A biologically inspired compound-eye structure, which composes of ~5,867 honeycomb-patterned microlenses, was fabricated on a hemispherical shell. The fabrication process was simple and low-cost, which involves a femtosecond laser-enhanced wet etching and casting process followed by a thermomechanical process to convert the film into a hemispherical surface. By optimizing the parameters of thermomechanical process to form the curvilinear surface, the experimental result shows that the microlenses are omnidirectionally aligned on the dome with lens diameters of ~85 µm and the angle between two lens of ~2°, and the individual microlenses have rudimentary focusing and imaging properties. The artificial compound-eye structure fabricated by this method has great potential applications in scale-invariant processing, robot vision, and fast motion detection.
© 2012 OSA
In nature, compound eyes of insects have unique and outstanding capabilities for wide field of view (FOV) imaging  and fast motion detection . They are the smallest compact vision systems, which exhibit miniaturized volume as well as low energy consumption . A compound eye, depending to the insect species, has 10 ~30,000 ommatidia spherically arranged on the surface of the eye, most of which are hexagonal-shaped with diameters ranging from 10 µm to 140 µm. Every single ommatidium can collect incident light and produce partial images of the objective separately, and the whole image will be constructed by these imaging mosaics, making the FOV of the compounds eyes reach to or exceed 180° . Compound eyes are sensitive to moving objects for a flicker effect [5, 6], which is essential for insects to escape from danger, catch and feed on for survival. Inspired by the compound eyes of insects, researchers hope to achieve artificial compound eye structures for applications in scale-invariant processing , robot vision , and wide-view-angle imaging [9, 10].
For most fabrication processes, however, direct generation of optical units such as ommatidia or microlenses onto curvilinear surfaces is a challenge. Therefore, alternative methods were developed, such as a planer microlens array combined with pinholes, which allows for independent imaging. But these planer compound eyes were still limited in their complex components and narrow view angles [11–13]. To minimize the size of the device and enlarge the view angles, omnidirectional-aligned microlens array is necessary, which requires a process to form microlenses on non-planar surfaces. Up to now, a few methods have been used to generate such 3D structures. For example, reconfigurable microtemplating , laser lithographic fabrication , soft lithography [15, 16], and hybrid sol-gel method . But these techniques need expensive facilities, long processing time and complicated fabrication process.
Herein, combine our previous developed method , an innovation approach is demonstrated to fabricate artificial compound eye structures. Firstly, we fabricated a honeycomb-patterned microlens array with overall dimensions of 10 × 8 mm2 on a planar PMMA sheet via the femtosecond laser-enhanced wet etching and casting process, and the sheet was then thermomechanically converted to a hemispherical shell by a heated glass ball. The temperature and the thickness of the sheet are elaborately controlled to avoid serious deformations of the hexagonal microlenses. The SEM observations and the optical performances of the structure indicate that although this method is simple, but is practical to fabricate such 3D-distributed microstructures.
The hexagonal-packed concave microlens array on glass is produced through three-step process as schematically depicted in Fig. 1(a) , and the details can be found in Ref . 2.5 mW femtosecond laser pulses (800 nm, 30 fs, 1 kHz) were focused onto a piece of silica glass by an objective lens (NA = 0.5), generating a hexagonal-packed modified spot array (see Ref .). The concave microlens array was fabricated by a treatment of hydrofluoric acid etching (5% diluted solution) for about 1 hour. Figure 1(b) shows the three-dimensional (3D) structure measurement of fabricated MLAs. The dimensions of a single microlens are 76.57 µm in diameter and 6.43 µm in sag depth. The uniformity of 3D-distributed microstructures and the excellent surface quality of microlens show that the femtosecond laser-enhanced wet etching method is practical for fabrication of honeycomb-patterned microlens arrays.
Casting and thermomechnical process are divided into four procedures (Fig. 1(c)). To form the convex microlens array on the planar sheet, liquid PMMA (dissolved the PMMA grains in chloroform solution) with a mass concentration of 0.10 g/ml was dropt onto the glass mold. After it was dried in open air, then it was peeled off by the ultrasonic bath in deionized water, and we obtained a PMMA lens array with thickness of ~195 µm. A glass spherical lens with diameter of 5 mm, which was fixed on a three-dimensional translation stage and heated to 120 ~140 °C. Then it was pressed into the film from the side without microstructures with a velocity of 1.25 mm/s, and then kept it for 1 minutes, ensuring the glass spherical lens was cooled down to the room temperature. Finally, the shell was peeled off manually.
