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Abstract
The Strepsiptera vision possesses intriguing features of a large field of view (FOV) and relatively high resolution compared to normal compound eyes. However, it presents a significant challenge of the mismatch between the curved compound eyelet lens array and the planar image sensor to image in a large FOV for artificial compound eyes (ACE). We propose what we believe to be a novel curved fiber compound eye camera (CFCEC) here, which employs coherent fiber bundles as the optical relay system to transmit sub-images curvilinearly. A total of 106 eyelets are arranged based on a scheme similar to the Goldberg polyhedron, with the advantages of uniform interval and minor edge blindness. Then, a prototype of the CFCEC is fabricated and assembled. A series of experiments are conducted to assess the FOV, contrast, resolution, and overlap rate of FOV of the prototype. The results prove that the CFCEC has a total FOV of up to 160°×160° and a total overlap rate of FOV of approximately 65%, demonstrating the promising potential of the CFCEC in various applications, such as panoramic surveillance, 3D detection, and motion tracking.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Compound eyes are the visual organs found in most arthropods, which consist of numerous ommatidia arranged on a convex surface. Within each ommatidium, incident light is collected by a lens and a crystalline cone, then conducted to the rhabdom and eventually detected by the optical nerve [1]. Profit from its inimitable structure, the biological compound eye possesses many intriguing features, including a large field of view (FOV), compact size, low distortion, and high sensitivity to motion [2]. However, each ommatidium can only form an image element for normal compound eyes, so the number of ommatidia limits the resolution. Notably, the Strepsiptera insect has an unusual compound eye characterized by far fewer but much larger lenses, which enables image formation within each eyelet, thus effectively improving the resolution [3–7]. Figure 1 compares the compound eye of a fruit fly and Xenos peckii, an endoparasite of paper wasps.
Fig. 1. (a) Compound eye of a fruit fly (b) Schematic diagram of an apposition compound eye (c) Compound eye of Xenos peckii (Ref. [6], Fig. 1(a)) (d) Schematic diagram of the Strepsiptera vision
The remarkable advantages of biological compound eyes attracted the interest of numerous research teams to propose various artificial compound eyes (ACE). Initially, research focused on planar ACE systems. In 2000, Tanida et al. introduced TOMBO, a compact imaging system in which one microlens corresponds to one photosensitive cell. [8]. However, the planar ACE systems have inherent structures, resulting in a small FOV. Currently, the research forefront lies in fully curved bionic compound eyes. In 2013, Song et al. presented a curved digital camera inspired by the arthropod eye, which achieved 160° FOV with 180 photodiodes interconnected by filamentary serpentine wire [9]. Floreano et al. developed a miniature curved artificial compound eye named CurvACE in the same year, which is a 180°×60° flexible imager with 42 × 15 pixels [10]. Although these studies achieved a large FOV, the resolution was still relatively low, subject to the current manufacturing process of curved sensors.
A crucial challenge to image in a large FOV is to match the curved compound eye array with the planar image sensor [11]. One common approach is to introduce an optical relay system [12]. Xu et al. reported a biomimetic curved compound-eye camera (BCCEC) with a FOV of 98°×98°, using an ultra-wide angle lens system as the optical relay system [13]. Subsequently, the team continued to improve the performance of ACE, such as multi-spectrum [14,15], wideband [16], and long working distance [17]. Besides, fiber image transmission components are also considered promising optical relay systems. Zheng et al. designed a curved bionic compound eye with a novel dome light cone to obtain the 3D position [18]. Xue et al. developed a multi-aperture bionic polarization compound eye system (BPCES) based on a micro-surface fiber faceplate and a curved polarizing film array [19]. However, ultra-wide angle lens systems and rigid fiber imaging transmission components cannot distinguish each ommatidium to avoid crosstalk like the biological compound eyes. In 2004, Hornsey et al. presented an electronic compound-eye imager named DragonflEye with a FOV of 150°×10°, employing coherent fiber bundles to bring the curved images array to re-image on a fiber interface plate [20]. In 2020, Ma et al. reported a bionic bee-like compound eye using a polished fiber as an ommatidium with a FOV of 120°×120°, capable of detecting the target orientation by analyzing light spot images based on a neural network [21]. In addition, many researchers work on extending the applications through image processing methods. Wang et al. reported an inverse imaging algorithm for large FOV image reconstruction [22]. Xu et al. optimized the algorithm based on the fast discriminative scale space tracker to detect and capture distant moving objects [13]. Wang’s team developed multi-position calibration methods based on biplane or bicylinder and evaluated the methods by 3D object detection [23,24]. The overlapping FOV can analyze light field information, and a method for estimating object depths based on the computational compound eye (COMPU-EYE) framework was proposed [25]. To the authors’ knowledge, an ACE with fiber that enables image formation in a large FOV has not been reported.
