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Abstract
In this paper, we demonstrate an adaptive liquid lens with a tunable field of view (FOV). The proposed liquid lens consists of an actuator and a lens chamber, the annular sheet is just placed on the liquid-liquid (L-L) interface in order to change the curvature and steer the tilt angle of the interface. Different from the conventional FOV adjustable lens combined with a liquid lens and a liquid prism, the proposed lens requires only one L-L interface to achieve the focal length change and FOV deflection. Moreover, the proposed lens reduces aberrations while maintaining high resolution. The experiments show that the optical power range is −27 m−1 to 30 m−1. It can realize the FOV deflection while tuning the focal length, with an angular resolution of 37"05. The proposed lens can be applied to telescopic system and microscopic system.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Optical imaging systems are now widely used in medical and biological [1,2]. With the expansion of application scope, higher performance indexes of imaging systems are required, such as larger FOV, higher resolution and lower distortion. One way to achieve large FOV is to use a beam steering device, which can achieve FOV deflection by changing the direction of the light passing through the optical system. Optical devices for beam steering traditionally consist of mechanical components, such as microelectromechanical system (MEMS) mirrors [3], rotating Risley prisms [4] and galvanometric mirrors [5]. However, these systems are often prone to failure due to mechanically moving parts and high energy consumption. Optofluidics techniques have been extensively studied in recent decades as an emerging technology used in a wide range of the tunable optical systems [6]. Liquid lens [7–10] overcomes the inherent defect of traditional solid lens, due to its variable focal length, simple structure, low power consumption [11] and fast response times [12]. To overcome the shortcomings of the mechanical beam steering device, an optofluidic component actuated by electrowetting-on-dielectrics (EWOD) is capable of simultaneously deflecting and shaping a beam in two dimensions is presented [13]. A tunable fluidic lens with a dynamic high-order aberration control is presented [14], which controlled by 32 azimuthally placed electrodes. Based on the Alvarez lenses actuated by a dielectric elastomer, an imaging system is built to realize ultra-wide varifocal imaging with a selectable region of interest [15], but the imaging system still have some drawbacks, such as high voltage actuation, large aberration, and a narrow FOV. Electrowetting liquid prism has a relatively mature application research in the fields of optical fiber communication [16], optical switches [17] and solar energy collection [18,19], but applications in the imaging systems are quite difficult. Our group proposed an electrically controlled telescope objective which can obtain tunable FOV [20], realized by a liquid prism. A multifunctional optofluidic (MO) lens with beam steering is demonstrated [21], which is actuated by EWOD. A liquid lens chamber and a liquid prism chamber are stacked to form the MO lens. Their common denominator is that the liquid prism can keep a relative high beam quality and adjust the FOV dynamically by using a transparent partition sheet between L-L interface. However, there are still the wave-front aberration and dispersion problems caused by the liquid prism itself. Besides, the transparent partition sheet can also affect the stability of the liquid prism.
In this paper, we propose an adaptive liquid lens with tunable FOV which consists of a movable annular sheet, an actuator and a lens chamber, which is filled with two different refractive index and immiscible liquids. The movable annular sheet is driven by magnetic force to change its position and tilted angle. The position change results in the curvature change of the L-L interface between two immiscible liquids, which in turn changes the focal length. The FOV can be dynamically adjusted by tilting the annular sheet. The focal length change and FOV of the liquid lens are controlled by one actuator. Therefore, the proposed liquid lens is very compact and easy to operate. We design and fabricate a prototype lens. In the experiment, the proposed lens optical power range is −27 m−1 to 30 m−1. It can realize the FOV deflection and zoom, with an angular resolution of 37"05, the proposed lens can be applied to telescopic system and microscopic system.
2. Device structure and principle
Figure 1 shows the device structure and mechanism of the proposed liquid lens. The proposed liquid lens consists of an actuator and a lens chamber, as shown in Fig. 1(a). The actuator consists of two clamps, two magnets, and a driving ring. The magnets can move up and down and be rotated 360 degrees on the horizontal plane, due to the clamps and driving ring, as shown in Fig. 1(b). The lens chamber consists of an upper chamber, a bottom chamber, a limit ring, an annular sheet, a magnetic ring, and two window glasses. The lens chamber is also filled with two different refractive index and immiscible liquids. A matched density helps to minimize the gravity effect and realize highly axis-symmetric liquid droplet, especially for large aperture lenses.
