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Abstract
Micro-lens array, an artificial compound eye vision system, provides a wide field of view and multi-perspective view. However, it has not been adopted as a computer vision application due to its limited visible range and high optical interference. In this research, a novel fabrication method for the flexible polydimethylsiloxane micro-lens array with a polytetrafluoroethylene light screen-aperture integrated layer was established by the simple protrusion method. The integrated layer provided longer visible range by one meter while maintaining the wide field-of-view of 100 °. The resulting images were used for obtaining depth information of a target as an example and for analyzing the rectangular and hexagonal arrangements of the micro-lenses for the future applications. With the improved visual range, wide field-of-view and flexibility, the fabricated micro-lens array can be applied to the small and curved CMOS image sensors in the future.
© 2021 Optical Society of America under the terms of the OSA Open Access Publishing Agreement
1. Introduction
Recent advances in the field of computer vision have enriched our lives with autonomous cars, drones, humanoids, and surveillance cameras, etc. Combined with other distance sensors such as ultrasonic sensors, infrared distance sensors, LiDAR, or Time of Flight(ToF) sensors, applications and potential of the vision system are limitless. Currently, the combination of different sensors is restricted to large robots or autonomous cars due to its requirement for the sufficient space and power. Therefore, equipping both the image sensor and distance sensor in small machines or endoscopy applications for narrow spaces is greatly limited. Moreover, the advancement of the computer vision system brought changes to the shape of the image sensors. The complementary metal–oxide–semiconductor(CMOS) image sensor has been researched and fabricated with the curved surface instead of the conventional flat surface. The curved image sensors are expected to improve the resolution, aberration, and illumination of the flat sensor, along with the reduced size and complexity of the whole vision system [1–3]. Therefore, the application of the curved image sensor to the vision system with the compact size and high performance can further strengthen its potential as a future image sensor system.
Micro-lens arrays, a biomimetic artificial compound eye, are great apparatus for the compact computer vision system and the curved CMOS sensor technology application due to its additional spatial information. The spatial information can be obtained since the multi-perspective imaging system provides multiple images of a target in one image plane along with a wide field of view [4,5]. However, due to its short-sighted vision and optical interference from adjoining micro-lenses, it has not been actively adopted to the current computer vision system. To recreate the spatial information acquisition and wide field-of-view, many studies have presented various fabrication methods of the micro-lens arrays by mimicking the structure of the superposition compound eye of the insects [6,7]. However, conventional micro-lens arrays do not resolve the optical interference from the neighboring micro-lenses which saturates the light intensity received on the image sensor, and only provides a very short visual range of a few tens of millimeters. To reduce the optical interference from adjacent lenses and external light sources, a few studies have actualized the light screening layer which corresponds to the pigment cell of the compound eye [8–12]. They adopted the light screen layer or barrier around each micro-lens to rectify the optical interference. Since the light screen around each lens functions as a wide aperture, the light screen increased the visual range of them. However, they lack a real aperture, which provides a further depth of field, and structural improvements, resulted in a short visual range of a few tens of centimeters. To increase the visual range of the micro-lenses, a research combined "foveated vision" and compound eye’s multi-aperture system [13]. This research greatly improved the visual range by 1 meter through a unique lens design that imitates the eagles’ eye. It demonstrated the versatility of the micro-lens multi-aperture system for small robots by improving the visual range through structural design. However, this study did not resolve the optical interference problem from adjoining lenses and external light sources since the materials used for the foveated vision are transparent. Therefore, there is ongoing effort to establish a pragmatic micro-lens array optical system. The optimal micro-lens array system will provide a better visual range and wider field-of-view while it can be located in smaller spaces or small machines and can fit on any curved CMOS image sensors for a superior optical performance.
