coated water droplet with theoretical the vertical perspective (xy plane). The microscopes used to calculations. Although the oil layer surrounding the water obtain the images of the droplet are calibrated so that the droplet is generally non-uniform due to gravity, as shown in droplet dimensions can be directly measured from the pixel the images in figure2, addition of the oil coating does not size of the droplet in the images. The accuracy of the droplet significantly change the overall shape of the water droplet

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Figure 5. Variation of the shape of the oil-coated water droplet system by applying pressure through a bottom tip. A metallic tip is first (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 fluidic lens system. (d) Sequence of microscope images of the droplet system demonstrating size and shape reconfiguration by either changing the volume or pressure on the droplet. or its transparency, but reduces the evaporation rate of the length corresponding to the distance resulting in a vertically water droplet by fivefold, from 0.072 to 0.014 mm2 min−1 collimated beam shape (figure3(c)). The horizontal and (figure2(e)). Although the oil coating does not completely vertical focal lengths are generally unequal because the eliminate evaporation, it does enable a single, millimeter-scale transverse shape of the lens is not symmetric (figure4(c)). water droplet to last for over an hour. Because the droplet This asymmetry arises from two competing effects, illustrated is still attached to the syringe, the gradual reduction in the in figure4(d). For smaller droplet volumes, attachment of the size of the oil-coated water droplet can be compensated by droplet along the shaft of the syringe causes elongation of the controllably dispensing water from the syringe. horizontal diameter a relative to vertical diameter c, yielding We next study the focusing properties of an oil-coated an oblate ellipsoidal shape. For larger droplet volumes, the water droplet as a function of water volume using the increasing effect of gravity on the droplet causes concurrent configuration depicted in figure3(a). Light diverging from a elongation of the diameter c and reduction in a, yielding single-mode fiber having a 5 µm core diameter is collimated a prolate ellipsoidal shape. As a result, the vertical focal by the droplet lens and then recorded by a camera placed length monotonically increases and the horizontal focal length a distance much greater than the focal length away from decreases and plateaus as a function of the increasing droplet the droplet. The fiber is aligned along the y axis (optical size (figure4(c)). Due to the competing effects of droplet axis) of the lens to mitigate astigmatism effects. For a attachment and gravity, there is only one droplet volume given volume, we measure two focal lengths of the lens: a that yields a symmetric transverse shape. When a symmetric ‘horizontal’ focal length corresponding to the distance from transverse shape is achieved, the horizontal and vertical focal the center of the lens to the fiber tip resulting in a horizontally lengths are matched, resulting in a beam shape that is fully collimated beam shape (figure3(b)) and a ‘vertical’ focal collimated (figure3(d)).

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Figure 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.

