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Abstract
Conventional optofluidic lens usually has only one interface, which means that the zoom range is small, and the ability to correct aberrations is poor. In this paper, we propose a hybrid driving variable-focus optofluidic lens. It has one water-oil interface shifted by an applied voltage and one tunable Polydimethylsiloxane (PDMS) lens deformed by pumping liquid in or out of the cavity. The proposed lens combines the advantages of electrowetting lens and mechanical lens. Therefore, it can provide a large focal length tuning range with good image quality. The shortest positive and negative focal length are ∼6.02 mm and ∼−11.15 mm, respectively. The maximum resolution of our liquid lens can be reached 18 lp/mm. We also designed and fabricated a zoom system using the hybrid driving variable-focus optofluidic lens. In the experiment, the zoom range of the system is 14 mm∼30 mm and the zoom ratio is ∼2.14× without any mechanical moving parts. Its applications for zoom telescope system and zoom microscope and so on are foreseeable.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
In a short span of time, optofluidics has been a key technology for stimulating advances in highly miniaturized and functional optics, since liquid-based devices are not only compact, but may also focus dynamically the light to a desired location in a controllable manner for convergence [1], switching [2], and trapping [3]. To realize optofluidic devices, many research efforts have been made to design and innovate integrated optofluidic components, including optofluidic waveguides [4], optical switch [2], optofluidic lenses [5–22] and many others [23–28].
The optofluidic lens is an important component of optical systems with apparent advantages over solid lens, such as reconfigurable geometry and tunable refractive index. Various techniques and tuning mechanisms have been explored to create optofluidic lenses, including stimuli-responsive [5][6], dielectric force [7–10], electrowetting [11–15], and fluidic pressure variation [16–22], liquid crystal [29–34]. Each approach has its own pros and cons. For example, a tunable optofluidic lens with stimuli responsive hydrogel has been proposed [5]. The shape of the water can be redistributed in the hydrogel ring, thus the shape of the water–oil interface can be controlled by temperature and PH. However, this approach of stimuli-responsive greatly sacrifices temporal resolution. Considering the response speed and power consumption, optofluidic lenses based on dielectric force and electrowetting are suitable to be integrated because of the direct voltage actuation. An adaptive dielectric lens using chevron-patterned electrodes has been demonstrated [7]. Similarly, a droplet of isotropic liquid crystal has been performed focal length tuning using the dielectric force [8]. Dielectrophoretic optofluidic lenses are attractive for practical applications due to low power consumption and fast response time. However, patterning electrode definitely restricts the aperture of dielectric lenses. Fortunately, Berge et al. has employed electrowetting to produce spherical lenses [11]. An external voltage is applied to modify the contact angle between the liquid and the lateral sidewall of the liquid container, thereby changing the droplet curvature as well as the focal length. Besides, an all-liquid dual-lens optofluidic zoom system has been proposed [12]. Since it is very difficult to find two liquids with large difference in refractive indices. Therefore, it suffers from a serious problem of low optical power. To increase optical power, optofluidic lens of floating water has been reported [13]. The double-faced optofluidic lens with a 2 mm aperture diameter achieves greater dioptric power than the optical properties of a conventional electrowetting-based liquid lens. However, the aperture is still small, and the lens chamber has a more complex pattern than the conventional type, as four different electrodes with different potentials are used. In comparison to other optofluidic lenses, an optofluidic lens based on fluidic pressure belongs to a mechanical lens. This kind of lens has the advantages, such as scalable lens aperture and large focus power change. Recently, researchers have demonstrated an elastomeric lenses, which can achieve biconvex or biconcave shape [16]. However, individual lens surface cannot be independently tuned. An electromagnetically driven variable-focus liquid lens using an elastic PDMS membrane has also been reported [17]. The optical performances such as the tunable range and the response time are demonstrated. However, elastic membrane based optofluidic lens usually encounters a disadvantage due to the effect of gravity effects. Therefore, it is still urgent to study innovative lens with good imaging quality and large focal length tuning range.
