Completely integrated , thermo-pneumatically tunable microlens

An integrated tunable microlens, whose focal length may be varied over a range of 3 to 15 mm with total power consumption below 250 mW, is presented. Using thermo-pneumatic actuation, this adaptive optical microsystem is completely integrated and requires no external pressure controllers for operation. The lens system consists of a liquid-filled cavity bounded by a distensible polydimethyl-siloxane membrane and a separate thermal cavity with actuation and sensing elements, all fabricated using silicon, glass and polymers. Due to the physical separation of thermal actuators and lens body, temperature gradients in the lens optical aperture were below 4C in the vertical and 0.2 C in the lateral directions. Optical characterization showed that the cutoff frequency of the optical transfer function, using a reference contrast of 0.2, varied from 30 lines/mm to 65 lines/mm over the tuning range, and a change in the numerical aperture from 0.067 to 0.333. Stable control of the focal length over a long time period using a simple electronic stabilization circuit was demonstrated. © 2011 Optical Society of America OCIS codes: (010.1080)Adaptive lens; thermo-pneumatic actuation; (120.0120) MTF. References and links 1. W. Qiao, F. S. Tsai, S. H. Cho, H. Yan, and Y. H. Lo, “Fluidic intraocular lens with a large accommodation range,” IEEE Photon. Technol. Lett.21, 304306 (2009). 2. W. Qiao, D. Johnson, F. S. Tsai, S. H. Cho, and Y. H. Lo, “Bio-inspired accommodating fluidic intraocular lens,” Opt. Lett.34, 3214-3216 (2009). 3. K. Aljasem, A. Werber, A. Seifert, and H. Zappe, “Fiber optic tunable probe for endoscopic optical coherence tomography,” J. Opt. A: Pure Appl. Opt. 10, 044012 (8pp) (2008). 4. H. B. Yu, G. Y. Zhou, F. S. Chau, F. W. Lee, S. H. Wang, and H. M. Leung “A liquid-filled tunable double-focus microlens,” Opt. Express 17, 4782-4790 (2009). 5. H. W. Ren, D. Fox, P. Anderson, B. Wu, and S. T. 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Lett. 85, 1128-1130 (2004). #137365 $15.00 USD Received 3 Nov 2010; revised 17 Dec 2010; accepted 17 Dec 2010; published 24 Jan 2011 (C) 2011 OSA 31 January 2011 / Vol. 19, No. 3 / OPTICS EXPRESS 2347 12. S. Grilli, L. Miccio, V. Vespini, A. Finizio, S. D. Nicola, and P. Ferraro, “Liquid micro-lens array activated by selective electrowetting on lithium niobate substrates,” Opt. Express 16, 8084-8093 (2008). 13. A. Werber, and H. Zappe, “Tunable microfluidic microlenses,” Appl. Opt. 16, 3238-3245 (2007). 14. M. D. Volder, and D. Reynaerts, “Pneumatic and hydraulic microactuators: a review,” J.Micromech.Microeng. 20, 043001 (2010). 15. N. B. Justis, D. Y. Zhang, and Y.-H. Lo, “ Integrated dynamic fluidic lens system for in vivo biological imaging,” Engineering in Medicine and Biology Society,IEMBS ’04. 26th Annual International Conference of the IEEE , pp.1256-1259 (2004) 16. F. Schneider, J. Draheim, R. Kamberger, P. Waibel, U. 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Introduction
Adaptive lenses are useful for a wide variety of applications, including beam steering and shaping, in cell phone cameras, in optical interconnects, intraocular lenses [1,2] and a variety of biomedical imaging systems [3].Recently developed double-focus microlenses extend the application range of liquid microlens technology [4].Two mechanisms have been widely employed for realizing adaptive lenses: shape change of liquid lenses [5,6] and refractive index change of liquid crystal lenses [7].Compared with liquid crystal lenses, adaptive liquid lenses deliver higher quality performance [8,9], for example, liquid filled lenses with an aspherical surface fabricated by SPDT for compensating spherical aberrations [10].Depending on the operation mechanism of adapative liquid lenses, these may be further separated into two categories: electrowetting lenses and mechano-fluidic lenses.The electrowetting liquid lens allows continuous focus change with applied voltage, resulting in fast response time [11,12]; however, high voltages are typically required.Mechano-fluidic lenses operate by pumping liquid into or out of a microfluidic lens chamber [8,13]; the curvature of a confining elastic membrane is changed as a function of the liquid volume displacement resulting in a change in focal length.
Mechano-fluidic lens systems, however, usually require external mechanical pumping components, which make the system large and impracticable with respect to integration.MEMSbased mechanisms may be considered for actuation, and a variety of pneumatic and hydraulic micro-actuators have been proposed [14]; piezoelectrically actuated micro-pumps [15,16], thermo-pneumatic micro-pumps [17] and a variety of pneumatically actuated optical devices [18] have been demonstrated.Piezoelectrically actuated micropumps have very distinct advantages in reliability and fast response speed.However, the required voltages are generally high between 10 and 500 V. Thermo-pneumatic pumps feature usually a large membrane displacement at low voltages and low power consumption.
In this paper, we show that integrated thermo-pneumatic actuation can be combined with a mechano-fluidic tunable microlens to realize a completely integrated pneumatically-tunable microlens system.A membrane-based fluidic lens is integrated with a thermal pump actuator and temperature sensor chip, and the optical performance is extensively characterized.The design, fabrication, and operation of the lens is discussed, along with an analysis of the thermal structure, properties of the liquids employed, design of the control circuitry and the response time of thermo-pneumatic lenses.