In this research, a novel fabrication process that reproduces a biomimetic superposition compound eye using polytetrafluoroethylene (PTFE) film and polydimethylsiloxane (PDMS) as a light screen-aperture and micro-lenses, respectively, was established. The integration of the light screen and the aperture were created by protrusion of PDMS liquid through the aperture holes created on the black PTFE film. To compensate for the viscosity level of the untreated PDMS for maintaining the hemispherical shape, PDMS was slowly cured at room temperature. Using the fabricated micro-lens array, example images were taken to demonstrate its visual range, field of view, and spatial data acquisition application. Lastly, arrangements of the micro-lenses were compared for next generation hemispherical micro-lens array applications.
2. Materials and method
2.1 Materials
Materials include polydimethylsiloxane (PDMS, Sylgard 184, Sigma-Aldrich, United States) with 10:1 of silicone elastomer base to curing agent ratio for the micro-lenses, polytetrafluoroethylene (PTFE, AF008AS, Alphaflon, South Korea) with 80 $\mu$m of thickness for the light-screen layer, microscope glass slide (M08-660-147, LK Lab Korea, South Korea) with a 1.1 mm substrate thickness for flatness, and perfluoroalkoxy polymer (PFA, PFA0050, Alphaflon, South Korea) with 50 $\mu$m of thickness as a supportive substrate for flexible micro-lens arrays.
2.2 Viscosity variance of PDMS
The PDMS with a 10:1 ratio of base to curing agent solidifies when it is left at room temperature for 48 hours or 35 minutes when it is heated at 100 °C [14]. However, the way that the PDMS behaves in between the liquid and the solid phase remains unclear. Few studies used the transitional phase of the curing, especially the moment prior to the PDMS mixture becoming solidified where its viscosity level is the highest. A recent study among them has shown that the PDMS droplets on a heated substrate provide higher contact angle with respect to curing time due to the increase of viscosity of the PDMS during its gel time that obeys the following Eq. (1) [15]
where $\mu$ is the dynamic viscosity in Pascal-second and t is time in seconds. In our experiment, the solidification of the 15ml PDMS in a capped 50ml falcon tube was completed after 7 hours of natural curing at room temperature. Partial gelation of PDMS was observed after 6 hours, and it was not able to spin-coat the PDMS afterwards since it merely flows behaving as several chunks of jelly. Therefore, 5 hours of natural curing was considered to be the last moment for the PDMS mixture to remain liquid with the highest viscosity, increasing the viscosity of the PDMS mixture by 16 times according to Eq. (1). The increased viscosity of the PDMS delays the time for the hemispherical shape to flatten which allows the lens-like shape that was initially formed due to the surface tension, to be maintained longer. Fig. 1. shows the viscosity changes of the PDMS droplets on two different substrates over time. The viscosity level of PDMS gradually increased as it was naturally cured at room temperature and the lens-like shape tends to maintain its form the longest when it was cured for 5 hours, whereas the freshly mixed PDMS immediately becomes close to the complete wetting status(‘0hr’ in Fig. 1.) on both substrates. Before 5 hours of curing, the PDMS still showed fluidic features with no observable differences. On PTFE film, however, it tends to make a dome shape earlier than when it was on the glass, but it flowed easily when tilted, meaning that the adherence level between the PDMS and the PTFE is relatively low. This behavior is beneficial for the lens formation on PTFE film because the PDMS would not flow over to the neighboring PDMS lens before it is cured. Beyond 5 hours of curing, the PDMS became a highly viscous liquid that does not lose its shape easily. By curing the PDMS slowly at room temperature, a higher viscosity was obtained, which enabled the mold-less formation of the micro-lens array. Post 6 hours of curing, the sample became a gel-like solid, losing its fluid characteristic.2.3 Fabrication process and result
The fabrication steps are as follows: first, the 10:1 ratio of PDMS was spin-coated for 60 seconds at 3000 RPM on a glass substrate, followed by 40 minutes of curing at 100 °C (Fig. 2(a) and Fig. 2(b)). After curing, PFA film was applied on top of the cured PDMS (Fig. 2(c)). Another layer of PDMS, that was cured for 5 hours at room temperature in a capped 50 ml falcon tube, was spin-coated onto a PFA film (Fig. 2(d)). Then, a PTFE film with laser-cut patterns was applied on the top of the PFA film (Fig. 2(e)). After a few seconds, the PDMS liquid soared upwards through the patterned holes on the PTFE film due to the subtle pressure applied by the weight of the PTFE film (Fig. 2(f)). Initially the surface tension of PDMS formed the lens shape, and the shape was maintained due to its viscosity. Lastly, the entire sample was cured on a hot plate for 30 minutes at 100 °C, the substrate was removed and the sample was cut out (Fig. 2(g)).
