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Abstract
This paper presents an electrowetting-actuated multifunctional optofluidic (EAMO) lens to improve the quality of computer-generated holography (CGH). A unique structure of the EAMO lens based on electrowetting effect is designed. When the electrodes of the EAMO lens are applied on different voltages, the functions of focal length change and aperture change can be achieved. Then the proposed lens is used in the reproduction system of the CGH due to the multiple functions. The experimental results show that the CGH with zoom function can be realized and undesirable light can be eliminated due to the unique structure of the EAMO lens. The focal length changes can be varied from 11.6 cm to + ∞ and -∞ to −150.6 cm. The aperture size changes can be varied from 10.1 cm to 6.7 cm. By using the proposed EAMO lens, high-quality CGH can be realized without moving the position of any components mechanically, while the setup of the CGH is greatly simplified.
© 2019 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
The computer-generated holography (CGH) based on the liquid crystal on silicon (LCoS) has already become a hot research field in the information display mainly due to the remarkable advantages of high resolution, large opening ratio and fast refresh rate [1,2]. Nowadays, with the developments of virtual reality (AR) and augmented reality (VR) technologies, zoomable and high-quality holographic display technology has become even more important. However, due to the pixelated structure of the LCoS and optical diffraction, the quality of the holographic reconstruction is disturbed by undesirable light [3,4]. The conventional method to eliminate the undesirable light is to use a solid filter and several solid lenses. And the system will be more complicated if the zoom function is to be realized [5,6].
In recent years, the optofluidic lenses with tunable focal length have found widespread applications in imaging, lighting, and optical communication. Several kinds of optofluidic lenses to replace the traditional solid ones in order to improve the quality of the holographic image in an adaptive integration system have been developed. Among the optofluidic lenses, liquid crystal (LC) lens and liquid lens are the most common design. As for the LC lens and LC-based devices, they have already been applied in the fields of optics and photonics due to the advantages of fast-response and optically switchable control [7–11]. Researchers have presented holographic projection systems with the LC lens to realize the function of continuously adjustable optical zoom [12]. However, the nematic LC lens is polarization-dependent, which would reduce light efficiency. Although the blue phase LC lens is polarization-independent, the focal length range is limited. As for the liquid lens, it usually has a tunable liquid-liquid interface which can be actuated by the methods of electrowetting, dielectrophoresis, elastic membrane, stimuli-responsive hydrogel and other methods [13–19]. In 2014, a holographic zoom system without high order diffraction images was proposed by using two liquid lenses and an extra fixed optical high pass filter [20]. Researchers hope that the holographic system cannot only automatically adjust the size of the reconstructed image, but also eliminate the undesirable light based on a simple structure. Unfortunately, such systems have not been implemented yet.
In this paper, we present an electrowetting-actuated multifunctional optofluidic (EAMO) lens which can be applied subtly in the holographic system. In contrast to the traditional liquid lens, the proposed EAMO lens can simultaneously realize the functions of a variable focus and a variable aperture. Compared with the electric controlled liquid lens and liquid iris [21–23], the work has the advantages as follows: (i) It has a large aperture size (~10.1mm). Nevertheless, the aperture sizes of the common designs are within 6 mm which will limit the real applications in imaging, lighting and display. Moreover, the proposed liquid iris can be precisely controlled during all the actuating and relaxing state. (ii) Compared with the previous works [24,25], the EAMO lens is used for the first time in holographic system. Not only the reconstructed image can be scaled, but also the undesirable light in the holographic system can be eliminated. (iii) By using the proposed EAMO lens in the holographic system innovatively, holographic zoom display can be realized without moving the positions of the components. Besides, the structure of the system is greatly simplified. As far as we know, such systems have not been implemented yet until now. In the future, the proposed EAMO lens can bring new breakthrough to head-mounted technologies based on holographic AR display.