Thermo-pneumatic actuation principle
As shown schematically in the cross-section of Fig. 1, the thermo-pneumatically tunable lens is based on separate pump and optical cavities in a microfluidic system.A liquid-filled lens cavity is bounded by a thin, distensible membrane, which forms the refractive lens surface.Inside this cavity are four thermal pumps, air-filled cavities with integrated heater and temperature sensor structures, separated from the lens cavity by a second set of flexible membranes.Upon heating, the air in the thermal pump expands, causing the membranes to likewise expand and compress the optical liquid.This compression, in turn, causes a distension of the optical lens membrane, and the resulting change in curvature gives rise to a tuning of the lens focal length.

Design and fabrication
The integrated tunable lens shown in cross-section in Fig. 1 is designed as a hybrid system, consisting of a silicon lens chip with a spin-coated polydimethylsiloxane (PDMS) membrane defining the lens aperture; a PDMS support ring with a heating chamber (the thermal pump) and a cavity for the optical liquid; and a glass chip with structured platinum heaters and temperature sensors.
We discuss in this section the design principles, the thermal model and considerations for the choice of optical fluids.

Thermo-pneumatic modeling
The working principle of the adaptive lens is based on thermal expansion of materials.When a voltage is applied to the Pt heaters found in the air-filled thermal pump cavities, Joule heating causes the temperature of the air inside this actuation chamber to increase, and consequently the air volume increases; the heater membrane is thus deformed and displaces the fluid in the optical chamber.Since the optical liquid can be assumed to be incompressible, the volume change of the air chamber will then cause a deformation of the lens PDMS membrane, thus changing the refractive power or focal length of the lens.
We can analyze the relationship between temperature and pressure changes by recalling that the thermodynamic relation between the absolute temperature T , pressure P and volume V of a system is given by the well-known ideal gas equation R is the gas constant and n is the amount of substance (gas) enclosed in the cavity, which is in our case air.The variation of volume and pressure when varying temperature is then given simply by where V 1 and p 1 are the volume and pressure at a set temperature T 1 , whereas V 0 and p 0 are the volume and pressure at room (or starting) temperature T 0 , which is 292 K in the present case.
As the temperature increases, the volume of air expands, and the pressure in the air chamber increases and overcomes the membrane stress.
In the current design, four identical thermal cavities with a diameter of 2 mm are fabricated to increase the air volume and hence displacement.Thermal balance channels are utilized to provide a uniform heating of the optical liquid.This arrangement ensures a stable focal point during the heating and cooling process.Since air has a low heat transfer coefficient, the system is robust with respect to fluctuations of the applied voltage.
Due to thermal cross-talk between the heating chamber and the optical liquid, an additional contribution to the deformation of the lens surface derives from the thermal properties of the liquid, based on the volume expansion coefficient and specific heat [19]; the volume expansion due to liquid expansion can be expressed, namely where V is the liquid volume, ∆T the temperature change, and β the thermal expansion coefficient of the optical liquid.