In this work, we propose a novel curved fiber compound eye camera (CFCEC) inspired by the Strepsiptera vision, which consists of 106 eyelets to achieve a total FOV of 160°×160° based on an eyelet arrangement scheme similar to the Goldberg polyhedron. The optical relay system of the CFCEC is the coherent fiber bundles, and the corresponding eyelet lens is customized. Then, a prototype of the CFCEC is fabricated and assembled, occupying a size of 140 mm × 140 mm × 100 mm. Further, a series of experiments have been performed to evaluate the image quality of the prototype. The results demonstrate the promising potential of the CFCEC in a wide range of applications, such as panoramic surveillance [26], 3D detection [18,23,27], and motion tracking [13,28].
2. Curved fiber compound eye camera (CFCEC)
The CFCEC comprises three major parts: a curved eyelet lens array to simulate the lenses, a coherent fiber bundle array to simulate the retinas and optic nerves, and a large-size image sensor to simulate the lamina. The complete object image is split into an array of sub-images. Each sub-image is captured by a respective eyelet lens and projected onto the input of a coherent fiber bundle, and consistently transmitted to the output. All the eyelets are independent of each other without crosstalk, and their outputs are directly coupled to the image sensor. As a result, all the sub-images are displayed on the computer. The whole process mimics the Strepsiptera vision. A mechanical dome and a fiber interface plate act as fixtures, holes maintaining one-to-one correspondence according to a specific arrangement scheme. Figure 2 illustrates the conceptual design of the CFCEC.
2.1 Overlapping FOV theory and eyelet arrangement scheme
The primary parameters for a curved ACE include the FOV of each eyelet 2θ, the inter-eyelet angle Δφ, the diameter of each eyelet d, and the radius of the curved eyelet array R. The interrelationship between these parameters is depicted in Fig. 3(a), so the fundamental condition for overlapping FOV is
The following derivation assumes that the object surface is parallel to the curved eyelet lens array. As the working distance increases, the scenes continuously approach the assumption [29]. The minimum working distance Lmin for overlapping FOV can be calculated by
Figure 3(b, c) depicts the overlapping FOV between adjacent two or three eyelets under the premise that the working distance exceeds Lmin. From the geometric relationship, the overlap rate of FOV between adjacent two eyelets OR2, or three eyelets OR3 can be calculated by
Fig. 3. (a) The interrelationship of primary parameters in compound eye array (b) The overlapping FOV between two eyelets (c) The overlapping FOV between three eyelets
The biological compound eye typically exhibits a hexagonal arrangement on a curved surface. However, the formation becomes unsustainable due to the decreasing interval between the ommatidia as the FOV increases. Polyhedrons are always a research field of great attention throughout the ages for their beauty and characteristics. In 2014, Schein and his coworker proposed a fourth convex equilateral polyhedron named the Goldberg polyhedron [30]. It demonstrates three significant structural characteristics: all faces are either pentagons or hexagons, all vertices are trivalent, and it possesses the rotational symmetry of an icosahedron [31]. It is represented as GP (a, b), where the values of a and b indicate the steps of pentagon-to-pentagon motion. Figure 4(a) displays three Gothenburg polyhedron, GP (3, 0), GP (3, 3), and GP (6, 0).
Fig. 4. (a) Three Gothenburg polyhedron, GP (3, 0), GP (3, 3), GP (6, 0) (b) Schematic diagram of the eyelet arrangement scheme and corresponding overlapping FOV
Figure 4(b) shows an eyelet arrangement scheme similar to the Goldberg polyhedron. The green eyelets are arranged around a pentagonal pattern, while the blue ones are arranged around a hexagonal pattern. The design involves the overlapping FOV between no more than three eyelets. The relationship of the overlapping FOV for both types is depicted in the box plots. Benefiting from the scheme, the interval between eyelets becomes increasingly uniform, and the edge blindness of total FOV becomes smaller on a large spherical surface. The total FOV 2ω and the total overlap rate of FOV OR can be calculated by
where N is the number of eyelet rings, M is the number of adjacent eyelets.2.2 Optical design
Inspired by the Strepsiptera vision, a coherent fiber bundle was employed to emulate the small retina of its eyelet. A coherent fiber bundle is an integrated optical component of multiple cores arranged in a regular pattern, and each core acts as a pixel. The two-dimensional image signal is consistently transmitted from the input to the output, as illustrated in Fig. 5(a). Its excellent flexibility challenges the conventional rule that optical systems must be arranged coaxially or in spatial folding patterns, resulting in increased degrees of freedom and compact size. Consequently, the coherent fiber bundle holds significant application potential in the fields such as medical and military [32].