3. Results and discussion
3.1 The artificial compound eye structure
Figure 2 shows the results of the fabricated artificial compound eye structure. Figure 2(a) is the SEM image and macro image of a fly’s eye found in nature . Figure 2(b) shows the macro image of the fabricated artificial compound eye structure. Figures 2(c) and 2(d) are the measurements of a scanning electron microscope (SEM). The artificial compound eye structure and the natural compound eye are similar in appearance.
On the surface of a dome, the hexagonal-shaped ommatidia with dimensions ranging from 84.69 µm to 91.53 µm, which is the result of different surface deformations of hemispherical shell (the details are demonstrated in section 3.3), therefore the number of ommatidia is figured out by equation: N = Shemi/Smicro, where Shemi is the surface area of the fabricated hemispherical shell, Smicro the area of a single lenslet, so N is about 5,867. The radius of curvature of a lenslet (ommatidia) is figured out by equation: R = (h2 + r2)2h, where r is half of the microlens diameter (D/2), and h the sag height of microlens, and we obtained the result ranging from 159.89 µm to 206.29 µm. The focal length f is obtained by equation: f = R/(n-1), where n is the index of refraction of PMMA, considering n = 1.49, so f is 326.31 ~421.00 µm. Furthermore, the value of numerical aperture of microlens, NA, is obtained by equation: NA = D/2f, and the result ranging from 0.11 to 0.13. The angle between the adjacent ommatidium’s optical axes is defined as the interommatidial angle: ΔΦ = D/REYE , where REYE is the radius of hemispherical shell, the result is 1.94° ~2.09°.
The most elementary limiting factor to the resolution of compound eye is the interommatidial angle of two adjacent ommatidia’s optical axes. In general, the resolution arises with the decrease of ΔΦ, and the sensitivity arises with the increase of diameter, D . Therefore the resolution and sensitivity will arise simultaneously on condition of increasing the radius of compound eye.
3.2 The optimization of the experimental parameters
In the process of converting the planar PMMA film to the hemispherical shell, the deformation is unavoidable. The critical two parameters related to the deformation are the thickness of the film and the thermomechanical processing temperature.
To optimize a proper PMMA solution concentration, which is related to the film thickness, four different concentrations (0.12 g/ml, 0.10 g/ml, 0.086 g/ml, and 0.075 g/ml) of the PMMA solutions are compared in the experiments. We used five pieces of silica glass with different sizes (5 cm2, 7.5 cm2, 10 cm2, 12.5 cm2 and 15 cm2), and dropped the PMMA solutions with different concentrations onto the glass sheets, until the dropt volumes on the glass sheets were saturated. When they were dried and peeled off, the thicknesses were measured. The relationship of the film thickness and the concentrations are depicted in Fig. 3 (a) . In the same solution concentration, the films thicknesses are approximately the same for different sizes of silica glass sheets. Therefore, the thickness of the films could be controlled by proper arrangement of the concentrations and dropping volumes of the PMMA solutions. Here we note that, in 0.12 g/ml mass concentration, the solution is too viscous and fast drying. It’s very easy to generate opaque white floccules in fabricated films. In 0.086 g/ml and 0.075 g/ml mass concentration, it’s easy to generate tiny bubbles in the films. In 0.10 g/ml mass concentration, the fluidity and viscosity of the PMMA solution are proper for casting process; the fabricated films are of high quality.
Six different temperatures are compared in the experiments to optimize a proper thermomechanical processing temperature. We heated six glass spherical lenses to different temperatures (60 °C, 80 °C, 100 °C, 120 °C, 140 °C and 160 °C), and fabricated six hemispherical shells with film thickness of ~142 µm. The relationship of dimensions of hemispherical shells and processing temperatures are depicted in Fig. 3(b). According to the formula: E = σ/ε, where E is the elastic modulus of PMMA material, σ the stress, and ε the strain under external force, the elastic modulus of PMMA in low temperature is larger than in high temperature (the details are demonstrated in section 3.3). In the same stress, the strain in low temperature is smaller than in high temperature. When the thermomechanical processing temperature is about 120 ~140 °C, it’s easy to form hemispherical shells on PMMA films. Beyond or below this range, it’s difficult to fabricate hemispherical shells with good qualities.
3.3 The analysis of the deformations
Measurements to the morphology of the planar PMMA film are shown in Figs. 4(a)-(b) . The surface structure of the PMMA replica is uniform and well-patterned (Fig. 4(a)). The three-dimensional morphology (Fig. 4(b)) shows that the microlenses structures are completely replicated. The inset indicates the line-scan of surface profilometry of the planar array. Radius of curvature of microlens is large compared to the sag heights.