From the above equations, it can be seen that a larger chamber results in larger volume change for the same temperature variation.Moreover, the thermal expansion of the optical liquid can serve as an extra actuation medium as long as the optical liquid does not have a significant change of the refractive index as a function of temperature.In the experiment, the optical liquid FC40 with thermal volumetric expansion of 0.0012/K and the immersion oil DF with 0.0005/K were chosen.The additional contribution to the focal tuning due to the expansion of the liquid is part of an integral effect leading to the desired membrane deformation.Calibrating the system, does not distinguish between different actuation mechanisms.The integral outcome which is correlated to the applied voltage is measured finally.

Fabrication process
The lens chip was fabricated by standard silicon fabrication in combination with PDMS technology.A 60 m thick PDMS membrane is spun onto the front side of the silicon substrate.The For analyzing the influence of the DRIE process on the PDMS membrane, AFM measurements have been taken as presented in Fig. 2. The surface roughness of the PDMS membranes after DRIE treatment varies between 14 nm and 33 nm rms.Compared to the topsides of the membranes, which didn't see the DRIE process, no degradation could be detected, the values are in the order of 30 nm rms.The partly improved surface quality after DRIE is mainly due to surface tension effects.The supporting ring is formed by a PDMS casting process, as shown in Fig. 3(a).PDMS is selected as the adaptive material for the tunable lens because of its low heat transfer coefficient and its ability of bonding with silicon and glass.The thickness of the membrane of the thermal pump is determined by the thickness of a foil between the two casting parts, acting as a spacer.To reduce air diffusion, and thus pressure leakage, through the PDMS, a 50 nm Parylene C layer was deposited by VDP (vapor deposition polymerization) on top of the membranes of the thermal pump [20].The membrane in the aperture area was removed by a hollow punch with a diameter of 4 mm manually.
Figure 3(b) shows a photo of the fabricated PDMS layer For the heater layer, as can be seen in Fig. 3(c), platinum is selected as the material for the heater and temperature sensor because of its good thermal stability and linear variation of resistance with temperature.A 10 nm thick titanium binding layer and a 150 nm thick platinum layer were deposited by electron beam evaporation and patterned by means of a lift-off process on the Pyrex glass wafer.Figure 3(d) shows a photograph of the heater chip.
After an oxygen plasma treatment (RF power: 10 %, activation time: 10 s, partial oxygen pressure: 1 mbar), the PDMS layer and glass substrate are bonded together.In a second bonding step, the silicon lens chip with the PDMS membrane is connected to the other side of the PDMS chamber by a similar oxygen plasma treatment.After plasma treatment, 12 hours holding time at room temperature and atmospheric pressure is required for stable bonds.
Figure 4 shows a photo of the completed integrated lens structure.The optical liquid is filled after these steps by inserting a syringe into the PDMS body.Bubbles are eliminated by using a second syringe for draining.After removing the syringes (diam-  eter: 0.6 mm), the openings in the PDMS bulk close automatically due to the high elasticity.