Fig. 5. (a) Schematic diagram of a coherent fiber bundle (b) the end face of a coherent fiber bundle via an optical microscope
The coherent fiber bundle selected in the CFCEC is the Asahi Kasei MCI-1000, which consists of 7400 cores within a 1 mm effective diameter. Additionally, it has an external diameter of 1.25 mm and a numerical aperture (NA) of 0.5. Its core material is PMMA, while its jacket material is PE. The coherent fiber bundle has an excellent image transmission effect in the visible wavelengths. Figure 5(b) is an end face of the coherent fiber bundle via an optical microscope, and the partially enlarged view demonstrates that the internal core arrangement is hexagonal. The cutoff frequency fc can be calculated by
where dc is the diameter of the individual core, its typical value is 12 µm, so fc is approximately 48lp/mm.The design specifications of the eyelet lens encompass three main aspects. Firstly, its NA should be lower than the coherent fiber bundle to ensure that incident light is fully received. Secondly, the position of its image plane must be at the input surface of the coherent fiber bundle. Meanwhile, its image height should be less than the effective radius of the coherent fiber bundle. Thirdly, its resolution should surpass the coherent fiber bundle. Hence, the root-mean-square (RMS) radius of the eyelet lens should not exceed dc, and the frequency transfer function (MTF) at the cutoff frequency should be greater than 0.3.
All eyelet lenses in the CFCEC share the same structure with the most compact possible formation and the largest possible FOV. The designed eyelet lens consists of one doublet and one single lens, as shown in Fig. 6(a). It has a focal length f of 3.66 mm and a total track length of 6.5 mm. The entrance pupil diameter d is 3 mm, the FOV 2θ is 16°, the NA is 0.38 (<0.5), and the image height is 0.49 mm (<0.5 mm). Figure 6(b) presents three significant criteria for the image quality evaluation: the spot diagram, the MTF curve, and distortion. As can be seen, the resulting RMS values are always less than 5.824 µm (<12 µm). The MTF values are higher than 0.4 (>0.3) at the cutoff frequency for the entire FOV. The distortion remains below 1.6%, indicating the CFCEC possesses low distortion, like biological compound eyes. Summarily, the optical design of the eyelet lens fulfilled all the above requirements.
Fig. 6. (a) Optical design of the eyelet lens (b) The spot diagram, MTF curve and distortion for different wavelengths and different FOVs
2.3 Prototyping
A prototype of CFCEC was manufactured and assembled, as shown in Fig. 7(a,b). A SMA905 connector was installed at the input of the coherent fiber bundle to connect an eyelet lens, as shown in Fig. 7(c). The eyelet lens had a mechanical diameter of 8 mm and a length of 19.5 mm, with front threads to the mechanical dome and rear threads to a coherent fiber bundle, as shown in Fig. 7(d). The inter-eyelet angle was set to 12°. Based on the above eyelet arrangement scheme, 106 eyelets were aligned in seven rings of the CFCEC. The total FOV of the CFCEC was 160° from Eq. (6). The mechanical dome was designed with a radius of 70 mm and a thickness of 6 mm to ensure sufficient internal space for each eyelet and processed by the five-axis machining method. The overall length of the CFCEC was set to 100 mm. All the outputs of coherent fiber bundles were densely inserted in the fiber interface plate, and their lengths at different positions were measured and customized solely to fix all the outputs at the same plane. A threaded adjustment ensured that each eyelet lens was forced onto the input of the matching coherent fiber bundle during instrument integration.
Given that it is a high risk to couple coherent fiber bundles with an image sensor directly at present, a macro lens with 25 mm focal length was selected to re-image the fiber interface plate onto a Hikvision MV-CH120-10GM industrial camera (Sensor: IMX304, Pixel resolution: 4096 × 3000, Pixel size: 3.45 µm). An extension ring increases the back focal distance to control the re-image FOV. The effective area consisted of 106 sub-images in 25 mm × 25 mm size. As a result, the pixels of each sub-image were 125 × 125. Table 1 sums up a list of the detailed parameters of the CFCEC.
Table 1. Parameters of the prototype CFCEC
3. Results and discussion
We conducted a series of imaging experiments to evaluate the performance of the CFCEC, including the FOV test, contrast and resolution test, and real-image experiments. The large FOV is one of the most remarkable features of the biological compound eyes. Figure 8(a) illustrates the experimental setup for the FOV test of the CFCEC. Three chess pieces were positioned at specific angles (the King at −80°, the Knight at 0°, and the Queen at 80°). The raw image captured by the prototype is presented in Fig. 8(b). It proved that the CFCEC achieved a total FOV 2ω of up to 160° with low distortion per the design. To calculate the FOV of each eyelet, a circle pattern (r = 2 cm) was placed in front of the central eyelet. The pattern was observed entirely when the working distance was 14 cm, so the FOV of each eyelet was calculated as 16° (2θ=arctan(2r/L). It should be noted that the enlarged images presented in this and subsequent figures were appropriately corrected to address the confusion of the sub-image directions due to the flexibility of coherent fiber bundles.