2. Mechanism and operating principle
2.1. Structure and mechanism of the EAMO lens
Figure 1(a) shows the structure of the EAMO lens and Fig. 1(b) shows the explosive view of the EAMO lens. The liquid iris part mainly consists of the iris substrate and the middle ITO substrate, as shown in Fig. 1(c). The liquid lens part mainly consists of the lens substrate, as shown in Fig. 1(d). For detail, an iris substrate, two cylindrical chambers and a middle indium tin oxides (ITO) substrate are stuck together as the liquid iris which is filled with a black conductive liquid (Liquid-1) and an immiscible liquid (Liquid-2). The iris substrate is designed with four microchannels for changing the aperture size. The lens substrate which is filled with a transparent conductive liquid (Liquid-3) and an immiscible liquid (Liquid-2) is stuck on the bottom substrate to realize the variable focus function. The iris substrate and the lens substrate are coated with an ITO electrode and a dielectric layer. When voltage is applied on the iris substrate, Liquid-1 rushes upward through the microchannels and the aperture size can be enlarged due to electrowetting effect, as shown in Fig. 1(c). When voltage is applied on the middle ITO substrate, Liquid-1 rushes towards to the center of the substrate and the aperture size is shrunk, as shown in Fig. 1(d). When voltage is applied on the lens substrate, the curvature of Liquid-2/Liquid-3 interface is changed and the focal length can be varied due to electrowetting, as shown in Fig. 1(e). So, the EAMO lens can achieve the functions of variable-aperture and variable-focus.
Fig. 1 Mechanism of the proposed EAMO lens. (a) Structure of the EAMO lens. (b) Explosive view of the EAMO lens. (c) State when the liquid iris is applied voltage on the sidewall electrode and the liquid lens is without voltage. (d) State when the liquid iris is applied voltage on the center electrode and the liquid lens is without voltage. (e) State when the liquid iris is applied voltage on the sidewall electrode and the liquid lens is applied voltage.
The actuation mechanism of the EAMO lens is shown in Fig. 2. Figure 2(a) shows the contact angle changes of the liquid lens during two states: with applied voltage and without applied voltage and Fig. 2(b) shows the contact angle changes of the liquid iris during two states: with applied voltage and without applied voltage. The liquid lens and liquid iris are both actuated by electrowetting effect, and thus they all meet the Young-Lippmann equation. The balance of the interfaces between Liquid-1, Liquid-2 and the dielectric layer tri-junction line is governed by the following equations [26,27]:
where γ12 is the surface tension between Liquid-1 and Liquid-2, θ0 is the initial contact angle without applied voltage, θ1 is the contact angle when voltage is applied, D is the thickness of the dielectric insulator, ε = ε0εr is the dielectric constant of the dielectric insulator and U is the external voltage applied on the ITO electrode. When the external force is applied on the liquid reaches to balance, as shown in Fig. 2, the liquid satisfies the following equation:where F represents the electric force of per meter. The mechanisms of the electrowetting in liquid lens is the same as liquid iris.Fig. 2 Actuation mechanism of the EAMO lens. (a) Contact angle changes of the liquid lens during two states: with applied voltage and without applied voltage. (b) Contact angle changes of the liquid iris during two states: with applied voltage and without applied voltage.
2.2. Fabrication of the EAMO lens
The fabrication procedure of the EAMO lens is described as follows. A polymethylmethacrylate (PMMA) substrate fabricated with four microchannels and an iris hole is designed as the iris substrate. The height and diameter of the iris substrate are 3 mm and 25 mm, respectively. The diameter of the microchannel and iris hole are 3 mm and 15 mm, respectively. The iris substrate, two cylindrical chambers, and an ITO sheet are stack together by using UV-331 glue to form the liquid iris. The lens substrate is hollowed out a cone whose top radius and bottom radius are 14 mm and 11 mm, respectively. The lens substrate and a PMMA substrate form the liquid lens with the height of 5 mm. The total height of EAMO lens is 15 mm. The sidewalls of the microchannels, lens substrate and middle ITO substrate are coated with a Parylene-C layer (~1 µm) as an insulator, followed by a thin Teflon layer (~5 µm, AF-1600, from DuPont). The surface tension of the Teflon layer is ~18 mN/m at 20°C. Deionized water dyed with ink is used as Liquid-1 (the density of the solution is 1.08 g/cm3) and phenylmethyl silicone oil (a density of 1.08 g/cm3, the viscosity is 300 mpa∙s) is used as Liquid-2. NaCl solution is used as Liquid-3 (the density of the solution is 1.08 g/cm3). The densities of filled liquids in the chambers are matched. Hence the EAMO lens can have a reasonable mechanical stability. We also list the characteristics of the liquids filled in the EAMO, as shown in Table 1 [27,28].
