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Abstract
In this paper, we propose a new method for image stitching using an electrowetting-based liquid prism. Several images were obtained by adjusting the voltages applied to four sidewalls of the liquid prism, and a panoramic image was achieved through an image stitching algorithm. The relationship between the tilting angle of the liquid prism and the normal vector of the liquid-liquid interface was presented. Novel fabrication method has been proposed to improve the performance of the liquid prism, including the addition of a new structure to prevent oil isolation, plastic chamber material, plastic laser cutting, and oil selection. The fabricated liquid prism has a size of 5 × 5 × 8 mm, a maximum beam steering angle of ±10.5 °, a response time of 19.1 ms, and a resolution of 14.25 lp/mm. The required number of images according to the overlapping area was presented through the simulation, and the image stitching using two or three images was demonstrated.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Image stitching technology [1,2] creates a wide field of view, like a panorama from images taken by a camera. Substantial research effort has been made image stitching algorithms, including a method of converting the entire image into one global homography [3,4] and a method of dividing the screen into several planes or meshes and using a different warping matrix for each segmentation [5,6]. In order to obtain a panoramic image through image stitching in this way, two or more partially overlapping images are required. If the overlapping part is too small, a fewer number of matched keypoints are obtained, which causes an unwanted image. And in an application such as Lidar that requires a rate of 50 Hz or more, it is important to obtain these overlapping images quickly. However, many image stitching studies do not consider how to obtain these images. In the present study, a new method of obtaining images for image stitching by using a liquid prism is proposed, and a panoramic image using a simple image stitching algorithm is obtained.
Electrowetting-based liquid prism is one of the beam steering methods. Electrowetting [7,8] is a mechanism where the contact angle of the electrolyte liquid is changed by an external voltage and there are many applications using this electrowetting phenomenon [9–14]. The electrolyte liquid changes the curvature of the surface as the contact angle changes on the conductor substrate. Compared with the conventional mechanical beam steering methods such as Risley prism [15–18], galvo mirror [19], and rotating polygon [20], liquid prism is available in non-mechanical beam steering version, which has no moving part and is power efficient, lightweight, and compact. Many liquid prism studies to increase the beam steering angle or operating speed [21–23] have been conducted, and these liquid prisms were applied to applications such as Lidar [24], laser scanners [25,26], and solar energy collection [27,28]. We also fabricated a liquid prism and combined it with a liquid lens to implement three-dimensional beam steering [29]. However, there was no attempt to measure the liquid interface with a quantitative value or solve the oil isolation problem that occurs in a cuboid-shaped liquid prism.
Here, we propose a novel fabrication process for the electrowetting-based liquid prism. The liquid prism was designed considering the tilting angle of the liquid-liquid interface, oil isolation, and equivalent circuit. This fabrication method differs from the conventional liquid prisms in several aspects, such as chamber material, chamber structure, and liquid composition. Therefore, the quality of the liquid-liquid interface was improved, which was demonstrated from the wavefront sensor. The beam steering angle and operating speed of the liquid prism were also measured, and the resolution test was performed. The relationship between the beam steering angle and the overlapping area was determined, and the required number of images for each condition was simulated. Two or three different images with an overlapping area were obtained by adjusting the beam steering angle of the liquid prism and image stitching was performed.
2. Liquid prism design
2.1 Tilting angle of liquid-liquid interface
Liquid prism uses four sidewalls to achieve a flat liquid-liquid interface forming an infinite radius of curvature (RoC). Since the interface of the liquid prism determines the performance of the liquid prism, it is necessary to design the interface and whole structure based on the operating principle of the liquid prism. Figures 1(a) and 1(b) show the normal vectors of the sidewalls of the liquid prism and the liquid-liquid interface, respectively. The normal vector of each sidewall is (1,0,0), (0,1,0), (−1,0,0), and (0,−1,0). The normal vector of the liquid-liquid interface can be expressed as
Fig. 1. Schematic of liquid prism operation. (a) Normal vectors of four sidewalls of the liquid prism. (b) Normal vector of the liquid-liquid interface. (c), (d) Contact angles according to the voltages applied to four sidewalls.
Therefore, the contact angles between the liquid-liquid interface and four sidewalls can be controlled by using this relationship, given arbitrary angles of φ and θ.