To enable greater control over the shape of the droplet condenser and objective lenses. The microscope configuration for any droplet volume, we incorporate a metallic tip below is depicted in figure8. Visible light from a light-emitting the end of the syringe that attaches onto the dispensed water diode is directed along the optical axis onto the lens. The lens droplet. The metallic tip is actuated in three dimensions, focuses the incoming light onto a sample and then collects with positioning accuracy of the order of '1 µm, using and collimates the reflected light. The collimated beam goes a three-axis mechanical linear stage (Newport ULTRAlign). through an aperture with a diameter of 1.38 mm and is This positioning accuracy is of the order of 0.1% of the then captured by a CMOS camera. The magnification of the total aperture size of the droplet. Inclusion of the bottom microscope is varied by changing the volume of the water tip provides physical support for the weight of the droplet droplet and then adjusting the tip–syringe separation until (permitting larger droplet sizes than previously possible the resulting image is free of distortions. Figure9(a) depicts without the tip) and enables tuning of the lens curvature, representative images of a calibration slide captured by the particularly along the vertical direction, by varying the microscope at various magnification levels. The calibration separation distance between the tip and syringe. An image slide consists of a series of parallel lines, where the pitch of a typical fluidic lens resulting from this configuration is spacing between successive lines is 10 µm. Magnification shown in figure5(c). The sequence of images in figure5(d) values are measured by comparing the actual size of the highlight controllable and reversible alterations of the droplet sample and the size of the image of the sample projected shape by either changing the droplet volume or varying onto the CMOS sensor. We position the calibration slide the tip–syringe separation. In particular, for a given droplet diagonally at an angle of 35◦ with respect to the horizontal. volume, the tip–syringe separation can be varied until a The diagonal position of the sample enables visualization of highly symmetric droplet shape is realized (figure6). The barrel [11, 21], pin-cushion [3] or mustache distortions along symmetric droplet shape possesses matching vertical and both the vertical or horizontal directions based on smearing horizontal focal lengths, a basic requirement for application as of the lines. Slight overall blurriness of the entire image at an imaging lens. Figure7(b) summarizes the focal lengths of larger magnifications (at 43× and 46×) is due to spherical a series of droplets, possessing symmetric transverse shapes, aberrations introduced by the spherical shape of the lens created using the modified dispensing and droplet shaping surfaces. As shown in figure9(b), this particular microscope configuration. configuration is capable of magnification values from 37× to 47×, with a corresponding field of view that ranges from 3. Reflection-mode microscope based on a droplet 170 to 120 µm. It should be noted that higher magnification lens values are possible by using smaller droplet sizes and lower magnification values are possible by using a larger tip size We next build a reflection-mode microscope where the capable of sustaining larger droplet sizes. The focal length of oil-coated droplet dispensed from the syringe acts as both the the lens, measured by recording the lens–sample separation

5 J. Opt. 14 (2012) 055501 F A Chowdhury and K J Chau microscope conﬁguration to accommodate the larger beam size from the light-emitting diode.

4. Transmission-mode microscope based on a droplet lens

The oil-coated droplet lens is next used as the objective lens in a microscope configuration using transmission-mode illumination. The microscope configuration is depicted in figure 11. Visible light from a light-emitting diode passes through a condenser lens and is focused 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 12(a) depicts images of various semi-transparent biological samples captured by the microscope at different levels of magnification. Slight blurriness near the edges of the images are attributed to Petzval field curvature effects [28] (as opposed to spherical aberration effects observed in the reflection-mode images in figure9). To qualitatively access 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-focused images in which the sample is positioned at the focal plane and near-focused images in which the sample is positioned slightly outside of the focal plane (figures 12(c) and (d)). Images captured using the droplet lens have comparable micron-scale resolution 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-focused images, but is more comparable to that of the near-focused Figure 7. (a) Experimental set-up for measuring the focal length of images. Nonetheless, the imaging capabilities of the droplet the tip-supported droplet system. By tuning the position of the are impressive considering the relative simplicity of our bottom tip, the shape of the droplet for any volume can be adjusted to achieve complete (horizontal and vertical) collimation of the implementation. optical fiber light source. (b) Focal length of the droplet system as a function of droplet volume and projected droplet area. 5. Modeling the optical properties of the droplet lens yielding the sharpest image, follows the same trend as the We model the droplet as a thick lens with geometrical focal lengths previously measured using the beam collimation parameters extracted from the images of the droplet configuration (figure 10). Larger droplet sizes are used in the (figure 13). The thickness of the lens, d, is the droplet diameter

Figure 8. Reflection-mode microscope using a fluidic lens composed of the oil-coated water droplet system. In this configuration, the fluidic lens emulates both the condenser and objective lenses found in a conventional optical microscope. A light-emitting diode emits visible light into a beamsplitter, which re-directs the light onto the fluidic 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 (Logitech C160).

