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We suggest a way to electrostatically control deformed geometry of an electrostatic deformable mirror (EDM) based on geometric modulation of a basement. The EDM is composed of a metal coated elastomeric membrane (active mirror) and a polymeric basement with electrode (ground). When an electrical voltage is applied across the components, the active mirror deforms toward the stationary basement responding to electrostatic attraction force in an air gap. Since the differentiated gap distance can induce change in electrostatic force distribution between the active mirror and the basement, the EDMs are capable of controlling deformed geometry of the active mirror with different basement structures (concave, flat, and protrusive). The modulation of the deformed geometry leads to significant change in the range of the focal length of the EDMs. Even under dynamic operations, the EDM shows fairly consistent and large deformation enough to change focal length in a wide frequency range (1~175 Hz). The geometric modulation of the active mirror with dynamic focus tunability can allow the EDM to be an active mirror lens for optical zoom devices as well as an optical component controlling field of view.
© 2016 Optical Society of America
1. Introduction
Optical components with miniaturized linear movement mechanism are widely used in recent electronics devices. For example, a coordinated lens module with voice-coil actuators is used for optical zooming in a smartphone [1] and a micro mirror with PZT actuators enabling precise linear movement is used for improving the accuracy of optical data storage [2]. An active lens with translational motion control based on film-type electro-active polymer has also been suggested for decreasing the thickness of an optical component [3].
However, current electronics devices rarely allow enough space installing the optical components that change their positions responding to the axial movement of the linear actuators. As an alternative to the axial movements of a lens, researchers have suggested concepts of self-morphing lenses for varying focus [4–15].
One popular approach for the morphing lenses is based on volumetric change of liquid in a chamber responding to pressurized injection of liquid [4–7]. There have been further advances in internal pressure control by piezoelectric (PZT) actuators [8], electroactive polymer [9,10], and thermal expansion [11–14]. Although the approaches have their own benefits from high optical transparency and large focal length variation, there is a difficulty in precise control of the geometry of the lens surface. Recently, a methodology, which is a combination of microfluidic pumping and electrostatic force, contributes to improving control the surface geometry of the liquid lens [15].
Another approach for tunable lens is the use of an electrowetting and a dielectrophoretic phenomenon. Based on the electrowetting principles, the control of electric field around hydrophobic liquid changes the surface geometry of a droplet [16–19]. If the liquid droplet is composed of dielectric particles, force direction in the non-uniform electric field drives the droplet morphed [20–23].
For a self-morphing mirror, researchers have been studied electrical controls of surface deformation methodologies. For example, an array of PZT actuators [24] enables precise controls of surface geometry distribution of a mirror. Instead of the linear actuator, a membrane mirror controlled by electrostatic force distribution has been suggested [25]. The initial purpose of the surface control of the mirror is to correct the distortion of wavefronts for adaptive optics systems [24–29]. Researchers have historically suggested active adaptive optics systems with multi-channel micromachined membrane deformable mirror (MMDM) from an open loop controlled device [28] to closed loop controlled system [29]. Previous works have focused on sub-micro scale deformation of the mirror surface which is generally required in wavefront correction.
The concept of the deformable mirror also contributes to dynamic focusing for composing optical devices [30–34]. Based on two active deformable mirrors, possibility of optical zoom devices has been studied [30,31]. Moreover, an electrostatic deformable polymer mirror with wide range of focal length variation has been suggested [32]. In addition, the mirror has been used for implementing auto focus camera [33], and optical zoom systems [34].
In this paper, we suggest a way to electrostatically control the surface geometry of a deformable mirror based on geometrical change of electrodes. Instead of using direct voltage variation on electrode arrays inducing electric field distribution, we change an electrode basement with different geometric structures and analyze induced deformation of the active mirrors. This paper introduces design concept and fabrication process of our electrostatic deformable mirror (EDM) which is composed of an active elastomeric mirror membrane and a geometrically modulated basement. We have observed geometrical deformation of the active mirror in accordance with driving voltages and geometric shapes of basements, and analyzed absolute focal length variation, ratio of focal length variation to driving voltage variation, difference of focal length variation at the same depth of deformation. Finally, we demonstrate active mirror and compare experimentally measured focal lengths and geometrically estimated focal lengths.