Fig. 2. Fabrication steps of the micro-lens array. (a) A glass substrate. (b) Spin-coat a layer of regular PDMS for adhesion. (c) Applying PFA film on top of the PDMS adhesive layer (d) Spin-coat a layer of the modified PDMS. (e) Applying the laser-patterned PTFE film. (f) Protrusion of the modified PDMS through the patterned holes. (g) After curing on a hot plate, remove the substrate and cut out the sample. (h) The fabricated micro-lens array.
The fabricated micro-lens array with PTFE screening layer is shown on the right-hand side columns of the Fig. 3. Each lens has a diameter of 500 $\mu$m with 100 $\mu$m of height, and they are 1.4 mm apart from each other. The distance between the lenses was optimized empirically to prevent the overlapping of the resulting images. Starting from the inner hole diameter $R$, the distance was increased by $R$ until it reached $20R$. The distance that showed the best result in the highest packing density available was approximately $12R$. The laser-cut inner hole has 120 $\mu$m in diameter. The diameter of the inner hole and the dimensions of the PDMS lens can be customized as small as the fiber laser can afford. The smallest possible pattern is 10 $\mu$m with the machine used (FM20CS, The Lasers, South Korea). However, due to the laser ablation, about 100 $\mu$m in diameter size was the smallest hole possible. Diameters between 100-200 $\mu$m on PTFE film offer the most reliable result regarding uniformity and consistency of the sample, with 40 $\mu$m thick PDMS coat on the substrate. Compared to the lens that was made with freshly mixed PDMS (left-hand side column of the Fig. 3), 5-hour-cured PDMS was able to maintain its hemispherical shape more reliably. Since both PTFE film and PFA film are elastic materials that can be bent or curved, as shown in Fig. 4(a), the micro-lens array with PTFE light-screen can easily be applied on any curved image sensor.
Fig. 3. The fabricated micro-lens array (Left column) The micro-lens array with freshly mixed PDMS. (Right column) The micro-lens array with PDMS cured at room temperature for 5 hours.
Once the PTFE micro-lens array is fabricated, it can be applied to any commercially available image sensors. In Fig. 4(b), a jig that was specifically designed to load the PTFE micro-lens array film onto the image sensor module with adjustable height for optimal focal length is shown. The micro-lens array was attached to the 3D-printed cover using an ethyl cyanoacrylate adhesive (Scotch Super Glue Liquid AD110, 3M, United States), then the cover part and the image sensor part were assembled by the screws and spiral springs at each corner. The spiral coil spring around each screw prevents the micro-lens array and the cover part from touching the sensor by repelling them while the screws hold the cover part from being separated from the camera module, allowing the precise adjustment of the distance between the micro-lens array and the sensor by tightening or loosening of the screws. The screw has 2 mm of body diameter and 10 mm of height in total. The single turn of all the screws elevates the cover by 0.2 mm. After obtaining an adequate focus, test images were taken using a modified USB camera (USB camera module megapixel USB camera, ELP); the pre-installed lens in front of the image sensor was removed and replaced with the fabricated PTFE micro-lens array.
