Microlenses with intrinsic tunability are of interestfor a wide variety of applications, particularly beamshaping, optical interconnection, and imaging.1 Thelast-named application is of particular relevance forendoscopy, in which a variable imaging system pro-vides an advantage for tissue imaging; no dynamicmicro-optical systems suitable for use in extremelysmall fiber endoscopes, with diameters of as little as0.5 mm at the distal end, have been demonstrated.Further application areas include biochip readers,2which require microlens arrays that are completelytunable, and beam shaping for optical switching.3
A limited number of concepts for tunable micro-lenses have been demonstrated by diverse approachesand technologies, such as by electro-wetting,4,5
through the use of liquid-crystal microlenses,6 cast-ing of poly(dimethyl siloxane) (PDMS),7,8 and adap-tive lenses driven by radiation pressure.9 Thelimitations on liquid lenses tuned by the electrowet-ting approach include requirement for high drivingvoltages and the requirement that only polar liquidsbe used. The liquid-crystal technique is hampered bythe possibility of nonuniformities in the electric field,which could lead to optical aberrations. Moreover,
both methods require the presence of electrodes,which can disturb the optical performance. The cast-ing method, finally, requires more than one sub-strate, leading to alignment and adhesion problems;the PDMS cast of the master substrate has to bealigned and fixed to the lens’s body such that mis-alignment and poor reproducibility frequently result.And the radiation-pressure-driven liquid–liquid in-terface lenses require a high-power laser for genera-tion of the lens meniscus.
In the present research, a novel type of microfluidicmicrolens is presented that overcomes a number ofthese limitations. As shown in Fig. 1, the membrane-based, liquid-filled tunable microlenses employ a50��m-thick, pressure-actuated PDMS membranestructured upon a silicon fluidic chip. This chip ismounted onto a Pyrex substrate, thereby forming afluidic cavity filled with a liquid of suitable refractiveindex. The body of the lens is then formed by theliquid, whereby the membrane curvature providesthe lens shape. Varying the pressure of the liquid byusing the fluidic system changes the shape of themembrane and thus the optical power of the lens. Asshown in the figure, both plano–convex and plano–concave lenses may be obtained. A microphotographof two distended, 400��m-diameter convex lenses isshown in Fig. 2.
2. Design and Fabrication
The membrane-based microlens is fabricated on asilicon substrate bonded to a Pyrex substrate; themembrane itself is a spin-coated PDMS layer on thefront side of the silicon wafer. The use of these ma-terials means that no cavity deformation takes placewhen pressure is applied and no critical alignment or
The authors are with Laboratory for Micro-optics, Institute ofMicrosystem Technology, University of Freiburg, Georges-Köhler-Allee 102, 79110 Freiburg, Germany. A. Werber’s e-mail address [email protected].
Received 15 October 2004; revised manuscript received 20 De-cember 2004; accepted 20 December 2004.
adhesion problems occur. The use of standard micro-electromechanical systems processing techniques,under clean-room conditions to ensure particle-freeoptical surfaces, implies that low-cost mass fabrica-tion of these lenses is possible.
Microlens fabrication is thus based on silicon pro-cess technology combined with a number of nonsili-con materials to yield the complete structure; asummary of the process is shown schematically inFig. 3. Processing begins with photolithography on asilicon wafer polished on both sides in which the lensopenings and the microfluidic channels are defined.In wet oxidation and subsequent plasma-enhancedchemical-vapor deposition oxidation steps, a maskinglayer is deposited. This layer is structured by photo-lithography and subsequently opened by reactive ionetching (RIE). The first oxide mask defines the con-
tours of the lens chamber, the fluidic channels, andthe reservoir, with a typical structure as shown inFig. 4. Circular lens openings with diameters of300–600 �m were defined along with the fluidic chan-nels and the reservoirs. In a second photolithographystep, a 12��m-thick photoresist layer is patterned.This second mask step defines the contours of the lenschambers and the reservoirs.