Optical liquids
The optical liquid in the lens cavity defines the optical behavior of the lens, such that an appropriate choice of liquid is essential for good lens performance.Moreover, important considerations are a high boiling point, low vapor pressure, absence of undesirable effects (such as absorption into, swelling of, or leakage through PDMS), suitable viscosity, optical transparency and an appropriate refractive index.Since we propose a completely integrated system here, liquid loss through the membrane, for example, could not be compensated such that liquids which diffuse through PDMS would quickly result in decreased performance.
A popular liquid choice for tunable lenses is very often water, or a mixture of water and ethanol, because of their compatibility with PDMS.For thermo-pneumatic actuation, these liquids are unsuitable due to their low expansion coefficient, low boiling point and formation of bubbles.In addition, many other liquids are unsuitable since they cause swelling of PDMS.Swelling can affect the integration of specific lens components such as membranes, liquid and  air chambers, and can also change surface properties leading to a detachment of PDMS from bonded material as glass or silicon.As a result, many types of oils are unsuitable for this type of lens.
We tested four different kinds of optical liquids for their suitability in this thermo-pneumatic structure experimentally [21]: glycerol, ethylene glycol, perfluorodecalin FC40(3M TM ), and immersion oil DF (Cargille Laboratories).For all four liquids, no swelling of the PDMS was observed and no leakage was detected.Perfluorodecalin (FC-40) and immersion oil were chosen to be optimal; with respect to the evaporation rate, the immersion oil is better suited than FC40, because of its much lower vapor pressure.

Control circuitry
For the stability of the adjusted focal length, an electronic control circuit for stabilizing the temperature was developed.The circuit is composed of a Wheatstone bridge, a comparator(National Semiconductor, LMC7211) and a pMOS power switch (Diodes, DMP2104V).Depending on the ratio of the resistance of the temperature sensor and a reference resistor in the Wheatstone bridge, the heater in the micro-lens is switched on or off to keep the temperature at the desired value.The schematic for this control circuit is outlined in Fig. 5.

Temperature distribution simulation
The temperature distribution in the lens structure is an important consideration for the optical quality, since the refractive index of optical material depends on temperature.Therefore, it should be assured that the temperature distribution of the optical liquid is homogeneous enough to ensure a good quality of the image [22].A decided advantage of the structure presented here, in which the optical lens liquid is not heated directly but displaced using thermal actuation of a separate chamber, is that the thermal gradients in the optical pathway are strongly minimized.
To verify this assertion, the multi-physics simulation software COMSOL was used to evaluate the temperature distribution in the optical liquid (FC40) as well as to study the relationship between the applied voltage and the generated temperature.The AC/DC module and heat transfer module in COMSOL were employed for these simulations.Table 1 lists the material properties used in the model.Figure 6 shows the lens structure as defined using the CAD tool Solidworks and modeled using COMSOL.The vertical static temperature distribution in the lens chamber is shown in detail in Fig. 7(a) for a bias of 3V applied to the heaters.The temperature gradient across the body of the lens is less than 4 • C in the vertical direction and less than 1 • C radially.The reason for the asymmetric temperature distribution in the complete cavity is the large input current at the common feed line.In particular, the right angle branch point causes some assymetry.Simulations show a thermal concentration point directly at the branch point.But nevertheless, in the region of the optical path, the radial temperature distribution is very homogeneous and in  The simulation result is compared to measurements of the air temperature in the thermal pump cavity, as shown in Fig. 8.The discrepancy between the two results is likely due to the fact that a static analysis was used in COMSOL, but the experiment reflects dynamic processes which determine the heat distribution.The temperature measurements were taken, following a time delay after setting the heater voltage, to allow the system to reach thermal equilibrium.

Characterization
The various components of the lens as well as the entire tunable lens system were characterized to verify their performance.The most important measurements were those of the characteristics of the thermal sensors, the functionality of the thermal pumps and the system optical behavior of the lens system.