Fig. 1. Device structure and operation mechanism of the proposed liquid lens. (a) Structure of the lens. (b) State of driving. (c) Initial state. (d) Positive state. (e) Tilt negative state. (f) Tilt positive state.
The magnetic ring is fixed to the outside of the annular sheet in order to control its movement, which can be driven by magnets. The annular sheet is just placed on the L-L interface in order to change the curvature and steer the tilt angle of the interface. Figure 1(c)-(f) show the cross-sectional view of the proposed liquid lens in different driving states. At the initial state, liquid-1 forms a convex shape at the aperture hole in the middle layer because of the surface tension and the gravity of the annular sheet itself, as Fig. 1(c) shows. The liquid lens behaves as a negative lens and diverts light if the refractive index of liquid-2 is larger than that of liquid-1. When the magnets on both sides of the liquid lens move upward simultaneously, the annular sheet also moves upward under the control of the magnetic force, because the volume of the liquids are not constringent, liquid-2 in the lens chamber is redistributed, pressing the interface to change its shape from convex to concave, as shown in Fig. 1(d), and the optical power of the liquid lens changes from negative to positive. Thus, the proposed lens can achieve the function of focal length tuning. When controlling the position of magnets at different heights, the annular sheet can be tilted to a certain degree, which makes the L-L interface to be tilted in the meantime, then the optical axis is tilted to achieve FOV deflection, as shown in Fig. 1(e)-(f). Thus, the proposed lens can also be used for beam steering and FOV adjustment. The tilt angle of the annular sheet is determined by the magnet height difference on both sides of the liquid lens. Maintaining the height difference of magnets while moving up and down, coupled with the rotation of the driving ring, can realize the FOV deflection while tuning the focal length.
At the initial state, the annular sheet suspends between the L-L interface, which is balanced by its own gravity and its buoyancy of the liquid. When moving the annular sheet changes the focal length to a positive or negative state, the annular sheet is subjected to magnetic force ${F_B}$ and the surface tension ${F_t}$ besides gravity and buoyancy, as shown in Fig. 2. The balance of the interfaces between liquid-1, liquid-2, and the annular sheet tri-junction line meets the following equation:
Fig. 2. Force analysis under the balance of the interfaces between liquid-1, liquid-2, and the annular sheet tri-junction line.
According to Eq. (1), we can calculate the contact angle $\theta $. In this lens, when moving the annular sheet change the focal length, the radius of the L-L interface (R) and the contact angle $\theta $ have the following relationship:
where r represents the radius of the aperture of the annular sheet. Therefore, the focal length can be calculated by substituting Eq. (2) into the following formula: where ${n_1}$ and ${n_2}$ represent the refractive indexes of liquid-1 and liquid-2.3. Experiment and result
To visually demonstrate the moving and deforming behaviors of the L-L interface, we first fabricated the device using transparent materials. The material of the lens chamber is polymethyl methacrylate (PMMA). The height and diameter of the proposed lens are ∼15 mm and ∼18 mm, respectively. The effective aperture is ∼7.5 mm. Liquid-1 is NaCl solution, which has a density of 1.07 g/cm3 and refractive index of 1.35. Liquid-2 is phenylmethyl silicone oil, which has a density of 1.07 g/cm3 and refractive index of 1.55. We use electric pushrods to drive the N35 magnets up and down, the characteristics of the electric pushrod and N35 magnet are listed in Table 1.