Defined by the second photoresist mask, the lenschambers and the reservoirs are then etched throughhalf of the silicon wafer by an inductively-coupled
Fig. 1. Cross-sectional diagram of a membrane-based microflu-idic microlens, showing its implementation as plano–convex andplano–concave lenses. The drawing is to scale for a microlens withdiameter d � 400 �m.
Fig. 2. Microphotograph of two distended plano–convex lensesachieved by application of positive fluidic pressure. The lens diam-eter of 400 �m is shown.
Fig. 3. Process summary: (a) Silicon wafer with both side SiO2
layer and with back side opened by RIE; (b) photoresist, spincoated and structured; (c) first ICP RIE etching; (d) spin coating ofprimer and PDMS; (e) second ICP RIE etching; (f) SiO2 removal; (g)bonding of the Pyrex wafer and patterning of the back-side chro-mium layer; (h) sawing and filling of the devices.
Fig. 4. Layout for a lens array with 400��m lenses.
plasma (ICP) RIE process. Afterward, the resist layeris removed in a plasma asher. This step is followed byfront-side spin coating of a thin PDMS film. We usedSylgard 186 PDMS material from Dow Corning. Toimprove the adhesion of the PDMS to the silicon orsilicon oxide, the substrate is coated with a primer,DC 92-023 from Dow Corning, of �3��m thickness.The thickness of the PDMS film is �50 �m, mea-sured with a surface profiler. This film is cured for 15min at 150 °C. This PDMS or silicone elastomer filmforms the pressure-actuated membrane, which en-closes the working liquid and ultimately defines thelens’s curvature.
As the lenses are arranged as arrays with differentdimensions and contours, one fluidic reservoir willprovide nine lenses with the required working liquidand pressure; in the future each lens will be con-trolled by an independent microfluidic system. In asecond ICP RIE etch step the lens chambers, thereservoirs, and the fluidic channels are etched simul-taneously, passivated by the structured SiO2 layer.The etching stops abruptly when the SiO2 layer at thefront side is reached because the etch selectivity10 toSiO2 is approximately 200 to 1.
Finally, the front-side SiO2 layer is removed in alast RIE step, resulting in the PDMS membrane’snow being freely stretched over the silicon lens cham-ber. To enclose the liquid cavity, a thin Pyrex wafer issubsequently bonded to the back side of the siliconsubstrate to cap the fluidic channels and chambers.Bonding is accomplished by a UV-curable optical ad-hesive, spun on as a very thin layer of �3 �m onto thePyrex wafer. After alignment, a UV flood exposurefollowed by an anneal at a temperature of 50 °C for24 h results in covalent bonds between the Pyrex andthe silicon substrates, and this ensures that thestructure remains mechanically stable.
Because the Pyrex wafer is fully transparent, notonly the lens chambers but also the fluidic channelsand the reservoirs are visible from the back of thebonded structure. To minimize scattering and crosstalk between the single lenses of the array, an aper-ture stop on the unpatterned Pyrex wafer is required.Such an aperture is made by use of a 100�nm-thickvapor-deposited chrome layer, subsequently struc-tured by a wet etch.
The wafer stack is then separated into individualchips, each with an array of nine lenses and onereservoir, by sawing. During this last step, the deli-cate PDMS membrane must be protected by a pho-toresist layer to prevent scratching during chipseparation. The protective resist coating is strippedin acetone, and the chips rinsed in deionized water.
To prepare the fluidic lenses for operation, one hasto introduce the liquid optical medium into the mi-crofluidic chambers; one accomplishes this filling bytaking advantage of capillary forces that essentiallyresult in a self-filling of the cavities. Two liquid mediawere employed: a mixture of 50�wt. % water and50�wt. % ethanol and a proprietary liquid fromCargille with a high refractive index �n � 1.600�. Inthe former case the addition of ethanol is important
to reduce surface tension and thus provide betterfilling, caused by capillary forces. The H2O:ethanolmixture working liquid provides a refractive index ofn � 1.3534, measured with a refractometer. Cavityfilling is accomplished in a vacuum chamber to de-aerate the liquid enclosed inside the small fluidicchannels. Any remaining bubbles quickly diffuse outof the system because the PDMS membrane is gaspermeable.