Temperature sensors
The Ti/Pt structures were used as heaters for the thermal pump but also as temperature sensors.Measurement of the temperature inside the air-filled pump chamber is essential for regulation of pressure and thus ultimately lens focal length.In this regard, stability of the Ti/Pt heater and sensor elements is an essential parameter [24].
To achieve a long-term stability of Ti/Pt resistance for a given temperature, roughly two hours of annealing at 250 • C in an oven at normal atmospheric pressure following deposition is required, as shown in Fig. 9(a).The resistance of three different sensor structures were measured and, in each case, the resistance drops down rapidly during the first hour and converges to a stable constant value after about 2 hours.
For the calibration of the temperature sensors, an oil bath method with a highly-sensitive commercial temperature sensor as a reference was used.As shown in Fig. 9(b), the measurement results after annealing do not show any hysteresis during the heating and cooling cycles, and show a linear increase of the resistance between room temperature and 175 • C. The variability of the resistance before annealing is mainly caused by diffusion of titanium since several nanometer thick Ti layer is used as an adhesion layer for the Pt film, which adheres poorly to the glass substrate.At high temperatures, Ti diffuses along grain boundaries through the platinum film, eventually reaching the top of the Pt surface.In ambient air, this titanium oxidizes, resulting in hillock formation on the platinum surface.AFM measurements of the surface before and after annealing are shown in Fig. 10, verifying this behavior.

Thermal pump
Figure 11(a) shows a detailed schematic cross-section of the thermal pump; there are four airfilled pumps in the lens chamber, symmetrically distributed around the lens aperture as outlined in Fig. 1.Thermal expansion of the PDMS membrane separating the thermal pump chamber from the lens chamber is used to displace the lens liquid and thus tune the lens; as a result, the deformation of the thermal pump membrane as a function of the heater temperature must be characterized.
A white light interferometer was used to measure the maximum deformation of the PDMS membranes of the thermal pump when the chambers are heated.tionship between the applied voltage and maximum deformation of the pump membrane.As can be seen, the deformation of the membrane due to the volume change of the air expansion is linearly dependent on the heater voltage and can be controlled precisely.Here, the resistance of the complete heating module is approximately 100 Ω, and the applied voltage ranges from 3 to 5 V. Hence the total power consumption of the chip, including all four heaters, is only between 90 and 250 mW.
From the ideal gas Eq. ( 2), the pressure calculates to 102.5 kpa for 3 V and 103.5 kpa for 5 V.

Optical characteristics
An essential aspect of tunable lens characterization is clearly its optical behavior, where focal length and modulation transfer function (MTF) are of primary interest.Figure 12 shows the measurement setup used for the determination of the focal length (back focal length is implied) and MTF [25].A multimode fiber of diameter d = 62.5 µm is used to approximate a point light source; the emitted light is collimated and the resultant approximately planar wavefront is When varying voltages are applied to the heaters of the thermal pumps, the focal length of the lens varies; the vertical microscope stage is then used to image the focal point on a CCD imager.
Figure 13 shows the tendency of the measured focal length and the corresponding temperature with respect to the applied voltage.
The refractive index of liquids depends on temperature.For the immersion oil DF, the temperature coefficient is −3.85 • 10 −4 /K at an absolute value of n = 1.515.From simulations we expect a maximum temperature change of 4 • C in the vertical direction of the optical aperture, so the refractive index change is 0.1%.Generally, the temperature coefficient for our used optical liquids is in the order of −3 • 10 −4 /K, the effect on the optical performance is expected to be small.Simulations show (see Fig. 7) that inside the optical aperture the lateral temperature distribution is rather constant in the order of 0.2 • C at each height or at each layer.So, the variation is mainly given in the axial (vertical) direction and no non-rotationally symmetric errors are introduced.
The thermal influence on the focal length or optical performance has to be separated from the effect of the deformed membrane.Accordingly, the membrane lens was replaced by a module with a flat glass layer on top instead of a flexible membrane.This element was combined with a commercial glass lens of focal length 6 mm.Studying the influence of the focus of the combined system with and without heating, no change in the focal length could be detected within the accuracy of the measurement setup.The system is able to resolve roughly 200 µm in focal length.