3. Discussion
3.1 Demonstration and spatial information acquisition
Each lens of the fabricated micro-lens array was a plano-convex lens with the measured radius of curvature of 800 $\mu$m. Using the lensmaker’s equation in Eq. (2) where $n_1$ being the refractive index of the air with a value of 1, $n_2$ is the refractive index of the PDMS with a value of 1.43, $R_1$ is the radius of curvature of the micro-lens with a value of 800$\mu$m and $R_2$ is the infinite radius of curvature. The resulting focal length $\it {f}$ of the thin PDMS micro-lens provides $\it {f} \approx 1860 {\mu }m$. This focal length value is useful not only in finding optimal distance between the lens system and the sensor plane, but also in obtaining simple spatial information.
Figures 5(d), 5(e) and 5(f) show the actual snapshots taken using the PTFE micro-lens array and the image sensor combined. Clear disparities of images were observed in each image. In Fig. 5(d), the printed version of the USAF-1951 resolution test chart(Fig. 5(a)) is shown on each lens. For each image obtained by an individual lens in the micro-array, the target image was shown differently; the left-most lens shows the target shifted toward the right, whereas the right-most lens showed the target slightly biased to the left from the center. Similar to the binocular vision system, the disparity obtained by the two lenses among the micro-lens array provides spatial information. From the disparity, the pixel-wise difference of the two images that appeared on the screen was obtained. In addition, the focal length ($\it {f}$) was secured using the Lens Maker’s Equation. Lastly, the distance between the two chosen lenses among the micro-lenses could also be acquired. Using a trigonometrical calculation, with these distance information as shown in Eq. (3) and Eq. (4), the distance between the target object and the micro-lens array can be computed. For example, images from each lens in Fig. 5(e) offered the distance information of a pawn placed far behind the rook. In the figure, a pawn was placed 30 cm behind a rook which was 10 cm away from the micro-lens array sensor. The actual distance between the pawn and the image sensor was measured to be 39.8 cm. The calculation required a simple trigonometric relationship from Eq. (3) and Eq. (4), also illustrated in Fig. 5(b).
From Eq. (3), f is the focal length of the lens obtained from the lens maker’s equation, d is the distance between each micro-lens (center to center), $D_0$ is the reference distance between the target object and the sensor to be used for calibration. In Eq. (4), $D_1$ is the distance value of the target object calculated based on the values obtained from Eq. (3), where $Disparity_{calibrated}$ is the calibrated value of $Disparity_{ref}$, which is the pixel-wise difference measured on the computer screen. Except for the disparity value we need to obtain from the image, the following information was readily available; focal length (f = 1.86 mm), the distance between each lens (d = 1.4 mm). The disparity value that is obtained first by image processing based on the number of pixels that appeared on the screen, then calibrated by Eq. (4) based on the reference object in a predefined distance. The measurement was done with the two lenses on the right-hand side of the upper row. Using the distance value of the rook($d_{rook}=10 cm$) which is already known, $Disparity_{reference}=0.79 mm$ and the calibration coefficient of 0.329 were obtained. Then, to acquire an unknown distance value, the distance of the pawn placed behind the rook in this case, the disparity value of the target object was obtained by image processing($Disparity_{pawn}=0.2$). By applying the calibration coefficient in Eq. (4), the distance value of the pawn ($D_1=39.57 cm$) was obtained which was close to the measured distance of 39.8 cm.
In addition to the measurement of distances, images from micro-lens arrays can be utilized to reconstruct the image into a single image by merging a group of the subset images to obtain various images in different focus, to compensate relatively low resolution, or even for motion detection of the surrounding objects [11,16,17].Fig. 5. Images taken using the fabricated micro-lens array and the image sensor. (a) Original image of USAF 1951 resolution test chart. (b) Disparity calculation schematics. (c) 3D printed goniometer and camera setup. (d) Resulting image taken by the micro-lens array showing the printed test target. (e) Appearance of a pawn behind the rook (right red arrow) and disappearance of the pawn (left red arrow). (f) Field-of-View test images of the micro-lens array. Red mark indicates the center of the goniometer.