The devices are operated by use of a silicone tubeglued to the fluidic reservoir entrance with UV-curable adhesive. A manually operated syringe and acalibrated pressure sensor were then used to definethe pressure exerted on the liquid, thereby leading tothe desired lens distension.
3. Characterization of the Microlenses
Characterization of the membrane microlenses wasaccomplished by use of a number of tools. Surfaceprofile measurements were made with a white-lightinterferometer (Zygolot New View 5022) or a mechan-ical surface profiler (Tencor P-11). The focal length ofthe microlenses was measured directly with a ZeissAxioplan2 optical microscope and Axiovision soft-ware to change the focal plane dynamically.
Using the white-light interferometer, we deter-mined the surface roughness of the tunable lenses tobe �9 nm �rms�. This is an excellent value, particu-larly when one considers that this is a micromechani-cal structure with a large surface-to-volume ratio. Weused the same measurement setup to measure thelens’s radius of curvature, from which the focal lengthcould be calculated, as a function of the applied pres-sure. The pressure of the liquid optical medium wasmeasured with a Motorola MPX5050 pressure sensorwith a resolution of 90 mV�kPa. Determination of themaximum lens height allowed the radius of curvatureto be calculated through
R �d2
8h �h2, (1)
where R is the radius of the lens, d is the lens diam-eter, and h is the maximum height. The focal lengthcould then be determined simply by
f �R
(n1 � 1), (2)
where f is the focal length and n1 is the refractiveindex of the liquid optical medium. These expressionsare based on the thin-lens approximation and aspherical lens profile.
The pressure range in the measurement series var-ied from 0 to 54 kPa, giving the results shown in Fig.5. For the highest pressures, the curvature radiussaturates at �0.2 mm, with controllable values rang-ing from 0.2 to 6 mm. We discuss its effect on focallength below.
sured by use of a mechanical surface profiler. In thiscase a needle with a tip radius of 2 �m and a coneangle of 60° mechanically scans the surface; becausethe PDMS film is soft, the scanning force was mini-mized and had a value of �1 mN. The measurementtip must be aligned such that the full diameter of thelens is scanned, thereby giving a true measure of thelens’s shape.
As can be seen from Fig. 6, the lens profile wasmeasured as a function of applied pressure in therange 4–54 kPa; the corresponding radii of curvatureare given in Fig. 5. The lens profile is not ideallyspherical for two reasons: the nonlinear deflection ofthe PDMS membrane and the fixed edge of the mem-brane, which leads to an inflection point at the lensedge. In the latter case the lens curvature at positivepressure is concave instead of convex, as would be thecase for a completely spherical lens. But an additionalaperture can minimize the aberrations that are dueto the lens edge. The nonlinearity of the elastic PDMSmembrane, however, is an intrinsic effect of the ma-terial and is not alterable.
Focal length was measured directly with the ex-perimental setup shown in Fig. 7. In this measure-ment the lens array is illuminated with acollimated, expanded laser beam (at � � 550 nm)from the back (i.e., Pyrex) side of the structure, cor-responding to the planar side of the plano–convexlens. The collimated light is then focused by each lensof the two-dimensional array; the lenses are thustested in transmission, corresponding to the normalmode of operation. One then determines the focallength for an individual lens by moving the auto-mated translation stage from focus on the wafer sur-face to the position where minimum beam waist isachieved; the total translation then corresponds tothe focal length.
The focal length is shown in Fig. 8 as a function ofpressure measured with this approach; for compari-son, the focal length as determined from application ofEqs. (1) and (2) to the surface profile data of Fig. 6 isalso shown. The measurements were performed withthe two liquid optical media available, with n1
Fig. 5. Lens radius of curvature as a function of pressure appliedto the liquid optical medium (ethanol and water) as measured bywhite-light interferometry.