A conventional optofluidic lens usually has one liquid-liquid interface, which can be deformed to achieve variable focal length. However, A liquid-liquid interface means that the zoom range is small, and the ability to correct aberrations is poor. In this paper, we propose a hybrid driving variable-focus optofluidic lens. It has one water-oil interface shifted by an applied voltage and one tunable Polydimethylsiloxane (PDMS) lens deformed by pumping liquid in or out of the cavity. The PDMS lens has a proper thickness (1.15 mm) to minimize the gravity effect of liquid. The proposed lens combines the advantages of electrowetting lens and mechanical lens. Therefore, it can provide a large focal length tuning range with good image quality. The shortest positive and negative focal lengths are ∼6.02 mm and ∼−11.15 mm, respectively. What’s more, the maximum angular resolution of our liquid lens can be reached 23′′. We also design and fabricate a zoom system using such a hybrid driving variable-focus optofluidic lens. In the experiment, the zoom range of the system is 14 mm∼30 mm and the zoom ratio is ∼2.14 × without any mechanical moving parts.
2. Structure and principle
Figure 1 shows the schematic cross section and the operating mechanism of our proposed optofluidic lens. Figure 1(a) describes a schematic cross section of our proposed lens and its components. It consists of a PDMS lens, an electrowetting (EW) lens, a thread sleeve, an upper tube, a bottom tube, a water channel, an actuator and a window glass. The EW lens is comprised of a circular truncated cone chamber hosting liquid 1 and liquid 2. The meniscus between the two liquids defines different refractive index boundary and surface tension, therefore behaves as a lens. The tunable PDMS lens deforms by pumping liquid 2 in or out of the cavity operated by electromagnetic actuator. The actuator is connected with the cavity through the channel. We optimized the thickness of the PDMS in order to make the elasticity far greater than gravity. For a uniform-thickness membrane under applied pressure, the shape deviation of a membrane due to gravity is given as Eq. (1) [35]. We see that the deviation from the ideal lens is inversely proportional to the third power of membrane thickness t. Increasing properly the membrane thickness is very effective in reducing gravity effects. Therefore, the vertical deformation of the PDMS lens caused by gravity effect can be neglected.
where E and v are Young’s modulus and Poisson’s ratio, respectively. Ap is a coefficient depending on the distribution of hydrostatic pressure. t represents the thickness of PDMS lens, and d represents the diameter of lens.
Fig. 1. Schematic cross-section and optical operating mechanism of our optofluidic lens. (a) Lens structure and its components. (b) Initial state. (c) Only PDMS lens is driven by current. (d) Only EW lens is driven by voltage. (e) Hybrid driving.
As shown in Figs. 1(b)-(e), we simplify the schematic of optofluidic lens without actuator. In initial state, the PDMS lens is flat acted as a parallel plate, while the EW lens forms a convex spherical surface due to the surface free energies. At present, our optofluidic lens acts as a negative lens, as shown in Fig. 1(b). According to Faraday’s law of electromagnetic induction, the generated lorenz force F depends not only on the current intensity but also on the current direction. Changing the amplitude of the current can vary the amplitude of the force, while changing the flowing direction of the current will change the force direction as well. Therefore, the hydrostatic pressure inside the chamber can be controlled by current, thereby changing the shape and focal length of the PDMS lens. When an appropriate current is applied to electromagnet, the magnet is excluded and pushed up. Liquid 2 in the lens cavity is squeezed into the actuator through channel. In this state, the PDMS lens presents concave. Our optofluidic lens has a stronger ability to diverge light than initial state, as shown in Fig. 1(c). The force F acting on the magnet as a result of the magnetic field can be described by Eq. (2):
where M is the magnetization of the magnet, B is the flux density of the applied magnetic field, and V is the volume of the magnet.Removing the magnetic field, a voltage is applied to the upper tube and bottom tube. The contact angle θ between liquid 2 and the wall is changed due to electrowetting effect, thereby changing the focal length of the EW lens. In this state, the PDMS lens is flat acted as a parallel plate, while the EW lens forms a concave spherical surface. Due to the refractive index of liquid 1 is larger than that of liquid 2, therefore, our optofluidic lens converges light, as shown in Fig. 1(d). The change of contact angle θ can be described by the following Young-Lippmann Eq. (3):
where θ0 is the initial contact angle between the conductive liquid and inner wall, and ɛ0, ɛ are dielectric constant in vacuum and the dielectric constant of the dielectric film, respectively, d represents the thickness of the insulting layer, U is the applied voltage, and γ12 represents two liquids’ interfacial tension.When applying voltage and proper current to the electrowetting lens and PDMS lens respectively, both lenses converge light. Hence our whole optofluidic lens has a stronger ability to converge light, as shown in Fig. 1(e).
