A spherical artificial compound eye which is comprised of an imaging microlens array and a pinhole array in the focal plane serving as receptor matrix is fabricated. The arrays are patterned on separate spherical bulk lenses by means of a special modified laser lithography system which is capable of generating structures with low shape deviation on curved surfaces. Design considerations of the imaging system are presented as well as the characterization of the comprising elements on curved surfaces, with special attention to the homogeneity over the array. The assembled system is the first spherical compound eye able to capture images. It is evaluated by analyzing resolution and cross-talk between the single channels.
©2007 Optical Society of America
One approach towards smaller and more compact optical imaging systems leads from classical imaging concepts to biologically inspired compound eye principles . Here, the imaging task is split to a number of channels instead of using a single channel. This causes an enormous volume reduction and an increase in field of view of the optical system but at the cost of comparatively low spatial resolution . Numerous applications adapting this principle include thin compound eye cameras and wide-field-angle visual sensors [3–8].
However, previous work on insect inspired artificial compound eyes concentrated on the realization of planar equivalents due to the technology related restrictions. Immanence of large field of view, avoiding of off-axis aberrations and no declining illumination with increasing field angle are connected with a perpendicular incidence for each channel and thus ask for a curved geometry . Nevertheless, the fabrication of a spherical compound eye requires the ability to pattern curved surfaces. One possible approach is to use reconfigurable microtem-plating , but this technology results in poor accuracy of the optics. Consequently, the presented resolution and field of view was not sufficient to obtain images. Recently, a different method for fabricating microlenses on conventional lens surfaces involving dispension of sol lenses individually onto a rotatable concave lens substrate has been proposed . This sol-gel process yields high quality lenses, but is extremely time-consuming and does not offer the the freedoms in design of direct lithographic processing.
Our method of structuring the lens array and virtual photoreceptors (”pinholes”) on curved surfaces employs a unique type of laser beam writer . The novel system has the opportunity to focus the laser beam perpendicularly onto the spherical substrate by a smart positioning strategy of the substrate and an extended adjustment range to keep the optics path length constant during exposure.
2. Theory and design
Basically, natural apposition compound eyes consist of some hundred up to tens of thousands of optical channels commonly referred to as ommatidia arranged on a spherical surface with radius R. The single channels are arranged in a non-uniform hexagonal array sampling the angular object space with the interommatidial angle ΔΦ. Each of the ommatidia consists of a lenslet with diameter D facing into a certain direction in object space and an associated photoreceptor unit in their focal length f. Only light coming from the small solid angle Δφ called acceptance angle is focused onto the small group of photoreceptors (here for simplicity assumed to be one of diameter d). Figure 1(a) shows a sketch of the natural principle. The light-sensitivity of the apposition eye is determined by the F-number (F/# = f/D), d and Δφ, which balances sensitivity and resolution by the size of the resolvable solid angle in object space . Inherent to natural apposition compound eyes is their large field of view (FOV) due to the spherical arrangement of the ommatidia and their low spacial information capacity, even though they usually show diffraction limited performance [15, 16]. The most obvious way of implementing an artificial counterpart suggests itself and would include structuring a lens array on the front side of a thin meniscus lens and a pinhole array onto the backside. This approach works well for planar equivalents , but for the curved apposition eye it would mean having to handle a meniscus of the thickness of the microlenses focal length which is typically in the order of magnitude of only several hundred microns. Consequently, a simplification of the much more complex natural archetype had to be accomplished by separating the main functional components and fabricating them onto two separate bulk lenses. The design principle is shown in Fig. 1(b) and consists of a lens array on a concave bulk lens and a pinhole array on a convex bulk lens in its focal surface.
The elements are concentrically arranged, meaning their distance equals the difference of the substrates radii of curvature, matching the focal length of the microlenses. The object is considered to be at infinity. The parameters of the system (number and pitch of channels, pinhole and lens diameter, focal length) result from the optical system design  and the radii of curvature of the lenses available as substrates. The additional constraint of Δφ = 2 ∙ ΔΦ must be taken into account, meaning that an alternating dark and bright of one line pair has to be resolved by two adjacent channels. The comparison of the adapted artificial spherical compound eye and the natural archetype shows an important difference leading to degraded performance of the designed system: the spacing between the array of microlenses and photoreceptors (pinholes) is filled by air while in nature it is mainly filled by the crystalline cone. In natural compound eyes, light guiding structures and non-transparent walls between neighbored ommatidia ensure that no light focussed by one lenslet can be received by an adjacent channels pinhole. Therefore, cross-talk is successfully suppressed, which would otherwise lead to ghost images and reduction of contrast. In our design approach the implementation of opaque walls has not been possible yet. The radius of curvature of the substrates and the focal length of the microlenses determine the ghost-free field of view and number of usable ommatidia. However, more channels were structured for demonstration of the full range of the modified laser lithography system described in Section 3. Since up to now photoreceptor arrays on curved surfaces with small radius of curvature are not available, we use a pinhole array as substitute which is imaged by a relay optics onto a conventional planar CCD-imager.