Table 1. Characteristics of the electric pushrod and N35 magnet
In the first experiment, the distance from the proposed liquid lens to object surface is 100 mm, and a camera is placed over the upper surface to record image. Another camera was placed on the lateral side of the device. It was used to record the curvature change of the L-L interface during actuation. Focusing characteristics of the proposed lens are shown in Fig. 3. Figure 3(a) plots the correspondence between annular sheet displacement distance and optical power of the proposed lens, and the experimental setup is shown in Fig. 3(b). It can be seen that as the annular sheet moves up, optical power of the proposed lens increases. The experiment demonstrates that the focal length can be varied from −37 mm to −∞ and from +∞ to 33 mm when the annular sheet moves from −0.33 to 0.34 mm. The range of optical power is quite large, up to −27 m−1∼30 m−1. In addition, when the optical power is small, the correlation between the optical power of the proposed lens and the annular sheet displacement distance is close to a linear relationship. The capture images of “ABCDE” specimen under different annular sheet displacement distance are shown in Fig. 3(c), on which the letters are clearly identifiable. It verifies that the proposed lens has good imaging quality. The focal length of the proposed lens is determined by the curvature of the L-L interface. Afterward, the curvature of the L-L interface is determined by the pressure difference caused by the annular sheet displacement distance, as shown in Fig. 3(d). The L-L interface height changes from 0 to 1.2 mm when the annular sheet moves down from 0 to 0.33 mm. The L-L interface height changes from 0 to −1.3 mm when the annular sheet moves up from 0 to 0.34 mm.
Fig. 3. Focusing characteristics of the proposed lens. (a) Correspondence between annular sheet displacement distance and optical power of the proposed lens. (b) Experimental setup. (c) Capture imaging of “ABCDE” specimen under different annular sheet displacement distance. (d) Side view of the deformation process.
The proposed lens can be applied in optical systems for adjusting the FOV. In the second experiment, the distance of the proposed liquid lens to object surface remains the same. Figure 4(a) shows the correspondence between deflection $\alpha $ of annular sheet and magnet altitude difference. The maximum deflection angle of the annular sheet is 3 degrees when the magnet altitude difference is 1.25mm. The images shown in Fig. 4(b) are taken at f = −90 mm with different FOV deflection angle. In this experiment, we define the horizontal plane on the right side as 0°. First, the two side magnets were moved simultaneously downward by 0.1 mm from the initial state to obtain the image at f = −90 mm. To move the letter “E” to the center of the FOV, rotate the driving ring to the 90°−270° direction, then move the 270° direction magnet upward by 0.7 mm and the 90° magnet direction downward by 0.7 mm. Then the two side magnets were moved simultaneously upward by 0.23 mm to obtain the deflection image at f = 70 mm, as shown in Fig. 4(c). FOV deflection in other directions operates similarly. Rotate the driving ring and tilt the annular sheet to a certain angle can drive the FOV deflection in different directions while keeping the focal length constant. This experiment proves that the proposed lens can not only tune the FOV, but also enlarge the viewing angle in an optical system.
Fig. 4. FOV adjustment characteristics of the proposed lens. (a) Correspondence between annular sheet deflection and magnet altitude difference. (b) FOV deflection of f = −90 mm. (c) FOV deflection of f = 70 mm.
To evaluate the imaging quality, we fabricate a prototype of the proposed lens which can be easily integrated into a lens system. The prototype consists of 7 elements, as shown in Fig. 5(a). The top shell, limit ring, upper chamber and bottom chamber are made of aluminum and treated with black oxidation. The inner and outer diameter of the upper chamber and bottom chamber are ∼14 mm and ∼22 mm, respectively. The material of the top and bottom window glass is BK7 in glass data of SHOTT [22]. The diameter of the top and bottom window glass is ∼12 mm. The annular sheet is made of PMMA. The inner diameter and thickness are ∼7.5 mm and ∼1 mm, respectively. All the elements are stuck together to form the prototype using UV331 glue. Figure 5(b)–(c) show the top and side views of the prototype, respectively. The size of the whole device is designed to be 22 mm (diameter) × 23 mm (height).
Fig. 5. Fabricated prototype of the proposed lens. (a) Elements of the proposed lens. (b) Top view of proposed lens. (c) Side view of proposed lens.
It is necessary to evaluate the image resolution for a lens. An experimental device for measuring image resolution is built, as shown in Fig. 6(a). A resolution target is added in front of a collimator. The proposed lens is placed in front of the CMOS camera. The image sensor we use is a 1/2.5” color CMOS (DS-UM501-H) with 2592 × 1944 pixel resolutions. When the light converges on the CMOS camera, the image of the resolution target can be obtained from the camera, and the image resolution can be judged according to the number of distinguishable fringes in the image. When the focal length is 50 mm, the angular resolution is about 39"23, as shown in Fig. 6(b). When the focal length is 150 mm, the angular resolution is about 37"05, as shown in Fig. 6(c). The resolution target is JB/T9328-1999. Besides, the angular resolution at 39"23 and 37"05 can be normalized relative intensity as shown in Fig. 6(d) and (e), respectively. From the test results we can conclude that the angular resolution is 39"23 at least.