According to the thin lens theory, the focal length of the hybrid driving variable-focus optofluidic lens can be expressed as:
3. Device fabrication
To prove the concept mentioned above, we first fabricated a prototype of the optofluidic lens. The prototype consists of 6 elements, as shown in Fig. 2(a). The upper and bottom tubes are made of aluminum which serves as the grounding and bias electrode of the EW lens. The inwall of the upper and bottom tubes are coated with a Parylene-N layer (∼2.5µm) as insulator and then coated by a 0.2µm Teflon layer (AF-2400, from DuPont, Wilmington, Delaware) as hydrophobic layer. The bottom tube is drilled with a channel to keep the lens chamber and the actuator chamber connected. The height and inner diameter of the upper and bottom tubes are ∼9 mm and ∼6.5 mm, respectively. The material of the window glass is BK7 in glass data of SHOTT. The diameters and height of the window glass are ∼8 mm and ∼0.5 mm, respectively. Next, liquid 1 is silicone oil as insulating liquid. And liquid 2 is NaCl solution, which acts as a conductive liquid. Two liquids are injected into the lens cavity. Table 1 shows the physical properties of the NaCl solution and silicon oil. And the PDMS lens is made of polymer (Sylgard 184, DowCorning) mixed by a weight ratio of 10:1. The thread sleeve is made of stainless steel. All the elements except thread sleeve are stuck together to form the prototype using glue. To guarantee perfect pinning between the PDMS and upper tube, the thread sleeve is screwed on the lens chamber based on screw thread, as shown in Fig. 2(b). The size of the whole lens is designed to be 10.5 mm (height) ×12 mm (diameter).
Fig. 2. Fabricated prototype of the hybrid driving variable-focus optofluidic lens. (a) All the elements of the device. The Bottom tube has a channel which connects the actuator of PDMS lens. (b) Assembled prototype.
Table 1. Properties of the materials we used
4. Operating process
To evaluate the imaging quality and assess focal length tuning range of our lens, we first simulated the proposed optofluidic lens in Zemax. The simulation results of the proposed optofluidic lens are shown in Fig. 3 and Fig. 4. Figure 3 reveals 2D layout of the proposed lens. Table 2 shows the profile of the refractive surface. Figure 4 shows the blur spot diagram of the proposed lens at typical focal length. From the spot diagram, we see that the diameter of the ray traced spot is relatively small. This means that the proposed lens has good imaging quality.
Fig. 4. Blur spots of the proposed lens. (a) f=7.5mm. (b) f=10mm. (c) f=12.5mm. (d) f=15mm. (e) f=20mm. (f) f=30mm.