Table 1. Characteristics of the liquids filled in the EAMO
2.3. Structure and principle of the holographic system
The structure of the holographic system is shown in Fig. 3. A laser, a filter and a solid lens are used to generate a collimated light. As shown in Fig. 3, the laser is produced by Changchun New Industries Optoelectronics Technology Co. and the model of the laser is MGL-III-532. The wavelength is λ = 526.5 nm and the power is 20mw. The solid lens is produced by Daheng New Epoch Technology Inc and the model is GCO-0202M. The distance between the solid lens and the LCoS is 25 cm, and the distance between the laser and the solid lens is 30 cm. The distance between filter and the laser is 5cm, and the focal length of the solid lens 30 cm. The type of LCoS is reflective, and its pixel number and pixel pitch are 1920 × 1080 and 6.4 μm, respectively. The distance between the LCoS and the EAMO lens is 15 cm, and the receiving screen locates behind the EAMO lens at 20 cm. When the collimated light irradiates the LCoS, diffraction image is composed into two parts, one is the multi-order diffraction beams caused by pixelated structure of the LCoS and the other is the multi-order reconstructed images of the hologram. The common method is to eliminate the undesirable light by using several solid lenses and mechanical irises, which makes the system complicated and bulk. As shown in Fig. 3, the replaced part is often used in the traditional holographic system and it consists of two solid lens and an iris [5,6]. The focal lengths of the solid lenses are the same and the iris is placed at the focal plane of the solid lens in order to eliminate the undesirable light. In this paper, the EAMO lens is used to replace the solid lenses and mechanical irises, which can simplify the system and display a desirable reconstructed image.
In order to realize the zoom function, a digital lens is loaded on the LCoS. Then the digital lens and EAMO lens form the zoom modules of the system, as shown in Fig. 4(a), where l is the distance between the light source and the LCoS, d1 is the distance between the LCoS and the EAMO lens, and d2 is the distance between the EAMO lens and the receiving screen. In the proposed system, the light source is collimated, so l equals infinity. In the holographic reconstruction, the LCoS is loaded with the CGHs of an object and a digital lens. According to the holographic diffraction theory, the size of the reconstructed image can be calculated as follows [25]:
where S is the size of the reconstructed image, p is the pixel size of the LCoS, λ is the wavelength, f1 is the focal length of the digital lens which is loaded on the LCoS, and f2 is the focal length of the EAMO lens. By changing the focal lengths of the digital lens and the EAMO lens, the magnification of the reconstructed image can be zoomed without moving any optical components of the system. At the same time, when the size of the reconstructed image changes, undesirable light can be eliminated by adjusting the aperture size of the EAMO lens. In this way, a holographic zoom system without undesirable light can be achieved. Figures 4(b) and 4(c) are two different states when different voltages are applied on the liquid lens and liquid iris. When d1 and d2 keep unchanged, the relationship between the focal lengths of the digital lens and the EAMO lens can be calculated according to Eq. (4). According to Eq. (5) we know that the size of the reconstructed image changes with the focal length of the digital lens and the EAMO lens. For different size of the reconstructed image, the size of the EAMO lens needs to be adjusted in order to eliminate the undesirable light. When the size of the reconstructed image is S = D1, the aperture size of the EAMO lens needs to be adjusted to D1, so the undesirable light cannot pass through the EAMO lens, as shown in Fig. 4(b). When the size of the reconstructed image is S = D2, the aperture size of the EAMO lens needs to be adjusted to D2, as shown in Fig. 4(c). In this way, the reconstructed image can be displayed on the receiving screen without undesirable light.Fig. 4 Principle of the holographic system. (a) Zoom modulates of the holographic system. (b) State when the size of the reconstructed image is D1. (c) State when the size of the reconstructed image is D2.