Fig. 6. Captured image of JB/T9328-1999 resolution target. (a) Experimental device for measuring image quality. (b) Focal length is 50 mm. (c) Focal length is 150 mm. (d) Normalized relative intensity of angular resolution at 39"23. (e) Normalized relative intensity of angular resolution at 37"05.
The proposed lens can be used in an imaging system. We tested the imaging quality of the proposed lens at different focal length. The experimental setup consists of a proposed lens, a convex lens, a CMOS camera and driving device, as shown in Fig. 7(a). The convex lens is used to undertake part of the focal power of the lens system. The numbers on the colored building blocks were imaged with the proposed lens. When the annular sheet moved 0.18 mm upward from the initial state, the focal length can reach ∼50 mm, as shown in Fig. 7(b). Then, the annular sheet was moved down by 0.07 mm, the focal length can reach ∼85 mm, as shown in Fig. 7(c). Compare these two figures, when the focal length is 85 mm there is chromatic aberration. We keep the focal length constant and change the tilt angle of the annular sheet for FOV deflection. The imaging quality of the proposed lens FOV deflection at f = 85 mm is shown in Fig. 8. Figure 8(b)–(e) shows the FOV deflection in four directions, up and down, left and right. Due to the excessive tilt angle of the L-L interface, there are astigmatism and chromatic aberration after the FOV deflection.
Fig. 7. Imaging quality of the proposed lens at different focal length. (a) Experimental setup. (b) f = 50 mm. (c) f = 85 mm.
Fig. 8. Imaging quality of the proposed lens FOV deflection at f = 85 mm. (a) Initial state. (b) Upward deflection. (c) Leftward deflection. (d) Downward deflection. (e) Rightward deflection.
To characterize the imaging performance of the proposed lens, we use a liquid lens and a liquid prism combination as a comparison. The RMS of dispersion spot and MTF of the two lenses can be obtained by ZEMAX simulation under the same FOV deflection angle, so as to get the performance of the lens, respectively. We simulate the two kinds liquid lens using ZEMAX, as shown in Fig. 9. 2D layouts are shown in Fig. 9(a)–(b). Figure 9(c)–(d) shows MTF values of the proposed lens and the combination lens are 0.30 and 0.10, respectively, when the focal length is 50 mm and spatial frequency is 10.2. At f = 85 mm and spatial frequency is 10.2, Fig. 9(e)–(f) shows MTF values of the proposed lens and the combination lens are 0.23 and 0.04, respectively. The OTF of the proposed lens is better than the combination lens at the same spatial frequency in cycles per mm. Therefore, we can conclude that the imaging quality of the proposed lens is better compared with the combination lens, with simpler structure.
Fig. 9. ZEMAX model. (a) Model of the proposed lens. (b) Model of the combination lens. (c) MTF of the proposed lens at f = 50 mm. (d) MTF of the combination lens at f = 50 mm. (e) MTF of the proposed lens at f = 85 mm. (f) MTF of the combination lens at f = 85 mm.
4. Conclusion
We demonstrate an adaptive liquid lens with tunable FOV. The proposed liquid lens consists of an actuator and a lens chamber, the annular sheet is just placed on the L-L interface in order to change the curvature and steer the tilt angle of the interface. Different from the FOV adjustable lens combined with a liquid lens and a liquid prism, the proposed lens requires only one L-L interface to achieve the focal length change and FOV deflection, and can control aberrations while maintaining high resolution. The proposed lens also has a large optical power range, up to −27 m−1∼30 m−1. It can realize the FOV deflection while tuning the focal length, with an angular resolution of 37"05. Its potential applications in telescopic system and microscopic system are foreseeable.
Funding
National Natural Science Foundation of China (61927809, 61975139).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data available from the authors on request.
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