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Figure 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 configuration (blue squares) and the fiber–lens separation in the beam collimation configuration (red circles). The error bars in the measurements in the microscopy configuration account for uncertainty in the position of the sample. The error in the focal length measurements using the beam collimation configuration results in error bars that are smaller than the size of the marker.

fitting 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 R2, respectively, and then scaling the pixel sizes in the image to real dimensions. The transverse shape of the lens is symmetric (as observed Figure 9. (a) Microscope images of a calibration slide captured at from the images of the droplet taken from both horizontal various levels of magnification using the fluidic lens microscope. and vertical perspectives (figure6) and further supported The pitch separation between adjacent lines on the slide is 10 µm. by observations of full beam collimation and distortion-free (b) Field of view and magnification of the microscope as a function of projected droplet area. 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. b along the optical axis and the height of the lens (or total Figure 14(a) illustrates an idealized biconvex thick lens aperture size) is 2r, which is approximately half of the total created using geometrical parameters extracted from images tip–syringe separation. We extract the radii of curvature by of the water droplet. Propagation of an arbitrary ray from

Figure 11. Transmission-mode microscope using a fluidic lens composed of the oil-coated water droplet system. In this configuration, a separate lens is used as a condenser lens to illuminate the sample and the fluidic 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.

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Figure 12. Microscope images of spinal cord tissue (first row), basswood stem (second row), cardiac muscle tissue (third and fourth row) and Penicillium (fifth row). Column (a) shows the images obtained using the droplet lens in the transmission-mode microscope configuration. Columns (b) and (c) show near-focused and best-focused 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-focused images, which matches the region imaged by the droplet lens.

free space, through the lens, and back into free space can be lens, d12 is the propagation distance of the ray within the succinctly described using a transfer matrix, M, given by [28] lens, and D1 and D2 are the powers of the refracting surfaces " # written as m m = 11 12 M (nl − 1) m21 m22 D = (2) 1 R " # 1 1 − D2d12/nl −D1 + (D2D1d12/nl) − D2 = (1) and d12/nl −D1d12/nl + 1 (nl − 1) D2 = . (3) where nl = 1.33 (corresponding to the visible-frequency −R2 refractive index of pure water) is the refractive index of the

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Figure 13. (a) Image of an oil-coated water droplet (taken from the horizontal perspective) adjacent to an optical fiber 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 fitted 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. Figure 14. Schematic of an idealized thick lens constructed using the geometrical parameters of the fluidic lens. (a) Two-dimensional and (b) three-dimensional perspective of the calculated ray Simplifying the m12 component of equation (1), we get trajectories of a collimated beam incident at normal incidence onto the thick lens. The focal length corresponds to the distance from the − m12 = D1 + D2 − (D2D1d12/nl) center of the lens to the convergence point of the rays. 1 1 (nl − 1)d12 = (nl − 1) − + . (4) R1 R2 nlR1R2 to the focal length measured from the center of the lens fp by The inverse of equation (4) is related to the distance from the lens that an incoming collimated ray propagates d fp = fh + − h . (8) until it intersects with the optical axis. Under the paraxial 2 approximation, d12 = d for all rays. The effective focal length, fh, of the thick lens can then be calculated by For each droplet size, we extract the geometrical lens parameters d, 2r, R and R from the images taken of − 1 2 1 1 1 (nl 1)d the droplet from the vertical and horizontal perspectives. = (nl − 1) − + . (5) fh R1 R2 nlR1R2 The focal length of the droplet is determined by analytical calculations under the paraxial approximation equations (5) Values of fh are determined with respect to the principal planes of the lens (as shown in figure 14), which are located at and (8) and a ray tracing simulation based on the transfer distances matrix method (equation (1)). Figures 14(a) and (b) show ray tracing simulation results of a collimated input beam incident fh(nl − 1)d h1 = − (6) onto a lens created using realistic parameters extracted from R2nl images of a droplet lens. The ray tracing simulations are and conducted for collimated illumination where the aperture fill factors (corresponding to the ratio of the illuminated aperture fh(nl − 1)d h2 = − (7) to the total lens aperture) are 30%, 70% and 100%. The results R1nl of the ray tracing simulations for the three fill-factor test cases from the vertices of the front and back surfaces, respectively. are depicted in figures 15(b), (d) and (f). For 30% fill factor, Given the symmetric biconvex lens shape in our experiments, the focal length measured from the ray tracing simulations where |R1| = |R2| = R and hence |h1| = |h2| = h, fh is related simply corresponds to the distance from the center of the lens