3. Fabrication of the elements
Laser lithography is a well established technology for patterning planar substrates allowing for structure sizes of down to half a micron with interferometrically controlled positioning accuracy. In most systems, laser radiation is focused onto a substrate covered by a photosensitive layer while the substrate is moved across the focus to expose the predefined pattern. The intensity of the laser beam can be modulated in correlation with the actual position to realize variable dose exposures. Subsequent wet-chemical development removes the areas with higher dissolution rates, exposed or unexposed areas depending on the kind of resist (positive or negative) . Usually the fabricated structures undergo a replication process like UV molding  or get transferred into the substrate by an etching process . This is due to the poor optical, thermal and mechanical properties of photoresist structures. Transferring standard lithographic technologies to non-planar substrates like lenses is only possible by extensive modification of the equipment. Additional requirements like the smart positioning strategy to avoid deviation of the designed structure shape and an extended z-movement to keep the length of the optics path constant during exposure have to be met. For the spherical compound eye we applied a unique laser lithography system (modified DWL400, Heidelberg Instruments) that fulfils the special requirements of exposing spherical substrates. First, the focusing lens can be moved in a wide range to adapt to the substrate sags of more than several millimeters. Additionally, the substrate table can be tilted within ±10° × ±10° along orthogonal axes to achieve normal incidence of the writing beam onto the substrate surface at the current position of exposure. This is essential to realize structures with low shape deviation. Figure 2(a) shows a sketch of the system’s basic functional components. These capabilities of the system and adapted software for data preparation allow for patterning of curved surfaces with radii of curvature of down to 10 mm.
Disadvantageous to direct gray scale exposure of the desired lens array is the approximation of the desired profile with a fixed number of discrete dose levels. In order to achieve high quality spherical microlenses we applied a reflow process  exploiting surface tension effects for the microlens formation and a subsequent UV replication. The fabrication process of the elements of the objective is sketched in Fig. 2(b). The first steps in fabricating the pinhole-array are sputtering the bulk lens (Ib) with chrome (IIb), spinning on photoresist AZ1505 (IIc) and softbaking the sample to evaporate the solvent. The novel laser-lithography system is applied for structuring the desired array of pinholes into the resist, followed by a wet chemical development process (IVb). Wet etching removes the areas where the resist has been removed in the previous step (Vb). Removal of the remaining resist reveals the final pinhole element. For fabricating the lens array on the concave substrate (I) the processes of spincoating AZ4562 (II), structuring and developing (III) are executed in the same manner, leading to an array of resist cylinders. Special treatment of the substrate areas that are not covered by resist and a stay in a solvent atmosphere causes the resist to melt again and form a spherical shape due to surface tension effects (IV). The volume of resist contained in each cylinder determines the radius of curvature and sag height of the particular lenslet due to volume conservation. After hardbaking the sample, the replication process can be applied by firstly creating a PDMS stamp on a lens with approximately the opposite radius of curvature (V). A UV-curing inorganic-organic hybrid polymer is dispensed onto a second concave lens (VI), the stamp and the new lens pressed together, the polymer cured and the two parts separated. Figure 3 shows a photograph of the fabricated array of 112 × 112 microlenses on the concave lens surface and microscopic images of a middle section and a corner section of the array to give a visual impression of the homogeneity and quality of the array. The characterization of its parameters is analyzed in the following section by evaluating surface scans. A section of scan data is shown in Fig. 4 as an example.
4. Characterization of the elements
The first important requirement for the fabrication of a homogeneous lens array by the method described above is the generation of a resist layer with suitable and homogeneous thickness over the area of interest of the curved substrate. In Ref.  it is stated that after the spinning process the resist thickness over a spherical sample is supposed to be homogeneous as long as the ratio r/R remains below 0.816, r and R being the radius on the substrate surface and the radius of curvature of the substrate, respectively. This assumes proper spinning parameters and viscosity of the resist. To check the suitability of the employed parameters a test substrate was spun with slightly diluted AZ4562 and the resist thickness was measured over the sample. The result of homogeneity of 3.92 μm ± 0.03 μm (corresponding to 1 %) in thickness over the sample is presented in Fig. 5, showing the applicability of spin coating for our application.
After ensuring the uniformity in resist thickness the resist cylinders undergo the structuring and subsequent reflow process as described above. The fabricated microlens array is measured using a mechanical profilometer of the Talystep type. An adjustment procedure ensures scanning across one line of lenses at their maximum sag height. First step of data analysis is to fit a sphere with the radius of curvature of the substrate to the data and subtract it to separate the array information. Secondly, proprietary array analysis software interprets the obtained scan by fitting spheres to each of the elements and evaluating parameters like radius of curvature, sag height, and vertex of the lenslets. The uniformity over the array is presented by means of the radii of curvature of the microlenses over the array in Fig. 6. Shown are the values for two scans in orthogonal directions over the resist array as well as for the replicated array for comparison and evaluation of the replication process. The average radius of curvature is (325 ± 4) μm, which is very close to the specified design value of 318 μm. The slight increase in the middle section of the array is presumably caused by a temperature gradient during the last temperature step of the reflow process, which was too short to allow for a homogeneous temperature over the curved substrate.