Next, the field-of-view (FOV) of the imaging system was measured using a 3D printed half-circle goniometer (Figs. 5(c) and 5(f)). The space between the black bars on the goniometer indicates 10 °angle, starting from the bar with a red mark at the center. The micro-lenses in the third column which has the red mark at the center showed 80 ° FOV with four spaces on each side from the center bar, whereas the one on its left (the second column) showed five gaps on the left side of the red mark and four gaps in the case of the one on the right. This implies that a single lens offers around 80 ° FOV, but in a micro-lens array system where multiple lenses are aligned horizontally, the FOV can be widened up to 100 °. Considering that the fabricated micro-lens array is flexible, the FOV can be widened up to more than 180 ° when a perfect hemispherical image sensor is provided.
3.2 Design considerations
3.2.1 Micro-lens formation and aperture
The micro-lens array was designed with the flexible materials for its future application on a curved CMOS image sensor. For the light screen-aperture integrated layer, a black PTFE film and a black polyvinyl chloride (PVC) film were considered for their flexibility. However, the PVC film could not endure the heating of PDMS at 100 °C, resulting in the heat distortion and the decreased yield rate. Therefore, the black PTFE film, which has a melting point of 329.1 °C was chosen between them due to its temperature resistance [18]. For the micro-lens array, the most commonly used material nowadays is the laser-assisted fused silica. However, the protrusion method could not be applied to the materials that are rigid because the material for the lens needs to protrude through to the other side of the light screen layer. Therefore, the PDMS and the photopolymers were considered for this fabrication process. The photopolymer, however, could not be completely cured when it was underneath the PTFE film, due to the UV-stable property of the PTFE [19]. Hence, the PDMS was adopted which also offers flexibility, transparency, ease of use, and low cost [20]. Conventionally, PDMS micro-lens arrays are fabricated using the stamping method or the mold injection method; PDMS is cured within the cast to maintain its shape easily since PDMS has a low viscosity level which allows it to spread flat rapidly. However, for our novel fabrication method that does not manipulate the mold for the shape formation of the lens, a more viscous PDMS is required to maintain its hemispherical shape longer for the formation of micro-lenses.
The size of each micro-lens was determined by the weight of the PTFE film and the thickness of the PDMS layer underneath. The subtle pressure created by the weight of the PTFE film made the PDMS liquid seep out, and the thickness of the 5-hour cured PDMS underneath the PTFE film determined the amount of the PDMS that can flow out of the holes. The 1 cm by 1 cm sized PTFE film weighed 12.5$\pm$1 g, resulting in 1.23$\pm$1 Pa of pressure onto the PDMS layer. Once the pressure was applied onto the PDMS layer with a high viscosity, the laser-cut holes were the only passage that the PDMS could bulge since the surrounding PDMS molecules barely moved and the PTFE film blocking the top pushed the liquid PDMS downwards. By Pascal’s law, a small amount of PDMS protuberated, creating the lens with its surface tension and longer-lasting shape due to viscosity. The PDMS did not ooze from the holes after the formation of a certain size of lens, since the weight of the PDMS lens that already passed through the hole suppressed the pressure of the PDMS attempting to protrude. The ratio between the inner hole diameter and the lens diameter was found to be approximately 1:4 with 1.2 cm by 1.2 cm sized PTFE film and 120$\pm$10 $\mu$m of the inner hole that created a 480$\pm$10 $\mu$m sized lens. The fluctuation of the size existed due to the inner woven mesh layer of PTFE film.