2. Design
Figure 1 shows an illustrated configuration of the proposed EDM, which is composed of a metal coated elastomeric membrane (active mirror) and a polymeric basement with an electrode (ground).
Fig. 1 An illustrated configuration of a electrostatic deformable mirror operating under a voltage applied between an active mirror and a basement (a) and basement geometry designed to be flat (left), convex (center) and concave (right) shape (b).
The EDM is designed to have an air gap of 1 mm between the active mirror and the basement. When an electrical voltage is applied across the components, the active mirror hemispherically deforms toward the stationary basement responding to electrostatic attraction force in the air gap. The deformed mirror returns to the flat state after the voltage off. Since the deformed shape of the mirror can be strongly related with electric field distribution between two electrode layers, for controlling the shape of the mirror we attempt to modulate the electric field distribution through change in the basement geometry from flat to convex or concave shape instead of using complicated electrode arrays inducing localized electric field distribution
3. Device fabrication
Figure 2(a) shows schematically illustrated fabrication steps of the EDM. An active mirror layer is prepared by pre-stretching a polymer, which is 3M VHB4905TM, membrane with area strain of 100%, fixing it on a surface of annular boundary pillar (thickness: 1 mm), and forming gold layer using a thermal evaporator under a perforated shadow mask. The thickness of the gold layer (80 nm) is carefully considered as to retain even surface without undesirable cracks on the coated area. Based on consideration of flexibility and anti-oxidation characteristics of a thin layer, we choose gold as a reflection material. After the pre-stretching process, the polymer film (an initial thickness: 500 μm) becomes a thin membrane and maintains tension on the frame due to its sticky characteristic. Except a flat basement, the structures of basements with concave or convex geometry are fabricated by a 3D printer and a gold layer (thickness: 50 nm) is constructed on the surface of the basements under a perforated shadow mask to make a ground electrode (diameter: 20 mm). Figure 2(b) shows cross-sectional profiles of the basements obtained from an optical profiler (Sensofar Plu neox 3DTM) and their photographs (inset). Finally, the EDMs are prepared by integrating the active mirror structure into each basement with different geometry. Figure 2(c) shows photographs of the prepared EDM prototype and a object image reflected on the active-mirror layer. It demonstrates that the surface of the active mirror layer is fairly smooth and flat enough to reflect a object image without any significant distortion.
Fig. 2 Schematic diagram of the fabrication process (a), photographs of a convex and a concave basement (inset) made with a 3D printer in which the stacking resolution is 16 μm and their cross-sectional profiles (b), and photographs of the fabricated EDM (c).
4. Numerical simulation
In order to estimate the influence of basements’ geometry on deformed shape of the active mirror, we performed numerical simulations for electrostatically induced deformation of EDMs with different basement geometry using a COMSOL Multiphysics®simulation software for electrical applications. Figure 3(a) shows details in the structural models that are used for the simulation. For modeling, a thin membrane (thickness: 0.5 mm, diameter of active area: 20 mm) is kept 1 mm distant from a flat surface on each basement. For the simulation, all parameters including material properties are determined by strictly reflecting experimental conditions. We also assumed that the electrodes with a uniform thickness are respectively established on the whole surfaces of the membrane and basement.
Fig. 3 Geometrical models of the EDMs with different basements (a) and a comparison of the numerically simulated cross-sectional profiles of the deformed mirrors when the deformed depth is 91.8 μm (b).
Under a condition producing consistent deformed depth of 91.8 μm, the simulated results indicate that shape of the mirror membrane deforming in response to the electrostatic force can be changed with the geometry of the basement, as shown in Fig. 3(b). Furthermore, the trend that the deformed shape becomes narrower as the basement geometry changes from concave to flat and convex one is consistent with experiment although there is a quantitative difference in the deformed shape between the simulation and the experiment.