Fig. 8. (a) Schematic diagram of the experimental setup for the FOV test of the CFCEC (b) The corresponding raw image and partial enlarged sub-images captured by the CFCEC
To assess the contrast and resolution of the CFCEC, we employed a checkerboard with a 12 × 9 grid size of 5 mm × 5 mm and a USAF1951 test chart (2 cm × 2 cm), which were placed at various angles, 10 cm away from the prototype. Figure 9(a-c) displays the enlarged sub-images of the central and marginal eyelets of the checkerboard with the corresponding raw images and the corresponding intensity profiles along the dotted lines. The Michelson contrast values were calculated as 0.81, 0.91, and 0.85 for 80°, 0°, −80° sub-images, respectively. Figure 9(d-f) displays the enlarged sub-images of the central and marginal eyelets of the USAF1951 test chart with the corresponding raw images. The resolution values were 2 lp/mm for all three eyelets. The results of contrast and resolution verify that the image transfer capability of coherent fiber bundles keeps consistent with bending. The current resolution of our prototype is insufficiently high due to the pixel coupling error. However, we believe the CFCEC has excellent potential to improve its resolution with the development of the coherent fiber bundle process and coupling technology.
Fig. 9. (a-c) The contrast test results of the central and marginal eyelets and the corresponding intensity profiles along the dotted lines (d-f) The resolution test results of the central and marginal eyelets
Further, two real-image experiments were conducted to analyze the overlapping FOV and working distance. Figure 10(b) exhibits the raw image of the logo of Tianjin University (shown in Fig. 10(a), 8 cm × 8 cm) captured by the CFCEC at a working distance of 15 cm in the laboratory. The logo was observed entirely in the enlarged sub-images of the center two rings, with precise edges and details. Slight blurring and blockage existed in certain sub-images, which might be attributed to defects in the end face of coherent fiber bundles during processing and assembly. Notably, the imaging result showed minimal overlapping FOV. The minimum working distance for overlapping FOV Lmin of the prototype is calculated as 21 cm from Eq. (2), which indicates that it is consistent between the experiment and theory. In contrast, Fig. 10(d) exhibits the raw image captured outdoors at a working distance of approximately 5 m, with the target shown in Fig. 10(c). It is evident from the enlarged views that there were overlapping FOVs between the central eyelet and eyelets of the second ring, and the rates are calculated as 16.3%, 12.7%, 18.5%, 17.9%, and 14.6%, respectively. The average overlap rate of FOV OR2 is 16% between two adjacent eyelets for the central one, close to the theoretical results of 14.5% from Eq. (4), while the average overlap rate of FOV OR3 is 3% between three adjacent eyelets for the central one. Consequently, the total overlap rate of FOV OR for the central eyelet could be calculated as 65% from Eq. (7). In addition, the enlarged sub-images in the box plot exhibit the background building from approximately 14 m to 16 m away captured by the CFCEC, revealing that the prototype possessed a long working distance and a large depth of field.
Fig. 10. (a) The logo of Tianjin University (b) The raw image and partial enlarged sub-images of the logo captured by the CFCEC (c) The picture of outdoor scene. (d) The raw image and partial enlarged sub-images of the outdoor scene captured by the CFCEC
4. Conclusion
In summary, we developed a curved fiber compound eye camera (CFCEC) here. Then a prototype of the CFCEC is fabricated and assembled, which consists of a curved eyelet lens array, a coherent fiber bundle array, a mechanical section and a re-imaging section. The prototype is capable of achieving a large FOV of 160°×160° with 106 eyelets in an arrangement scheme similar to the Goldberg polyhedron, occupying a size of 140 mm × 140 mm × 100 mm. A series of imaging experiments are conducted to evaluate the performance of the CFCEC, including the FOV test, contrast and resolution test, and real-image experiments.
In future research, we will focus on two main directions of the structure and applications. Regarding the structure, the current prototype is relatively bulky. The CFCEC has excellent potential for miniaturization if the SMA905 connector is instead of a simplified one. Given the cost and risk, the current prototype does not directly couple the coherent fiber bundles with the image sensor. The integration can significantly improve the imaging performance and system stability of the CFCEC. Regarding the applications, the CFCEC holds promise for panoramic surveillance by reconstructing large FOV images. Furthermore, the CFCEC acquires sufficient overlapping FOV information, paving the way for 3D measurement and motion tracking.
Funding
National Natural Science Foundation of China (42175097).
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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