The thickness of the PDMS also determines the size of the lens. For the size of the fabricated lens demonstrated in this study, the adequate thickness was 40$\mu$m. The thickness of the PDMS was precisely adjusted by the spinning speed and time of the spin-coater (ACE-200, Dong Ah Trade Corp, South Korea). With the PDMS cured at room temperature for 5 hours, spin-coating was done for 10 seconds at 1000 RPM followed by 50 seconds at 3000 RPM. Due to the high viscosity of the PDMS, the resulting thickness was relatively thicker than the regular PDMS spinning result with 40$\pm$2$\mu$m, whereas the untreated PDMS was measured 20 $\mu$m of thickness when measured with a digital caliper (Mitutoyo Vernier Calipers, Mitutoyo Corp., Japan). The 40 $\mu$m of thickness was sufficient to fill all the inner space of the array of 5x5 patterned holes on an 80 $\mu$m thick PTFE film. Then, with the rest of the PDMS that gently protruded through the hole due to the weight of the film, the lenses were created. When the PDMS thickness was the exact amount to only fill the cylindrical shape inside the inner hole as shown in Fig. 6(a), the size of the lens became the same as the inner hole diameter. In that case, the thickness was the same 40$\mu$m, due to the widened inner diameter that requires more amount of PDMS to fill the space. The micro-lenses were formed by protruding the PDMS through the small inner hole (Fig. 6(b)), instead of adjusting the inner hole size itself to exactly fit the desired size of the lens(Fig. 6(a)). This design fully utilized the PTFE light screening layer which also works as an aperture. The fabricated lenses were in spherical lens instead of aspherical lens which inherently does not accompany spherical aberration at the edge of the lens. Therefore, having the PTFE light screen not only reduced the excessive incoming light intensity but also decreased the aberration at the edge of the lens as shown in Fig. 6(d), performing a role of a small aperture.
Fig. 6. Comparison of the lens size adjusting methods and resulting spherical aberration. (a) Lens size adjusted by the size of the inner hole with fixed PDMS thickness. (b) Lens size adjusted by the thickness of the PDMS with fixed inner hole diameter. (c) Schematic description of the method (a). (d) Schematic description of the method (b).
In Table 1, fabrication method and performance indexes of the insects’ compound eyes mimicking micro-lens arrays were compared. Compared to other widely used techniques, the advantage of the protrusion method is a simpler fabrication process, which is optimized for the light screen-aperture integrated design with a lower cost. Even though the photolithography, compression molding, injection molding, and 3D printing methods provide great precision, these methods are not suitable to fabricate our design with the desired materials due to technical difficulty. In addition, the proposed method does not require an extensive machinery or a designated mold for the lens design, which leads to the lowest cost. The disadvantage of the protrusion method is in the material limitation for the lens and the stability. Since the material must flow through the holes of the light screen layer, rigid materials such as the fused silica cannot be used for this fabrication method. The stability is relatively lower compared to other fabrication processes since the protrusion method relies on the viscosity of the material. For the performance comparison, the micro-lens array from this work showed the longest visual range along with the Thiele’s foveated micro-lens array. With the same visual range, the micro-lens array from this work demonstrated wider FOV with 100 °, due to the small aperture. As previously mentioned, the flexibility of the fabricated micro-lens array allows its application to the curved CMOS sensor. Song showed the widest FOV of 160 ° by hemispherical micro-lens array-photodetector-integrated structure, mimicking the insects’ compound eye. However, the degree of FOV can differ by its design. Even though Keum’s and Zhang’s micro-lens arrays were applied on a hemispherical surface, their FOV was limited to 68 ° and 86 °, respectively. These limited FOVs are due to the recessed positions of their micro-lense arrays. Since our micro-lens array design does not have a recessed design while it can be curved into any curvature including hemispherical shape, we can obtain a wider field of view with a curved CMOS image sensor.
Table 1. Fabrication method and performance comparisons of micro-lens arrays.
3.2.2 Micro-lens arrangements
Conventional micro-lens arrays with either rectangular or hexagonal arrangements show the difference in their packing density which refers to the number of lenses per area. The packing density, or a "fill factor" is determined by the gap between the lenses, lens diameter, and pitch of the lenses [21]. The rectangular shape (78.5 $\%$) has a lower packing density than that of hexagonal shape (90.5$\%$) [21]. With PTFE light-screen, the hexagonal arrangement has more efficiency in terms of the number of images. However, as shown in Fig. 7, the hexagonal arrangement lacks the ability to manage noise around the edge of the resulting image because the gap between each lens cannot be completely blocked by the light-screen. It was expected that the hexagonal arrangement would have better light sensitivity compared to the rectangular arrangement since it has more area receiving the light. However, as the gray value comparison suggests from Figs. 7(b) and 7(d), the peak value did not show a noticeable difference between the two arrangements.