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Figure 15. Comparison of focal lengths measured using the beam collimation configuration to focal lengths calculated using the analytical model under the paraxial approximation and the ray tracing simulation using (a) 30%, (c) 70% and (e) 100% fill factors. The results of the ray tracing simulations using (b) 30%, (d) 70% and (f) 100% fill factors. to the well-defined convergence point of the rays with the the lens to the point where the diameter of the cone formed by optical axis. For 70% and 100% fill factors, the rays no longer the rays is minimum, known as the circle of least confusion, P converge at a single point due to the strongly diffracted rays LC. Figures 15(a), (c) and (e) compare the focal lengths incident at distances further from the optical axis and the focal calculated under the paraxial approximation and simulated length instead corresponds to the distance from the center of with the ray tracing simulation with the focal lengths

10 J. Opt. 14 (2012) 055501 F A Chowdhury and K J Chau the focal length measurements more closely match those calculated under the paraxial approximation. As the droplet size decreases to less than the aperture stop dimension, the paraxial approximation fails and the focal lengths are better modeled using ray tracing simulations with high fill 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 figure9. The sharpest images are obtained at lower magnifications (using larger droplets) and the blurriness increases at higher magnifications (using smaller droplets). It should be noted that the focal lengths measured using the beam collimation configuration for all droplet volumes are consistent with ray tracing simulations using a 70% fill factor. Assuming that the beam emanating from the fiber has a small divergence angle, proportionality between the droplet aperture size and focal length yields an approximately constant fill factor. Overall consistency between the focal lengths measured using the beam collimation and microscopy configurations and the calculated focal lengths (which assume that the lens is composed solely of water and neglect the presence of the thin oil layer) suggests that refraction due to the thin oil coating surrounding the water droplet does not significantly influence the focusing properties of the lens.

6. Limitations

The most significant limitation of building an imaging system based on a suspended droplet is the 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 Figure 16. (a) Comparison of the focal lengths measured using the dampening stages. Evaporation has been mitigated, but microscope configuration to focal lengths calculated using the not eliminated, by coating the droplet with a thin layer analytical model under the paraxial approximation and the ray of silicone oil. We have also compensated for reductions tracing model using various fill factors. (b) Tip–syringe separation in the size of the oil-coated droplet due to evaporation of the lens versus the droplet size. The size of the aperture stop is by controllably dispensing water from the syringe. This shown by the dotted gray line. For tip–syringe separations exceeding the aperture size, the corresponding images have reduced compensation method, however, is dynamic and limits the spherical aberrations (denoted as SA in the plot), and for tip–syringe potential applicability of this approach for obtaining stable separations less than the aperture size the images have greater microscope images. We believe that further reduction in the spherical aberrations. The magnification provided by various droplet evaporation rate of the droplet can be achieved by housing the sizes are labeled, corresponding to the microscope images shown in system in a sealed and humidity-controlled environment, or figure8. housing the entire syringe and droplet system in an immiscible fluidic environment. Another limitation of our implementation measured via beam collimation. Analytical calculations using is alignment sensitivity due to fluctuations in the optical axis the paraxial approximation and the ray tracing simulations for as the droplet size changes. This effect has been mitigated 30% fill factor consistently over-estimate the experimentally by using a light-emitting diode with a wide emission angle measured focal lengths for all droplet sizes. Increasing the and a CMOS sensor area larger than the droplet size, both fill factor decreases the focal length values extracted from the of which reduce the sensitivity of the image to the optical ray tracing simulations. Ray tracing simulations using a 70% axis location, but could be further reduced by developing fill factor yield focal length values most closely matching the an alignment system that automatically adjusts the position experiment. of optical elements with respect to the size of the droplet. We next compare the calculated focal lengths to the It should also be noted that the focal length tuning range focal lengths measured using the microscope configuration studied here is smaller than that studied using other fluidic (figure 16). The microscope includes an aperture stop lens implementations. The focal lengths studied here were that restricts the beam size to a diameter of 1.38 mm. in the lower limit because of its application as a microscope When the droplet size exceeds the aperture stop dimension, objective, which requires short focal lengths. Future work will

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