5. Performance
Figure 4 shows a comparative study for the deformation behavior of the active mirrors with different basement geometries. For the performance test, leads on the active mirror and the electrode on the basement are connected to high voltage and ground, respectively. During electrostatically induced deformation, the cross-sectional profiles of the mirrors are obtained from an optical profiler. For each type of the basement, the electrical voltage dependent focal length is derived from computationally fitting a parabolic equation shown in Eq. (1) to the center area of the profile ( ± 6 mm from the center). The equation appears as
where x, y is x-y coordinate of the cross-sectional profile, d is estimated deformed depth and f means the absolute value of an focal length.Fig. 4 Performance tests of the EDMs with different basement: voltage and deformed depth dependent focal length profiles (a and b), comparison of the cross-sectional profiles of the deformed mirrors under two different deformed depths (c).
Figure 4(a) shows input voltage dependent focal length variations for EDMs with three types of basements. Although, theoretically, initial focal length of EDMs should be at the infinite position, experimentally measured initial focal lengths are at around −350 ~-270 cm which have almost zero deformation depth. The EDMs exhibit a consistent trend that focal length becomes shorter as voltage increases since higher voltage leads to larger deformed depth of the mirror due to enhancement of electrostatic force pulling the mirror toward the basement. However, during operations of the EDMs, we found that the range of the focal length clearly differs with the basement type. The EDM with the convex basement reaches the shortest focal length (−16.6 cm at 2.5 kV) and the concave type reaches −61.1 cm of focal length at the same voltage. As a first reason, the effect of gap distance between the mirror and the basement with a ground electrode can be considered since the electrostatic force can be strongly correlated with the distance between the electrodes. In the case of the convex basement, the gap distance at the center of the active mirror is 0.7 mm, whereas those of the active mirrors with the flat and concave basement are 1 mm and 1.3 mm, respectively. Under a constant input voltage, the EDM with the convex basement that possesses the smallest gap distance at central area produces larger deformation than the EDM with the flat basement or the concave one. The relatively large deformation results in shortening focal length of the EDMs, suggesting that the gap distance is an important factor to modulate the focal length of the EDM.
Particularly, we intensively consider possible differences in deformed geometry of the mirrors according to the basement types. As shown in Fig. 4(b), when the EDMs are electrically activated to have a similar deformed depth, an EDM with the convex basement consistently exhibits shorter focal length than other types of the EDM while the EDM with a concave basement provides longer focal length. Figure 4(c) exhibits cross-sectional profiles of the deformed mirrors when their deformation depth is 50 μm (Left graph) and 90 μm (Right graph) respectively. As expected, the figures show that the geometries of the mirrors are different with basement type and the measured differences by basement modulation are larger than estimated differences by numerical simulation. We can clearly observe the use of the convex basement leads to narrower bell-shaped deformation since it can induce stronger electrostatic force around the central area than other basements. It means possibility of reducing driving voltage compare to other shapes. From the parabola equation (Eq. (1)) fitted to the measured profiles, we found that the focal length of the mirror can be shortened as much as 37.7% (−61.01 ~-37.99 cm) for concave basement and 40.4% (−32.58 ~-19.42 cm) for convex basement when the deformed depth of the mirrors are 50 μm and 90 μm, respectively. We also notes that there is no significant distance error between the profiles and the fitted curves in the structure modulated area (a circular area with a radius of 6 mm at the center of the active mirrors) suggesting an effective region to be used as an active mirror with less spherical aberration. Solid line at the figure means distance error between measured profile and parabolic curve is less than < 1 μm.
Finally, in order to investigate dynamic behavior of the EDM, deformation responses of the EDM with a convex basement are measured by using a EM4SYS laser scanning vibrometer during operations of the EDM with continuative sinusoidal input signals. Under a constant input voltage of 2.4 kV, deformed depth of the active-mirror is fairly consistent in a frequency band (1 ~20 Hz). After a frequency band with a decreasing trend, the deformed depth sharply increases as high as 52 μm to a fundamental resonance frequency of 160 Hz (Fig. 5(a)). Although the deformed depth becomes much smaller as the frequency is beyond 160Hz, the frequency dependent deformation response exhibits that the EDM is capable of producing rapid response to a wide bandwidth of about 115 Hz with a fairly consistent deformed depth (deviation: < 10%).