The principle of the LCoS is shown in Fig. 5. It consists of a glass substrate, a liquid crystal layer, a polarizing plate, a reflecting mirror and a silicon substrate. Through the interaction of the incident light and the liquid crystal molecules in the pixel structure, the LCoS can function as a diffractive optical element. When light is irradiated on the LCoS, the distribution of liquid crystal molecules is changed by the driving voltage, and the optical path difference is [29,30]:
where ne is the refractive index of the extraordinary light, no is the refractive index of the ordinary light, d is the thickness of the cell and λ is the wavelength of the light.3. Experiments, results and discussion
3.1. Experiments and optical properties of the EAMO lens
The proposed EAMO lens is fabricated as described in Section 2.2. In the first experiment, when the voltage is applied on the middle ITO substrate with U<37V, the dyed liquid cannot move as the threshold voltage is 37V. When the voltage (37V<U<75V) increases, the dyed liquid stretches to the middle of the substrate due to electrowetting effect. When the voltage exceeds U>75V, the dyed liquid cannot stretch further because of the contact angle saturation. The aperture changes of the liquid iris when voltages are applied, as shown in Fig. 6. The measured maximum and minimum aperture sizes are 10.1 mm and 6.7 mm, respectively.
Fig. 6 Aperture changes of the liquid iris when voltages are applied. (a) U = 0V. (b) U = 45V. (c) U = 50V. (d) U = 55V. (e) U = 60V. (f) U = 65V. (g) U = 70V. (h) U = 75V.
To measure the power consumption, a resistor of 100 kΩ is connected in series to the liquid iris, and the maximum current is measured to be ~51 μA at 75 V. The maximum power consumption is ~3.8 mw. The measured aperture sizes and current of the liquid iris driven by variable voltages are listed in Table 2. As we can see from Table 2, the rate of the aperture size change is the same as the applied voltage changing from 45 V< U < 75 V. That is to say that when ΔV = 15V, the aperture size can be tuned 1.5 mm. While, when the applied voltage is changed from 60 V< U < 75 V, the aperture size can be also tuned 1.5 mm. It can be also proved that the liquid iris has a reasonable stability.
Table 2. Measured aperture sizes and current of the liquid iris
To evaluate the performance of the liquid lens during actuation process, a CCD camera (From YVSion, type of YS-HU800C, China; 2/3” COMS) is used to record the image changes. A printed letter ‘a’ is placed 5 mm away below the liquid lens. An upright virtual image can be observed as the object is always within the focal length of the liquid lens. In this principle experiment, liquid-2 is not filled in the lens chamber. When the voltage U (<40 V) is applied on the sidewall of the lens substrate, the liquid/liquid interface cannot change. The threshold voltage of the liquid lens is 35 V. In this state, the liquid lens has the shortest focal length, as shown in Fig. 7(a). When the voltage varies from 35 V-80 V, the focal length changed accordingly, as shown in Figs. 7(b)–7(f). When the voltage U >80 V, the focal length is changed a little due to the contact angle saturation.
Fig. 7 Focal length changes of the liquid lens when voltages are applied. (a) U = 0V. (b) U = 40V. (c) U = 50V. (d) U = 60V. (e) U = 70V. (f) U = 80V.
The focal length is changed when different voltages are applied, as depicted in Fig. 8. We have measured the focal length changes five times and collated the data into error bars graph, as shown in Fig. 8. The experiment demonstrates that the focal length can be varied from 11.6 cm to + ∞ and -∞ to −150.6 cm when the voltage is changed from 0 to 80 V. As we can see from Fig. 8, when the liquid lens works as a positive lens, the shortest focal length can reach ~11.6 cm, while when the liquid lens works a negative lens, the shortest focal length can only reach −92.6 cm. The mainly reason may be that the driving voltage exceeds to 80 V, the conducted liquid has already reach to contact angle saturation. Thus, the curvature of the liquid-liquid cannot be changed further. The focal length cannot be shortened, either.