Table 2. The profile of the refractive surface
To evaluate the performance of the proposed lens during focusing, we performed experiment based on the simulation results. We placed the target which is composed of letters “CD” in front of the lens. A high-speed camera was placed behind the proposed lens to record the image. The object distance is ∼20 mm. The distance from the test lens to camera lens is 50 mm. The distance from the camera lens (YS5020-10M43, YVSion, China) to camera (FT-U32000C, Fangte Technology Co., Ltd, China) is 17.5 mm. During the recording process, we adjust the camera position, so that the object can be always imaged on the camera. When the voltage applied on the EW lens gradually rises to 40 V, the contact angle of the EW lens gradually decreases, which results in the increase of the optical power. Thus, the image increases gradually. When the voltage reaches to 80 V, the contact angle of the EW lens is saturated. The image does not continue to grow larger. Then we applied suitable current on the actuator of PDMS lens. The sagittal height of PDMS lens changes with the increasing of the current. The focal length of whole lens continues to change as the increasing of the current, so the image increases gradually again. The results are shown in Fig. 5(a). Once removing voltage and current, the image is gradually restored to its initial state. In order to obtain negative focal length of the optofluidic lens, we applied a small and suitable voltage to the EW lens, which is in the negative focal length state. Then we changed the current direction on the actuator, correspondingly. As the current increases, the image becomes smaller and smaller, as shown in Fig. 5(b). The corresponding values of voltage and current are marked in Fig. 5. Ultimately, we removed the voltage and current, the image is gradually restored to its initial state, accordingly. In the process of driving, there is no obvious distortion.
The focal length is also measured with respect to an applied voltage and current by using a custom-built testing system consisting of a collimator (FPG-7, Hua Zhong Precision Instruments Co., Ltd., China), a glass lens, a complementary metal oxide semiconductor (CMOS) camera and the proposed lens, as shown in Fig. 6. Positive optical fluidic lens can collect light directly without glass lens, as shown in Fig. 6(a). When the optical power of the proposed lens is negative, it is necessary to use a glass lens to converge the incident light, as shown in Fig. 6(b). And the negative focal length is calculated according to Eq. (8):
where f is the focal length of our proposed lens, fs’ is the focal length of the solid lens, f0’ represents the focal length of the lens system, and d is the distance between solid lens and the proposed lens.Fig. 6. The experimental setup for measuring the focal length of the varifocal liquid lens. (a)Measuring device for positive focal length. (b)Measuring device for negative focal length.
The resolution and the pixel size of the CMOS are 2592 × 1944 and 2.2 µm × 2.2 µm, respectively. We adjusted the location of COMS. The acquisition plane of CMOS is just the focal plane of the lens, and the spot is the smallest. The distance between the acquisition plane and lens center is the focal length. Figure 7 shows the relationship between the curvature and focal length. And partial corresponding voltage or current are also shown. Figure 7(a) depicts the change of the radii in the positive focal length range. The negative focal length working area of the proposed lens is shown in Fig. 7(b). We see that the shortest positive and negative focal length are 6.02 mm and −11.15 mm, respectively. When the radii tends to be infinite, the focal length of the proposed lens is infinite. Therefore, the whole focal length can be tuned from 6.0 mm to +∞ and from −11.2 mm to -∞.
Fig. 7. The focal length of the proposed lens. (a) Positive focal length region. (b) Negative focal length region.
As an optical imaging device, imaging quality is a very important criterion for evaluating the quality of a device. The setup for testing the imaging ability is shown in Fig. 6. The improvement is to place a resolution target between the filter and the collimation system. In this experiment, the proposed lens is a negative lens at the initial state. In order to measure the image quality, we used a solid lens for converging light. The resolution is ∼15 lp/mm, as shown in Fig. 8(a). When applied voltage and current on the proposed lens, it acts as positive lens. The focal length gradually decreases, as the voltage and current rises. Therefore, the image will become smaller. When the voltage is 60 V and the current is 60 mA, the image is shown in Fig. 8(b). And further increases in the applied voltage and current up to 80 V, 6 mA, respectively, the lens has a stronger ability to collect light, as shown in Figs. 8(c)-(d). The resolution is ∼18 lp/mm. The blue square solid line in the Fig. 8 is parallel to the image contour of the resolution target. Therefore, the proposed lens does not have distortion due to the horizontal placement of the imaging device.
Fig. 8. Image of the resolution target of proposed lens. (a) Negative focal length state. (b) Positive focal length state.