Fig. 5 Dynamic response tests of the EDM: frequency dependent deformed depth profiles (a), time-deformed depth profiles duing operation with repetitive square input signals (2.4 kV at 10 Hz) (b) and repetitive sinusoidal input signal (2.4 kV at 115 Hz), respectively (c), and hysteresis curves of the deformation responses (d).
As shown in Fig. 5(b), operating tests under repetitive square input signals (2.4 kV at 10 Hz) reveals that the active-mirror becomes a deformed state with a short rising time (5 ~7 ms) before being stabilized and it is reversibly and rapidly recovered to rest state. Even at high-speed operations with sinusoidal input signals (2.4kV at 115Hz), the deformation responses are fairly revesible with a consistent amplitude (amplitude deviation: < 1%) and follow the input signals with a small time delay (< 1 ms), indicating that there is no significant phase delay in the operating frequency band corresponding to its bandwidth, as shown in Fig. 5(c). From hysteresis curves that are obtained by replotting frequency dependent time-deformed depth profiles, we also found that the deformation responses retain only small hysteresis during dynamic operations of the EDM with frequencies (32 ~160 Hz), which is wide enough to cover bandwidth although the hysteresis becomes higher at 256 Hz. The small hysteresis can be correlated with the prestretching treatment of the elastomeric membrane since the prestretching of polymeric materials can lead to reducing their viscoelastic characteristic, as shown in Fig. 5(d). The results indicate that the EDM is capable of providing dynamically controllable focal length in a wide frequency range.
6. Demonstration
Figure 6 is a demonstration showing reliability of the focal lengths obtained from experiments. For the demonstration, an optical system allowing a collimated laser beam reflected on an EDM to be scattered on a translucent glass is prepared, as shown in Fig. 6(a). During operations of the EDM, we observed the beam scattered on the glass, which is 80 cm distant from the EDM. In order to compare focal lengths obtained from the optical system with the estimated ones from geometry analysis shown in Fig. 4(a), we select input voltages required for collimated laser beam to be focused at 80 cm from the EDMs with different basements. The input voltages for the EDM with the convex, flat and concave basements are 1.2 kV, 1.74 kV and 2.25 kV, respectively. When cross-marked the voltages on a profile showing the voltage dependent focal length in Fig. 4(a), the input voltages correspond to the voltage for the focal length of −80 cm, as shown in Fig. 6(b). The correspondence is also visually proved by comparing relative size of beam spots projected on a translucent glass, as shown in Fig. 6(c). The diminutive spots in the three images indicate the focal length of the EDM is closed to −80 cm. On the contrary, defocused spots are larger than the size of the focused spot.
Fig. 6 (Visualization 1) An optical system for reliability test of the focal length variation (a), the comparison of focal length obtained from numerical calculation and experiment (b), and images of spots of collimated laser beam reflected from the EDMs during operation with different input voltages (c).
Difference in the spot size at the same range of input voltages is crucial evidence that the range of focal length of an EDM can be changed with the basement type. It indicates that geometric change in the basement can induce the modulation of deformed geometry at the active mirror in the EDM, and it leads to significant change in the range of the focal length (Visualization 1). Moreover, the projected circle does not show a serious distortion of circular shape and light intensity variation.
In order to investigate focusing properties of beams reflected from the EDM, we measured focal spot sizes of the beams and their spatial intensity distributions on a focal plane by using a BeamGage program and a Ophir Photonics SP620U camera. The beam generated from a He-Ne laser propagates to the EDM after being collimated by two lens. The size of the beam is reduced at an aperture stop with a diameter of 5 mm. Figure 7(a) shows changes in spot size of a focusing laser beam responding to focal distance variation of the EDM that can be changed with input voltages. The spot size on the focal plane almost linearly increases from 55 cm to 188 cm as the focal length changes from −24 cm to −125 cm. Figure 7(b) shows the spatial intensity distribution of the focusing beam with a focal length of −102 cm and spot size of 162 μm. The intensity at the center has a Gaussian shape and side rings of high-order diffraction is very small, suggesting that the EDM acts properly as a lens within a diameter of 5 mm.