Switch time is the key parameter to measure the performance of the EAMO lens. In our experiments, we use a synchronous controller to link the power supply to the digital timer (@Shanghai instruments co. LTD, Type of 411B). When the voltage is applied to the EAMO lens, the digital timer can be started at the same time. When the voltage is removed, the digital timer will stop immediately. When the liquid iris is applied to voltage, the aperture size of the liquid iris will be shrunk due to the electrowetting effect. The aperture size can be changed from maximum to minimum; If we remove the driving voltage, the dyed liquid filled in the chamber will rush to the sidewall of the chamber freely due to the high surface tension. The aperture size can be changed from minimum to maximum. To measure the switch time of the liquid iris, we first define the actuating (relaxing) time which is the time when the aperture size is changed from 10.1 mm (6.7 mm) to 6.7 mm (10.1 mm). The results are shown in Fig. 9. The measured actuating time and relaxing time are ~330 ms and ~186 ms, respectively. As we can see from Fig. 9, the actuating time is longer than the relaxing time, the main reason is that the dyed liquid reaches to its original state not only by the driving voltage, but also by the high liquid-solid surface tension.
Fig. 9 Switch time of the liquid iris. (a) Times when the aperture size changes from 10.1 mm to 6.7 mm when the liquid iris is applied voltage. (a) Times when the aperture size changes from 6.7 mm to 10.1 mm when the liquid iris is without voltage.
Figure 10 shows the response time of the liquid lens. We define the actuating (relaxing) time which is the time that the focal length changes from 11.6 mm (−150.9 mm) to −150.9 mm (11.6 mm). The measured actuating time and relaxing time are 110 ms and 290 ms, respectively. As we can see from Fig. 10, the relaxing time is longer than the actuating time, which is just opposite compared with Fig. 9 drawn above. The main reason is that the liquid lens is actuated by the driving voltage. While during the relaxing time, there is no voltage applied on the liquid lens. Thus, the relaxing time is longer than the actuating time.
3.2. Experiments of the holographic system
In the holographic system, a laser (λ = 526.5nm) is used as the light source to irradiate the LCoS. The type of LCoS is reflective, and its pixel number and pixel pitch are 1920 × 1080 and 6.4 μm, respectively. The distance between the LCoS and the EAMO lens is 15 cm, and the receiving screen locates behind the EAMO lens at 20 cm. Then a magic cube is used as the object, as shown in Fig. 10(a). Then green scene is calculated according to image processing and green hologram is generated by using iterative algorithm, as shown in Figs. 10(b) and 10(c).
In the holographic reconstruction, green CGH is loaded on the LCoS. When the voltage is applied on the EAMO lens, the focal length of the digital lens can be adjusted by loading the corresponding CGHs on the LCoS. Then the reconstructed image can be seen on the receiving screen, as shown in Fig. 11, where Fig. 12(a) is the result when traditional solid lens is used in the holographic system and Fig. 12(b) is the result when driving the liquid lens. In order to improve the diffraction efficiency, the blazed grating is loaded on the hologram [31]. By changing the aperture size of the liquid iris, high-order diffraction images and high-order diffraction beams can be eliminated, as shown in Fig. 12(c).
Fig. 11 Process of the holograms. (a) Original object. (b) Green color scene. (c) Hologram of the green color scene.
Fig. 12 Reconstructed results of the monochrome scenes. (a) Traditional reconstructed image. (b) Reconstructed image when only liquid lens is actuated. (c) Reconstructed image when the EAMO lens is actuated.
In order to verify the zoom characteristics of the system, EAMO lens and digital lens change the focal lengths according to Eqs. (4) and (5). By controlling the voltages applied on the EAMO lens, undesirable light can be eliminated completely, as shown in Fig. 13. Moreover, from the results we can see that the size of the reconstructed images can be adjusted. Compared with the results of Fig. 12(a), the image quality has been greatly improved.