2.2 Oil isolation of liquid prism
Figure 2 shows the oil isolation problem of the conventional liquid prism. The liquid prism is generally a cuboid structure, and two liquids have a certain initial contact angle. The RoC of the DI (de-ionized) water (r) can be calculated as
where ${\theta _i}$ is the initial contact angle of the liquid and d is half the length of one side of the liquid prism. The shape of the water is formed by the curvature distance from the center of the square. However, the structure has a different distance from the center to the sides as shown in bottom view in Fig. 2(b). Therefore, the oil fills in the corners and penetrates to the bottom of the structure. As the voltage is applied to the sidewalls, the contact angle (θ’) decreases and the RoC(r’) of the water increases. Therefore the oil in the corners moves toward the center of the chamber and interferes with the operation of the liquid prism. For example, the initial contact angle of the conventional liquid prism is 154 °, which means that the oil tends to stick to the sidewall more than water. And the initial curvature becomes 1.11d, which is smaller than the square diagonal length of $\sqrt 2 d$, which causes an oil isolation problem. To solve this oil isolation problem, an additional structure whose shape is the same as the isolated oil is needed in the prism as shown in Fig. 2(d). This additional structure replaces the area where the oil would exist under the water, which prevents the oil isolation. The relevant fabrication process is mentioned in Chapter 3. Although the additional structure has the disadvantage of reducing the beam steering area, it effectively solves the oil isolation problem.Fig. 2. Schematic of oil isolation problem. (a) Oil isolation in the liquid prism. (b) Side/bottom view of the liquid prism of the initial state. (c) Side view of the liquid prism when the RoC of the water increases. (d) Additional 3D printing structure.
2.3 Equivalent circuit of liquid prism
In electrowetting, the voltage across the dielectric layer on the electrode is slightly different from the voltage applied to the entire circuit because water also has resistance and capacitance value. In a typical application using electrowetting such as a lens, because the same voltage is applied to all electrodes, the total voltage and the voltage applied to the dielectric layer are different, but, there is no difficulty in controlling the voltage applied to the dielectric layer. However, the proposed liquid prism operates by applying different voltages to the four sidewall electrodes; therefore, it is difficult to control the voltage applied to the dielectric layer of each sidewall because the voltages affect each other. Figure 3 shows the equivalent circuit of the electrowetting-based liquid prism. Rw is the resistance of water, Cw is the capacitance of water, Cd1 to Cd4 are the capacitances of the dielectric layer on sidewall, and Vac1∼Vac4 are the voltages applied to the sidewall electrodes. The impedance of water (Zw) and Vac(n) are expressed as
Therefore, the magnitude of the voltage applied to each dielectric layer becomes lower than the applied voltage due to the impedance of the water and the actual value is calculated as
3. Fabrication process
The fabrication process of the proposed liquid prism is shown in Fig. 4. It differs from the conventional method of fabricating the liquid prism in several aspects such as chamber material, chamber structure, and liquid composition. Polycarbonate (PC), which is a strong and tough thermoplastic polymer, was selected as the chamber material. By changing the chamber material from glass to plastic, the whole device could be made more lightweight. Indium Tin Oxide (ITO) and Silver (Ag) layers were deposited on the PC substrate with thicknesses of 10 nm and 7 nm, respectively. In this case, ITO acts as an adhesion promoter, improving adhesion between the polycarbonate substrate and Ag. A 2 µm layer of parylene C was deposited as a dielectric layer through chemical vapor deposition, followed by application of a 0.3 µm hydrophobic layer of Teflon by dip coating. These dielectric layers prevent each sidewall of the liquid prism from being connected. Then, the substrate was cut with a laser cutting device, VLS 3.50. Laser irradiation power and speed should be adjusted for a smooth cross section. The total size of one piece was 8 mm × 10 mm, and two 4 mm × 0.5 mm grooves were drilled in the middle. The distance between the two grooves was 5 mm, which is the sidewall part of the liquid prism. A PC-based liquid prism chamber was manufactured by assembling four cut pieces. This method allows the liquid prism to be made with the correct size. The additional 3D printing structure was made to prevent oil isolation as mentioned in Chapter 2.2. The 3D printing chamber and the ITO glass were assembled to the liquid prism chamber. Then, two immiscible liquids were injected into the chamber. The non-conductive liquid consisted of a mixture of hydrogenated terphenyl and 1-bromonaphthalene, and deionized (DI) water with 0.1% sodium dodecyl sulfate (SDS) was selected as the conductive liquid. The selected non-conductive liquid is more stable because it has no reactivity with parylene C and Teflon and it has a higher refractive index than the mixture of 1-chloronaphthalene and dodecane used in the conventional liquid prism [29]. Finally, the device was covered by 3D printing gasket and glass and was sealed with UV adhesive. As shown in Fig. 4(h), when there is no 3D structure, the oil is isolated, which causes the oil to move toward the center of the chamber during operation. By using the 3D structure, it was confirmed that the oil isolation problem was solved.