Fig. 6. Complete lens profile measured by a mechanical profilerfor a 500��m-diameter lens as a function of applied pressure in therange 4–54 kPa.
Fig. 7. Measurement setup for focal-length measurement. A col-limated laser beam illuminates the lens array from the back side.The light is focused by each lens, such that the lenses of the arrayare tested in transmission. One determines the focal length for anindividual lens by moving the translation stage in the z direction atthat point where the beam waist is minimal. The amount by whichthe translation stage was moved corresponds to the focal length.
Fig. 8. Focal length of the membrane lenses as a function ofapplied pressure as measured directly and as calculated from op-tical surface profile measurements.
� 1.35 and n1 � 1.6. It can be seen that the focallength varies from 1 to 18 mm, saturating at �1 mmfor high pressures. The two characterization ap-proaches yield values in close agreement, supporting
our assertion that the lens profiles are close to spher-ical.
The lens aberration was evaluated by use of thetopological data acquired by the surface profiler.
Fig. 9. Wave fronts and MTFs at several pressures: (a) 11, (b) 21, (c) 40, and (d) 54 kPa. The wavelength in this simulation was determinedat � � 550 nm. Dashed curves show the diffraction limits. PV, peak to valley.
These data were approximated by a sixth-order poly-nomial describing the membrane surface at severalpressure values. Subsequently a model of a tunablemembrane microlens was implemented with the Ze-max optical design program. The model comprisedthree parts: a 200��m-thick Pyrex layer, a liquid lenschamber, and the deflected membrane. The mem-brane surface was represented as an even asphere byuse of the polynomial coefficients derived above. Therefractive index of the Pyrex layer was nP � 1.4731,and that of for the liquid was n1 � 1.6057, both at awavelength of 546.1 nm. To minimize the aberrationcaused by the lens edge we used a 300��m aperture inthe simulation.
The simulation was made at four pressure values:11, 21, 40, and 54 kPa. Figure 9 shows the wave frontand the modulation transfer function (MTF) for thesepressures. Based on the aberrations, the Zemax pro-gram calculates a list of the Zernike coefficients byusing Zernike fringe polynomials. The coefficientsrepresent the spherical aberrations of first, second,and third orders. Table 1 illustrates the sphericalaberrations based on the Zernike coefficient data, andTable 2 shows the peak-to-valley aberration of thedifferent wave fronts, based on Fig. 9.
4. Discussion
A decided advantage of this tunable lens design com-pared with competing tunable microlens concepts isthe ability to vary lens curvature through a range ofpositive as well as negative values. Application ofpositive pressure results in plano–convex lenses, andby application of negative pressure the lenses becomeplano–concave. These two operating modes are illus-trated in Fig. 10 for a membrane with 300��m diam-eter operated at 4 and 0.2 kPa. A limited distension
�3.5 �m� was used for this measurement because thewhite-light interferometer is unable to measure pro-files steeper than �7.73º from the horizontal.
Further optimization of the lens structure, partic-ularly with respect to membrane thickness and elas-ticity, as well as the range and accuracy of pressuresrequired for achievement of a desired lens shape,requires a more-detailed understanding of the staticsof the membrane. To this end, was employed theAnsys finite-element modeling package to simulatethe membrane deflection as a function of various pa-rameters; a typical result, for a membrane with anelasticity modulus of 4 MPa, a thickness of 50 �m,and a diameter of 400 �m, is shown in Fig. 11. Acomparison of lens distension as measured by data isshown in Fig. 12. The consistently lower magnitudesof distension as measured by the surface profiler aredue to the fact that this approach distorts the mem-
aSpherical aberrations of first, second, and third orders as functions of four pressure values. The aberrations are rms values, given inwaves for a wavelength of 550 nm.
Table 2. Wave-Front Aberrations
Pressure (kPa)
Wave FrontAberration
(�)a
11 0.240721 0.255240 0.189854 0.5856
aPeak-to-valley aberrations of the wave fronts of Fig. 9. Theaberrations are given in waves for a wavelength of 550 nm.