5. Application in zoom system and discussions
We designed and assembled an optofluidic zoom system using the fabricated prototype to test the imaging quality and zooming ability. The optofluidic zoom system consists of a hybrid driving variable-focus optofluidic lens, a glass lens and a CMOS camera, as shown in Fig. 9. The hybrid driving variable-focus optofluidic lens is the crucial part to realize zooming by deforming actuation. The glass lens is used to undertake part of the focal power of the zoom system and correction of partial aberration. The CMOS acts as the image plane. In the conventional zoom system, several optofluidic lenses must be packed together to form a compound lens. Different from the conventional optofluidic zoom system [36][37], the proposed system has only one tunable lens. Thus, the system is compact and easy operation.
We simulated the proposed zoom system using Zemax. In the optimization, the radii (r1, r2, r4, r5) are set as variables which are varied to produce the desired focal lengths. And r3 picks up r2. To get the suitable focal power, we first optimized radii of the optofluidic lens and solid lens to get the solution for each focal length in Zemax. Then we fixed the parameters of solid lens, and retained the change of curvature radii of the optofluidic lens to obtain the desired focal length. The rear working distance is always ∼17 mm. The merit function is constructed based on the default merit function and the two requirements.
where f is the desired focal length, RMS is the root mean square of the blur spots, and the target value is 0. f1 (r1, r2) are calculated based on ray trace method. f2(r1, r2) is included in the Default Merit Function in Zemax.The 2D layout of simulation is shown in Figs. 10(a)-(c). The modulation transfer function (MTF) is shown in Figs. 11. We see that the MTF of the proposed lens approaches that of diffraction limit, which indicates good imaging quality. We implemented experiment based on the simulation results. The object distance is ∼1000 mm. The material of the solid lens is CAF2 in glass data of SHOTT. The verification platform is constructed to verify the zooming function of the system. A toy car acts as the object. And a COMS camera is used to collect images. The zooming results are shown in Fig. 12. We can gradually adjust the applied voltage on the EW lens and current of the PDMS lens. All the images are at a given magnification where best focus is found. On the premise of ensuring good imaging quality, the image is magnified by approximately ∼2.1×. In this state, the applied voltage of the EW lens is ∼56 V and the applied current of the PDMS lens is −0.85 mA. The experimental results agree well with simulation results, which confirms the feasibility of zooming system with single optofluidic lens. In this experiment, we see that the magnification is mainly determined by the optofluidic lens. The glass lens plays a role in correcting aberrations partly. Because the zoom range of the PDMS lens is large enough, the deforming of the PDMS lens plays another role to refocus the image onto the CMOS while zooming.
Fig. 10. Zoom system using the hybrid driving variable-focus optofluidic lens. (a)f=14mm. (b)f=20mm. (c)f=30mm.
Fig. 11. Optical performances of zoom system using the hybrid driving variable-focus optofluidic lens. (a)f=14mm. (b)f=20mm. (c)f=30mm.
Fig. 12. Captured images of different magnification of zoom system. (a) Initial state, U1=0, I1=0. (b)1.3×, U2=60 V, I2=−0.75 mA. (c)2.1×,U3=65 V, I3=−0.85 mA.
6. Conclusion
We proposed a hybrid driving variable-focus optofluidic lens. It has one water-oil interface shifted by an applied voltage and one tunable PDMS lens deformed by pumping liquid in or out of the cavity. The proposed lens combines the advantages of electrowetting lens and mechanical lens. Therefore, it can provide a large focal length tuning range with good image quality. The shortest positive and negative focal length are ∼6.02 mm and ∼−11.15 mm, respectively. The maximum angular resolution of our liquid lens can be reached 23′′. We also designed and fabricated a zoom system using the hybrid driving variable-focus optofluidic lens. In the experiment, the zoom range of the system is 14 mm∼30 mm, and the zoom ratio is ∼2.14× without any mechanical moving parts. Its applications for zoom telescope system and tunable microscope and so on are foreseeable.
Funding
the National Key R&D Program of China (2017YFB1002900); the NSFC (61927809).
Disclosures
The authors declare no conflicts of interest.
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