The deformations of PMMA films are closely related to the temperature. Beyond the glass transition temperature, PMMA is in a rubbery state. Under external force, the conformations of molecular chains vary quickly, which gives rise to the extension of macromolecule segmers, and then causes substantial deformation. But the elastic modulus in rubbery region is much smaller than in glassy region. Figure 5(a) [21, 22] indicates the elastic modulus of polymer vary about 4 orders of magnitude in the process of glassy to rubbery transition. So the stresses of PMMA thin films in rubbery region are very small, even though the strains of films are large. In addition, because of the intrinsic stabilization of hemispherical structure, the fabricated artificial compound eye structures won’t deform and collapse for a very long time.
In the process of forming a hemispherical shell, the microlenses on the top of dome sustained a larger stress and a longer contact time than on the flank. So the strains of microlenses on the top of dome are larger than on the flank. Figure 5(b) shows the relationship of relative deformation rate of microlens diameter with respect to the x-axis of nine microlens on the same longitudinal section of the dome. Two sheets of planar PMMA films with different thickness are converted into hemispherical shells; the maximal values of relative deformation rates are on the tops of shells, which ranging from 19.12% to 25.79%; the dimensions of microlens on the flanks of shells are deformed smaller than on the tops, the relative deformation rates on the edges of shells ranging from 5.49% to 9.50%. Different deformations lead to different diameters of fabricated ommatidia. Similarly, the nonuniformity of ommatidia sizes can be found in natural compound eyes . Also, from Fig. 5(b), we conclude that the diameter deformation decreases as the increases of film thickness. But it is more difficult to convert the thick film into a hemispherical shell than the thin film; a proper range of film thickness is 100 μm ~160 μm.
3.4 Optical testing
It is the fact that no spherical image converters are available; there is no appropriate way of producing an image with the shown artificial compound eye structure at the moment. To evaluate the shape uniformity and functionality of fabricated artificial compound eye structure, a simple testing system was built up (Fig. 6(a) ). First, a beam of He-Ne light was restricted by an aperture. Next, the light transmitted through the artificial compound eye structure, and then the light was collimated by a convex lens. Finally, the light was projected on a CCD detector. Although in the process of forming a hemispherical crown, the profile of planar MLA is changed, but the diffraction pattern of spherically arranged microlens illustrating the order and shape uniformity of artificial compound eye structure (Fig. 6(b)). The bright region is the diffraction pattern of microlens. The opaque walls structure between channels for prevention of cross talk is missing, resulting in the interference of diffraction patterns or the socalled Moire-fringe, which causes the dark region in the diffraction pattern. This kind of interference can be reduced by using a small diameter of microlens. Also, a projection experiment was performed to demonstrate the imaging function of fabricated artificial compound eye structure (Fig. 6(c)). First, the artificial compound eye structure was fixed on the movable sample stage of an optical microscope. Next, the sample was illuminated with tungsten light from below through a projection sheet, which was a transparent plastic sheet with printed black letter “a” on it. Finally, the miniaturized letters were projected onto the CCD of the optical microscope. A series of hexagonal array of miniaturized letters “a” were observed (Fig. 6(d)), letters a in the same layer were in focus. This demonstrates the capability of fabricated artificial compound eye structure to be employed as functional optical devices.
Comparisons of key parameters between the fabricated artificial compound eye structure and those found in nature [23–25] are listed in Table 1 . The results show that both the dimensions and the optical property of artificial compound eye structure are very close to those found in nature. There still exist some differences between the fabricated and the natural one, like the diameter, and the number. But our method to fabricate artificial compound eye is flexible, smaller microlenses and less ommatidia number can also be achieved in this method.
The fabrication method we proposed in this paper has a flexibility and potential in fabricating PMMA artificial compound eye structure. By using such a very simple method, we obtained a bionic artificial compound eye structure. On the surface of artificial compound eye structure, the hexagonal-shaped ommatidia have diameters ranging from 84.69 µm to 91.53 µm. There are about 5,867 ommatidia on the artificial compound eye structure. The size of artificial compound eye structure can be conveniently controlled by choosing glass spherical lenses with different radius; also, the number and diameter of ommatidia can be easily controlled in mold fabrication process. This simple route to fabricate artificial compound eye structures gives us more freedom to tune the size of MLA mold. Furthermore, the glass MLA mold can be used repeatedly, and this improves the efficiency of fabrication of artificial compound eyes undoubtedly, decreases the unit cost of fabrication at the same time.
This work is support by National Science Foundation of China under the Grant Nos. 61176113 and the Fundamental Research Funds for the Central Universities.
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