MTF
The intensity distribution of the focal point on the CCD imager (corresponding to the point spread function) is recorded for a given sampling area of the CCD as a function of focal length.This two-dimensional intensity distribution corresponds to the raw data from which the MTF is calculated by two-dimensional Fourier methods; details of the measurement approach are given in [25].MTF measurements of the tunable lens are shown in Fig. 14.The cutoff frequency of the optical transfer function, using a reference contrast of 0.2, varied from 30 lines/mm to 65 lines/mm over the entire tuning range.The MTF curves at different applied voltages or adjusted temperatures show that the best performance is achieved at approximately 34 • C, corresponding to a focal length of approximately 4.4 mm.The membrane attached to the surface of the Si chip with a circular boundary does not have an ideal spherical or parabolic surface such that the aspheric curvature will influence the optical transfer quality.The inflection point of the membrane profile near the aperture edge moves with incresasing temperature and correspondingly the asphericity changes with focal length, giving rise to different MTF curves.

Bubbles
One issue which may befall liquid-filled mechano-fluidic lenses is the generation of gas bubbles during the initial filling of the optical liquid into the chamber.Bubbles in the lens chamber affect the stability and repeatability of the tuning as can be seen in Fig. 15(a): the observed drift between the heating and cooling cycles results because the volume of the optical liquid varies as long as bubbles are present.This behavior can be seen for repeated cycles of heating and cooling, and as a result, the focal length cannot be repeatably and reliably set.Bubbles can be avoided by inserting two syringes through the PDMS layer into the chamber: one syringe fills liquid into the chamber and the other drains the bubbles out.
After removing all air bubbles in the immersion oil, the repeatability improved markedly for heating and cooling cycles.The focal length was measured twice within 48 hours, leading to the hysteresis-free characteristics of Fig. 15(b).Figure 16 shows images of a test object (an "F") at different applied voltages, hence different focal lengths, of the tunable lens.Such a measurement only provides a qualitative description of the optical performance, since proper optical characterization involves measurement of MTF and focal length, as done above.Nevertheless, these images were taken with an additional lens of fixed focal length in the optical path for a better adjustment of the aperture and no significant differences between the images are seen.For all focal lengths, the distances in the optical setup were adjusted such that the total magnification was roughly the same.

2.6V 3V
3.6V 4.8V 4.4V Finally, to evaluate the performance of the electronic control circuit, the focal point was monitored over a period of 40 minutes using a microscope.The result showed no variations in the intensity and the corresponding focal length variation was below ±200 µm within 40 min; the stability of the electronic control system is thus given.

Response time analysis
For some applications, the focus tuning speed is a very important parameter.Thermo-pneumatic lenses can realize fine tuning of the focal point, with slow heating or cooling speed, controlled by a suitable temperature circuit.For such small focus variations, the system responds in order of a second.
For wide tuning of the focal length as for example from 20 mm to 10 mm by heating, and then backwards by passive cooling, the input power and response time is shown in Table 2.
The response time strongly depends on the input power for the heating process [26], and on the material choice for the cooling process [27].At the moment no active cooling is performed.The materials used are PDMS (thermal conductivity 0.18 W m −1 K −1 ) for the thermal pump body and glass for the substrate (0.9071 W m −1 K −1 ), both with low thermal conductivity.Using Si (148 W m −1 K −1 ) as lens substrate with an etched aperture would increase the response speed for cooling significantly.
The response speed of the lens is determined by the pressure rate in the air chamber and increases with the heating rate.This is the reason why the response time decreases when using higher input power.

Conclusion
A self-contained, tunable liquid lens with an integrated thermal actuation mechanism has been designed, fabricated and tested.Experimental results demonstrate that this lens may be stably and repeatedly tuned in focal length over a wide range, requiring only low applied voltages.
A unique feature of this system is that it does require complicated external control and actuation systems.Future work will address an improvement of the lens response speed, through optimization of the thermal pumps and inclusion of integrated cooling structures.