Fig. 4. Fabrication process of the proposed liquid prism. (a) Polycarbonate (PC) chamber material. (b) ITO (10 nm) and Ag (7 nm) deposition. (c) Parylene C (2 µm) deposition. (d) Teflon (0.3 µm) deposition. (e) Laser cutting. (f) Assembling the trimming pieces. (g) Liquid dosing. (h) Solving the oil isolation problem. (i) Sealing.
4. Liquid prism performance
4.1 Beam steering angle
Figure 5 shows the operation of the liquid prism. As shown in Fig. 5(a), (a) green LED (λ = 520 nm) light source was used as the incident beam, and it was made to be parallel using a lens. The collimated beam passed through the liquid prism and was formed on a check-patterned paper. Figure 5(b) shows how the shape of the interface and the apex angle change depending on the voltages applied to the liquid prism. The shape of the liquid-liquid interface between the water and oil was convex at the initial state. When the same voltages (30 V) were applied to the four sidewalls of the liquid prism, the shape of the liquid-liquid interface became flat where the light beam passed through the liquid prism without refraction. When different voltages were applied to the four sidewalls, the interface between the liquids was tilted and acted as a prism. Figure 5(c) shows beams formed based on operation at various voltages. The contact angle of the liquid is determined by the Young-Lippmann equation, $\cos \theta = \cos {\theta _1} + ({{\varepsilon_0}\varepsilon /2d\gamma } ){V^2}$, where θ is the contact angle after applying voltage V, θ1 is the initial contact angle, ɛ is the dielectric constant, d is the thickness of the dielectric layer, and γ is the surface tension. The beam steering angle (δ) was calculated using the displacement of the liquid spot (D) and the distance between the liquid prism and the check-patterned paper (L).
The maximum beam steering angle of the liquid prism was ±10.5 °, where the voltages applied to the four sidewalls were 35 V, 25 V, 20 V, and 25 V, respectively. Beam steering angle of ±5 ° was also measured as the tilting angle of the liquid-liquid interface was changed by adjusting the voltages across the sidewalls of the liquid prism.Fig. 5. Beam steering angle of the liquid prism. (a) The schematic of the light beam control using the liquid prism. (b) Changes in the liquid-liquid interface of the liquid prism depending on the applied voltages. (c) Displacement of the liquid spot in different applied voltages and the calculated beam steering angles.
4.2 Flatness of liquid-liquid interface
As shown in Fig. 6(a), (a) Shack-Hartmann wavefront sensor, which measures RMS wavefront error and RoC, was used to measure how flat the interface of the liquid prism was. For comparison, an ideal reference liquid prism whose interface between the water and oil is perfectly flat was fabricated. The reference liquid prism were made with two types of apex angles, each with 0 ° tilting and 38 ° tilting. The proposed liquid prism also operated at 0 ° and 38 °, and the wavefront of the beam was measured. Figures 6(b)–6(e) show values demonstrating that the liquid-liquid interface of each liquid prism is flat. For the reference liquid prism, the RMS wavefront errors were 0.175 λ and 0.170 λ when the apex angles were 0 ° and 38 °, respectively. The values of RoC were 2820.2 mm for 0 ° and 2968.8 mm for 38 °.
Fig. 6. Flatness measurement of the liquid prism. (a) Optical setting for flatness measurement and two types of liquid prism. (b) 0 ° tilting of the reference liquid prism. (c) 38 ° tilting of the reference liquid prism. (d) 0 ° tilting of the proposed liquid prism. (c) 38 ° tilting of the proposed liquid prism.
For the proposed liquid prism, the RMS wavefront error were 0.178 λ and 0.174 λ when the apex angles were 0 ° and 38 °, respectively. The values of RoC were 2525.2 mm for 0 ° and 2445.1 mm for 38 °. The average RMS error rate of the proposed liquid prism compared to the reference liquid prism was calculated to be 2.7%. It is demonstrated that there was little difference compared to the perfectly flat interface of the reference liquid prism.
4.3 Response time
Since image stitching requires at least two images, it is advantageous to shoot as fast as possible. When using the proposed liquid prism, the operating speed of the liquid prism has a great influence on the overall speed of the image stitching system. The response time of the proposed liquid prism was measured by a high-speed camera. The liquid prism operated from the initial state (0 V for all electrodes) to the flat state (25 V for all electrodes) and was also operated backward. As shown in Fig. 7, the resolution of the camera was 20.8 megapixels and video clips were taken at a 1200 frames per seconds (fps) recording setting, which takes 1 frame per 0.83 ms. Both the forward process and the backward process took 23 frames, which means the response time of the liquid prism is about 19.1 ms.