The low surface deviation of the lenses is proven by giving a 3D interferometric measurement in Fig. 7(a) for visual impression and a section of the scan including a spherical fit and the deviation from the perfect sphere in Fig. 7(b). The total RMS (root mean square) value is about 20 nm, which is in the order of magnitude of the clearly visible noise of the profile measurement.
In order to demonstrate the uniformity of the array the deviation of the microlenses is plotted in Fig. 8 for the measured scans. These PV (peak to valley) and RMS values are calculated by the special array analysis software mentioned above and show the diffraction limited performance of the lenslets.
The parameters of the pinhole array (diameter and distance) were measured with a microscope. Different areas on the element were observed to obtain an average value. Table 1 holds a synopsis of important parameters of both of the arrays, the substrates as well as parameters of the assembled compound eye characterized in the next section.
5. Optical testing
A combination of different translation and rotation stages was set up to actively align the elements concentrically and laterally, so that each pinhole is facing its corresponding microlens (see Fig. 9). The pinhole surface is imaged onto a conventional CCD-camera by a C-mount objective due to the unavailability of curved photoreceptor arrays. A C-mount objective was sufficient because it introduces field curvature, which is advantageous when imaging a spherical surface to a plane image sensor.
Optical characterization with respect to ghost-free field of view and resolution was done by viewing test targets that were digitally projected onto a rear illumination screen. A point source for measuring the angular sensitivity function (response to a point source) was simulated by a microscopy lamp in the distance of 1.5 m and a 2 mm (angular extension 0.076°, ≪ Δφ) aperture instead of the test screen.
First, the image of a radial star pattern which is often used to detect the optical cut-off frequency of an imaging system, was investigated. The captured image is presented in Fig. 10(a), where dark and bright spots indicate defects in the chrome layer of the pinhole element.
The lack of cross-talk avoiding structures leads to generation of ghost images that can clearly be seen all around the middle section. Determining the ghost-free field of view (FOV) was done by measuring size and distance of an object, it only covers about 40 × 40 of the 112 × 112 channels. This corresponds to a solid angle of 10.3° × 10.3° instead of 31° × 31° FOV which would in theory be achievable with the fabricated array size.
The cut-off resolution of the spherical compound eye was determined to be 0.3° per linepair by the angular diameter of the circle of confusion (1.7°) in the imaged radial star pattern shown in Fig. 10(a). The capability of the system to resolve spatial frequencies down to its Nyquist frequency is proven by imaging bar targets of different line pairs per FOV (see Fig. 10(b)–(e)). The bar targets and the picture in Fig. 10(f) are taken with the ghost-free FOV only. The interommatidial angle ΔΦ can be obtained by experimentally determining the Nyquist frequency. Little overlap in the individual channels field of view is required for high resolution. The response to a point source in Fig. 11 shows that the signal is recorded mainly in one ommatidium with low power in the pinholes of the adjacent channels. The angular sensitivity function is plotted in Fig. 11(b). From this diagram the FWHM can be determined, which corresponds to the resolution of one line pair or rather Δφ.
The first image-providing artificial spherical compound eye objective based on the apposition principle was presented. It consists of an array of microlenses and an array of pinholes arranged on spherical surfaces of close radii of curvature. The fabrication employs a unique laser lithography system for generating microstructures with low shape deviation on curved surfaces. Application of a reflow process followed by replication by UV-molding of the microlens array ensures the high optical quality of the element, leading to a Nyquist-limited performance of the assembled device. Fabrication aspects force the design to depart from the natural principle, leading to a severe constraint of the usable field of view due to the appearance of ghost images. The realization of cross-talk avoiding structures should be explored in the future to reduce this problem and make more channels usable for image formation.
The current lack of image sensors on curved bases with a sufficiently small radius of curvature actually expels the demonstration of a fully functional miniature curved artificial compound eye. Recent work on arrays of organic photodiodes promises to solve this problem for future trials. The technology we used for master origination of equal high-quality microlenses on a spherical surface could also be used for structuring the (organic) curved semiconductor image sensor.
We greatfully acknowledge the support, helpful discussions and technical contributions of our colleagues Andreas Braüer and Peter Dannberg. This work was partly funded by the ”Deutsche Forschungsgemeinschaft” within the project ”3D micro- and nanostructured optics” and by the German Federal Ministry of Education and Research (BMBF) within the project ”Extremely compact imaging systems for automotive applications”.
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