Fig. 7 Focusing properties of the beam reflected from the EDM: focal length dependent beam spot sizes on focal planes (a) and spatial intensity distribution of the focusing beam at the focal length of 102 cm (b).
We measured Strehl ratios to evaluate an optical performance of the EDM in an imaging system. The Strehl ratio is defined as a ratio of the peak image intensity from a point source using a lens with some aberrations to the maximum intensity using an ideal lens. Table 1 shows the Strehl ratios of the EDM at different focal lengths. The Strehl ratio decreases as focal length increases. It is assumed that more aberrations generate due to deformation of the active-mirror in the EDM when higher voltage is applied. However, the average Strehl ratio is 0.84 which is up to Marechal criterion (0.8). It means that the EDM has a qualified optical performance enough to be used for an optical imaging system.
Table 1. Strehl ratios of the EDM with different focal lengths.
In the case of high driving voltage condition, undesired deformation can be occurred due to inhomogeneous stress distribution as well as too large geometrical change to maintain parabolic curve. It causes some aberrations with a wavefront error and degradation of the optical performance of the EDM. In order to estimate the deformation, we measured a 3-dimensional morphology of the EDM with a concave basement. The EDM with a 2 cm-diameter was tested under applying an input voltage of 3 kV. As shown in Fig. 8(a), the surface of the EDM maintains almost uniform like lens in all area without any deformation such as shrinkage and wrinkle. Figure 8(b) shows images obtained by using the EDM with input voltages of 0, 1.3, and 1.6 kV. Dot pattern with a period of 0.8 mm was used for observation of aberrations intuitively. The image is vivid without an input voltage (0 kV), however the image of dot pattern is blurred at the edge of the EDM under voltages and its area becomes larger as the voltage increases. In spite of degradation of the image, the clear image was obtained within range of the circle area of about 6 mm-diameter in a case of 1.6 kV (a focal length is about −50 cm). We found that the EDM has aberrations even though deformation of the surface do not occur irregularly under high voltages. However, clear images were obtained within a well-defined area and the area could be expanded by optimizing basement structures and analyzing aberration of the EDM.
Fig. 8 A 3-dimensional morphology of the EDM under an input voltage of 3 kV (a) and images of periodic dot pattern acquired by using the EDM with different input voltages of 0, 1.3, and 1.6 kV (b).
7. Conclusion
In this work, we report a new approach to electrostatically control the curvature of an electrostatic deformable mirror (EDM) by changing the geometry of a basement electrode. The change of basement induces geometrical variation of electric field between an active mirror membrane and a basement. The proposed EDM has a fast response time up to 175 Hz and shortening focal length to −16.6 cm in the case of convex basement, and it shows perfect parabolic deformation within the area with a diameter of 12 mm without respect to basement shape. The convex basement has a good advantage in shortening focal length and reducing driving voltage, the flat basement is recommended to induce parabolic deformation with low aberration problem and the concave basement can show better focal variation range in a specific input range.
This work includes an initial progress to a structural approach for geometrical control of EDM without use of discrete electrode patterns. Since it seems there are trade-off conditions in the selection of basement geometry, users can easily replace basement electrode for their purpose of optical control. For more advanced work, we can think about an active morphable basement which is composed of one or multiple sets of shape memory materials, micro-pneumatic chamber, electro-active polymer and etc. For example, self-deformable structure like pressure based tunale fuid lens can be used as transformable basement coated with flexible electrode. This design may realize a more practical and versatile active mirror in the future.
In aspect of application of the proposed active mirror, dynamic focal length control function of the proposed active mirror can be applied to general optical devices including mirrors requires fast focal length control allowing spatial restriction. For example, we can consider an active mirror installed in a periscope, a binocular telescope, a confocal microscope and optical sensors for dynamic and automatic focusing.
Acknowledgments
The work reported here was supported by the Pioneer Program of Korea National Research Foundation (2013M3C1A3059557), the Creative Research Program of ETRI.
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