Fig. 13 Results of the holographic zoom system. (a) Zoom state-1. (b) Zoom state-2. (c) Zoom state-3. (d) Zoom state-4.
3.3. Discussion
At present, the three-dimensional display has encountered some bottlenecks. Due to the pixel size limitation of the LCoS, the size of the reconstructed image is very small. Currently, the minimum pixel size of the commercial LCoS is ~3.74µm. In this paper, the EAMO lens is used to realize the zoom function of the holographic display. For liquid crystal lenses and liquid lenses, they both have their own advantages. The liquid crystal lens has the advantages such as fast response and low voltage, while the liquid lens has the advantages such as polarization independence and low cost. We hope that liquid crystal devices can be more widely used in holography in the future. This work also hopes that the liquid devices and liquid crystal devices can be combined with each other in the future and promote the development of display together.
The advantage of the proposed EAMO lens is its high integration with an easy fabrication process and it can be applied on CGH to eliminate the undesirable light. As we can see from Fig. 3, most of the holographic systems contains several parts of solid lenses and mechanical iris, which would lead a bulk optical system. While, when the EAMO lens is applied in the system, at least two solid lenses and one mechanical iris can be replaced. Thus, the proposed EAMO has the advantage of high integration. As for easy fabrication, most of electrowetting-actuated liquid irises have to be designed with several typed of annular electrodes based on photolithography. However, the propose electrode of the liquid iris is a whole sheet of an ITO glass. Besides, the liquid lens part and liquid iris part are stack by UV-331 glue easily. Thus, we comment that the EAMO lens has the advantages of high integration and easy fabrication.
While some optical properties can also be improved. As we can see from Fig. 6(h), the aperture shape is irregular when the driving voltage is raised up to 75V. That may result from the simple structure of the ITO substrate which has no limitation to the liquid when the liquid stretches into the center. We can design an annular ITO electrode to make the liquid flow into the center regularly. Besides, the response time of the EAMO lens is not fast enough, which may be due to the high viscosity (300 mpa∙s) of the phenylmethyl silicone oil. We can choose one kind of density-matched silicon oil with a low viscosity to enhance the response time. However, it will lead to liquid vibration when the voltage is actuated. For this we should make a tradeoff between the mechanical stability and fast response. The repeatability of liquid device is limited during use. Due to the volatilization of the liquid, the EAMO lens cannot be used indefinitely. In addition, the voltage has influence on the EAMO lens. The EAMO lens itself will absorb light, so the transmission of the system will be reduced. The repeatability of liquid device is limited during use. Due to the volatilization of the liquid, the EAMO lens cannot be used indefinitely. When light passes through the EAMO lens, undesirable light is eliminated by adjusting the size of the iris, so the light intensity of the reconstructed image will be reduced accordingly. Besides, the EAMO lens itself will absorb light, so the transmission of the system will be reduced. Therefore, compared with the traditional reconstructed, the intensity of the reconstructed image by using the proposed liquid lens is weaker, as shown in Fig. 12. In the experiment, high-quality holography zoom system with green component is realized. For color holographic reproduction, chromatic aberration may appear due to the different wavelength of the lasers, which is another important issue in holographic display. In the next work, we will study the color holographic display based on the EAMO lens and hope to make some contributions to the development of holographic display technology.
4. Conclusion
In this paper, we present an EAMO lens to improve the quality of CGH. Compared with the traditional optofluidic lens, it has the advantages of high integration and easy fabrication. Besides, it can be applied on the holographic system with a function of eliminating the undesirable light. The experiments show that the focal length changes can be varied from 11.6 cm to + ∞ and -∞ to −150.6 cm with the response time of 110 ms and 290 ms, respectively. The aperture size changes can be varied from 10.1 cm to 6.7 cm, with the response time of 330 ms and 186 ms, respectively. The EAMO lens can improve the quality of CGH, especially in holographic zoom system.
Funding
National Natural Science Foundation of China (NSFC) (61805169, 61805130).
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