Fig. 7. Gray value comparison between the rectangular arrangement and the hexagonal arrangement with a USAF-1951 test target located at one meter away. (a) Rectangular arrangement with red line segment indicating the region of analysis. (b) Gray value analysis result of the red line in Fig. 7(a). (c) Hexagonal arrangement with red line segment indicating the region of analysis. (d) Gray value analysis result of the red line in Fig. 7(c).
Ultimately when the fabricated flexible micro-lens array is attached on a curved surface instead of the flat, the Cartesian coordinate system is arduous in obtaining spatial information from the resulting image since the arrangement lies on a curvature that requires extensive computation. The spherical coordinate system, or the polar coordinate system, is more suitable for processing spatial information in this condition where the distance measurement needs to be done in a 3-dimensional space [22]. The simplicity of the hexagonal arrangement in terms of the spherical coordinate computation in a 3-dimensional space is shown in Fig. 8. With regard to the flat surface (upper row), both rectangular and hexagonal arrangements have three levels of layers including the reference micro-lens in the blue area. When these micro-lens arrays were laid on a curved surface as shown in the lower row of the Fig. 8, the number of orbits increased dramatically in the case of the rectangular arrangement compared to the hexagonal arrangement for the same level of the layer. For the two micro-lens array arrangements with $n$ layers of lenses, the number of total orbits are as shown in the Table 2.
Table 2. Numerical comparison of the the number orbits for the arrangements.
The number of total orbits follows the equations below:
where $O_{rect}$ and $O_{hex}$ are the total number of orbits for the rectangular and the hexagonal arrangements respectively, and $n$ is the level of the layer. The rectangular arrangement has about twice as many distinct orbits than the hexagonal arrangement. The increased number of orbits indicates the increase in complexity of the calculation for spatial data processing. Therefore, the hexagonal arrangement is more beneficial than the rectangular arrangement in terms of both packing density and computational power budget, even though it lacks the ability to deal with the noise around the edge.Fig. 8. Comparison of the rectangular and the hexagonal arrangement on a curved surface. The colored area in the upper row indicates the level of layers from the reference micro-lens (blue area). The red vertical line and the white orbital circle indicate the reference micro-lens, and groups of outer micro-lenses that share the same polar angle from the red line, respectively.
4. Conclusion
In this research, the light screen-aperture integrated flexible micro-lens array was fabricated by the protrusion fabrication method. The screen-aperture integrated design showed superior visual range of one meter while maintaining its wide FOV of 100 °, compared to the conventional micro-lens arrays. Along with the longer visual range and the multi-perspective nature of the artificial compound eye, the distance data was obtained from the resulting images as an application example. In addition, the potential usage of the flexible micro-lens array for the curved CMOS image sensor was suggested for the wider field of view. The arrangements of the micro-lens arrays were compared for both 2D and 3D. In both cases, the hexagonal arrangement was advantageous in packing density and computational simplicity, which implies that the hexagonal arrangement is potentially the better arrangement for the curved surface computer vision application.
These above-mentioned improvements and analysis demonstrate the potential of our micro-lens array to overcome the current limitations of the micro-lens arrays and to further enable micro-lens arrays to be suitable for the future computer vision systems. Considering its relatively longer visible range and latent ability to obtain spatial data acquisition, our micro-lens array can be applied to computer vision systems for small robots, and endoscopy applications where better distance measuring with a small size is required.
Funding
Agency for Defense Development (UD190018ID).
Acknowledgments
This research was supported by a grant to Bio-Mimetic Robot Research Center Funded by Defense Acquisition Program Administration, and by Agency for Defense Development (UD190018ID). The authors would like to thank Sindoh, Korea, for providing a 3D printer (DP200) for the research.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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