Fig. 10. Contours measured with a white-light interferometer forthe tunable lenses operated in (a) plano–convex and (b) plano–concave modes; the measurements are for a 300��m diameter lensoperated at 4 and 0.2 kPa, respectively.
brane, despite the low pressure of the stylus. As aresult, the measured results are smaller than thesimulated and interferometry-based values.
Simulation results for lens height profile as a func-tion of pressure are shown in Fig. 13. The simulatedheight profiles are similar to the measured datashown in Fig. 6. The gradient of curvature at the lensedge agrees with the experimentally acquired curva-tures. The lens height varies moderately between the
simulation and the experiment because of distortioncaused by the surface profiler.
The minimization of spherical aberration is a keyaspect of membrane lens design. The maximum first-order spherical aberration was obtained at a pressureof 54 kPa. This value of 0.217 � at a wavelength of550 nm is acceptable. But this value can be achievedonly with a predefined aperture of 300 �m, applied toa lens with a diameter of 400 �m. This apertureblanks the nonspherical areas at the lens edges andthus improves the optical performance. As can beseen from Table 1 and Fig. 9, the spherical aberrationdecreases with decreasing pressure.
Simulation of the MTF, as illustrated in Fig. 9,confirms these aberration results. Two curves areplotted for each pressure value: the dashed curves inFig. 9 depict the diffraction limit and depict the bestMTF value for the lens aperture, limited only by dif-fraction; the solid curves below are the real MTFs,determined for the membrane surface. The best con-trast is achieved with the lens at a pressure value of20 kPa, as shown in Fig. 9(b). The worst contrast isfound for the pressure of 54 kPa, as shown in Fig.9(d). The resolution, represented as the maximumspatial frequency, depends on the numerical apertureof the lenses, so the resolution increases with highernumerical aperture and thus increases with increas-ing pressure.
Further design considerations are the means forapplication of pressure, pressure variations, repeat-ability, and aging. The application of constant pres-sure over an extended period of time can be achievedonly by use of a pressure controller with a precisemicrovalve. Maintaining constant pressure is impor-tant to prevent variations in the focal length duringthe imaging period. The repeatability and aging ef-fects have not yet been investigated in detail, but wehave not observed any hysteresis in membrane de-flection, especially with low maximum pressure val-ues. Extremely high pressures may overstretch thePDMS membrane, causing plastic deformation andthus leading to nonreproducibility effects.
Finally, the PDMS membrane is stable and flexiblein a temperature range from �50 ºC to �200 ºC, butthe stability of the refractive-index liquid must alsobe considered. Volatile liquid combinations, such asH2O:ethanol mixtures, are therefore not suitable forlong-term use in such a lens system.
5. Summary
A new liquid microlens, bounded by a microfabri-cated, distensible membrane and activated by a mi-crofluidic liquid-handling system, has been describedand characterized. The fully enclosed structure andpressure-dependent mode of operation allow the lensto be tuned over a wide range of positive and negativecurvatures, such that a micro-optical element withtunability over a wide range results. As the liquidoptical medium of the lens is fully enclosed and needsto be transparent only at the operating wavelength, awide range of materials, with a correspondingly widerange of refractive indices as well as dispersive
Fig. 11. Typical Ansys result for a distended membrane, 50 �mthick, with a pressure of 50 kPa.
Fig. 12. Comparison of maximum lens distension as a function ofpressure as measured by interferometry and surface profiling andcompared with simulation results.
Fig. 13. Lens profile as predicted by an Ansys simulation for a50��m-thick PDMS membrane with 400��m diameter.
power, may be employed in future generations of thedevice.
The lens technology also permits the assembly ofmulticomponent lenses, such as tunable achromaticdoublets. Through the use of appropriate liquid opti-cal media, tunable achromatic microlens systemsmay be fabricated, providing even greater flexibilityfor a variety of applications.
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