Fig. 1 .
Fig. 1.Schematic design of the thermally tunable lens, with the device dimensions shown.The lens cavity is filled with an optical liquid and the chambers of the thermal pump are filled with air.Thermal expansion of the air causes compression of the liquid and distension of the lens membrane, shown as a concave surface at the top of the structure.

#
137365 -$15.00USD Received 3 Nov 2010; revised 17 Dec 2010; accepted 17 Dec 2010; published 24 Jan 2011 (C) 2011 OSA membrane comprises a mixture of silicone polymer and a curing agent (Sylgard@186, Dow Corning Corp).Subsequently, a DRIE (deep reactive ion etching) step is employed onto the backside to create the lens aperture.The etch process uses the PDMS membrane as an etch stop.

Fig. 3 .
Fig. 3. Fabrication of the support ring and heater element: (a) fabrication of the support ring by a standard casting process.(b) photo of the PDMS ring forming the lens cavity.(c) fabrication of the heater layer using a standard lift-off process for the heater and sensor structures.(d) photo of the heater layer.

Fig. 4 .
Fig. 4. Photograph of the integrated tunable microlens: the silicon wafer is mounted on the PDMS layer.The curvature of the distended lens is seen at the top.

Fig. 5 .
Fig. 5. Schematic of the temperature control unit.R S : reference resistor, R T : variable sensor resistor.

Property PDMS [ 17 ]Fig. 6 .
Fig. 6.CAD model of the thermopneumatic tunable lens, consisting of a silicon chip, a PDMS layer, an optical liquid, a thermal pump, and a heating layer on a glass chip.(a) Temperature distribution of the optical liquid with a bias of 3 V applied to the heaters.(b) Temperature distribution of the thermal pump with a bias of 3 V applied to the heaters.

Fig. 7 .
Fig. 7. Temperature gradient in the lens body: (a) vertical direction and (b) radially, for a bias of 3 V applied to the heaters.

Fig. 8 .
Fig. 8. Measurement and simulation results of the temperature in air cavities of the thermal pump

Fig. 9 .
Fig. 9. Characterization of sensor elements.(a) Resistance of 3 sensors of different geometric structure at room temperature after different annealing times at the same annealing temperature (250 • C ) in air ambiance; (b) relationship between resistance and temperature after annealing

Fig. 10 .
Figure11(a) shows a detailed schematic cross-section of the thermal pump; there are four airfilled pumps in the lens chamber, symmetrically distributed around the lens aperture as outlined in Fig.1.Thermal expansion of the PDMS membrane separating the thermal pump chamber from the lens chamber is used to displace the lens liquid and thus tune the lens; as a result, the deformation of the thermal pump membrane as a function of the heater temperature must be characterized.A white light interferometer was used to measure the maximum deformation of the PDMS membranes of the thermal pump when the chambers are heated.Figure 11(b)  shows the rela-

Fig. 11 .
Fig. 11.Vertical deformation S of the thermal pump as a function of voltage applied to the heaters.

#Fig. 12 .
Fig. 12. Diagram of the back focal length and MTF measurement setup.An approximate point source at an infinite conjugate is generated by a multimode fiber and a collimator lens.A manually controlled microscope platform is used to fix the microlens under test.Objective lenses of different magnification are used for the variation of the image size of the focal point of the lens under test.A high quality CCD records the image.

#Fig. 13 .
Fig. 13.Measured back focal length as a function of the applied voltage using the optical liquid FC40.The dashed line is an empirical fit through the back focal length data.The solid line is a linear fit through the corresponding temperature values.

Fig. 14 .
Fig. 14.Experimentally determined MTF curves of the thermo-pneumatically actuated lens at different temperature values and hence back focal lengths.The back focal lengths for a given temperature are determined from Fig. 13.

Fig. 15 .
Fig. 15.(a) Change of the focal length tuning characteristic due to the presence of bubbles in the liquid using immersion oil.(b) Variation of focal length without bubbles.

Fig. 16 .
Fig. 16.Images of an F target for different focal lengths

Table 2 .
Material properties used in the simulation model.