4.4 Resolution test
In order to take an image using the proposed liquid prism, the change in resolution when passing through the liquid prism should be minimized. The USAF 1951 resolution target and a smartphone camera (Samsung galaxy S9) were used for measurement. As shown in Fig. 8(a), the camera lens was able to resolve element 1 in group 4, which means it has a resolution of 16.00 lp/mm. Figure 8(b) shows that the liquid prism was attached to the front of the camera lens and the liquid prism was operated with the flat 0 ° tilting. With proper alignment, the region containing element 6 in group 3 was able to be resolved, with a resolution of 14.25 lp/mm. This resolution decrease occurs because the interface of the liquid prism is not perfectly flat, and there is an RMS error of the wavefront passing through the interface. There is a slight decrease in resolution, but it is just only a one-step difference in the USAF chart, where there is no obstacle to taking the images.
Fig. 8. USAF 1951 resolution measurement of the proposed liquid prism. (a) Reference resolution measurement. (b) Resolution measurement with the liquid prism.
5. Imaging test
5.1 Image stitching algorithm
Image stitching requires multiple images, and these images can be obtained by changing the tilting angle of the liquid prism. Image stitching was performed in the following steps, as shown in Fig. 9(a). Keypoints from two images were detected based on SIFT (Scale Invariant Feature Transform), which remain invariant in rotation, scale, or illumination [30]. These keypoints from two images were matched, and the homography matrix was estimated using the RANSAC algorithm [31]. Finally, a warping transformation was applied using the obtained homography matrix. However, when the beam steering angle exceeds a certain angle where there is little overlap between the two images, image stitching is not possible as shown in Fig. 9(b). From several simulations, it was demonstrated that image stitching failed when the overlapping area of the two images was less than 5.5% where the beam steering angle of the liquid prism was ±9.4 °. Therefore, in the present experiment, two or three images were stitched together to create a panorama depending on the beam steering angle of the liquid prism.
Fig. 9. Image stitching process with the proposed liquid prism. (a) Schematic of method for obtaining a panoramic image. (b) Image stitching algorithm.
5.2 Result images
Both Fig. 10 and Fig. 11 show the results of image stitching from the input images taken using the liquid prism. Figure 10 shows the results when the beam steering angle is less than ±9.4 °, which can be stitched with two images, and Fig. 11 shows the results when the beam steering angle is more than ±9.4 °. Figure 10(a) shows the images taken with the beam steering angle of the liquid prism set to ±5 °. The matched keypoints between these two images can be obtained from image stitching algorithm, which is based on an OpenCV configuration environment, as shown in Fig. 10(b). Using these matched keypoints, a perspective transform was applied, and the final panoramic images were obtained, as shown in Fig. 10(c). Figure 11(a) shows the images taken with the beam steering angle of the liquid prism set to ±10.5 °, and 0 °. As shown in Fig. 11(b), keypoints with the three input images were matched in the same way. Figure 11(c) shows the final panoramic images with the three input images. The maximum field of view (FOV) was increased by 21 ° compared to the camera’s FOV.
Fig. 10. Image stitching results with two images. (a) Two input images taken from the beam steering angle of −5 °, and +5 °. (b) Keypoints matching. (c) Panoramic image made from two input images.
Fig. 11. Image stitching results with three images. (a) Three input images taken from the beam steering angle of −10.5 °, 0 °, and +10.5 ° liquid prism (b) Keypoints matching. (c) Panoramic image made from three input images.
6. Conclusion
In conclusion, image stitching with the electrowetting-based liquid prism was achieved. The liquid prism operation was modeled, and the novel fabrication method including the additional 3D printing structure, PC chamber material, a laser cutting, and oil composition, was proposed. And several performance measurements of the liquid prism were performed such as the beam steering angle, flatness of the liquid-liquid interface, operating speed, and resolution. The minimum required number of images according to the overlapping area was presented through the simulation. Two or three images were obtained by changing the tilting angle of the liquid prism, and the panoramic image was obtained by applying the image stitching algorithm. Further research, including increasing the beam steering angle and lifetime, decreasing the response time, and perfectly flattening the liquid-liquid interface, will be conducted. And 2D image stitching will be performed by taking four images in a diagonal direction.
Funding
Ministry of Science and ICT, South Korea (2020R1F1A1074089).
Acknowledgments
This work was supported by the BK21 program.
Disclosures
The authors declare that there are no conflicts of interest related to this article.
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